Volume 22, Issue 1

To improve heat dissipation performance of panel-type radiator for transformer, this study investigated the flow and heat transfer characteristics of semi-detached inclined trapezoidal wing vortex generator (SDITW) in a closed channel on the air-side of the radiator. The SDITW was compared with the inclined delta wing (IDW) and inclined trapezoidal wing (ITW) channels. The effects of SDITW relative separation height ( e 1 / e 2 ), longitudinal pitch ( p l ), blockage ratio ( e /(0.5 H )), and inclination angle ( α ) were analyzed. First, compared with the IDW and ITW channels, the SDITW channel generates stable corner vortices and produces weaker transverse vortices and lower flow resistance due to the semi-detached structure of the wing. For Re = 5,125–15,375, the overall heat transfer performance (performance evaluation criteria; PEC) of the SDITW channel increases by 0.5–8.9 and 1.7–4.9% as compared with IDW and ITW channels, respectively. Furthermore, for the same e /(0.5 H ) and α , both the Nusselt number ratio and friction factor ratio of SDITW channel increase as e 1 / e 2 and p l decrease. For p l = 70 mm, the SDITW channel exhibits a relatively better overall heat transfer performance. For the same e 1 / e 2 and p l , the PEC of SDITW channel is maximum and the overall heat transfer performance is best when e /(0.5 H ) = 0.3 at Re = 10,250 and α = 30°–60°.

With particular attention to the effects of an electromagnetically induced resistive force on homogeneous–heterogeneous processes and the related homogeneous heat effects, the Casson fluid flow towards a stretching sheet at the magnetohydrodynamic stagnation point is investigated in detail. In this situation, the Laplace approach helps decipher the subtleties of the first-order kinetics governing the fluid’s motion. Notably, the fluid dynamics are largely determined by the homogeneous behaviour expected in the surrounding environment, forming a strong correlation between catalyst temperature on the wall and surface activity. Using conventional differential systems, our analysis gains a great deal from the modified Laplace decomposition method, which allows non-linear systems to be computed and examined. In order to improve understanding, numerical findings are included, and graphs are skillfully used to examine the subtleties of different factors. The in-depth examination also includes the complicated patterns of concentration and temperature, providing insightful information on the intricate interactions between forces and effects in this dynamic system.

In this study, high-speed mid-infrared Mach–Zehnder electro-optical modulators in x-cut lithium niobate (LN) thin film on sapphire were designed, simulated, and analyzed. The main optical parameters of three types of Mach–Zehnder modulators (MZMs) (residual LN with thickness of 0, 0.5, and 1 μm) were simulated and calculated, namely, the single-mode conditions, bending loss, separation distance between electrode edge and lithium niobate waveguide edge, optical field distribution, and half-wave voltage–length product. The main radio frequency (RF) parameters of these three types of MZMs, such as characteristic impedance, attenuation constant, RF effective index, and the –3 dB modulation bandwidth were calculated depending on the dimensions of the coplanar waveguide traveling-wave electrodes. The modulations with residual LN thickness of 0, 0.5, and 1 μm were calculated with bandwidths exceeding 140, 150, and 240 GHz, respectively, and the half-wave voltage–length product achieved was 22.4, 21.6, and 15.1 V cm, respectively. By optimizing RF and optical parameters, guidelines for device design are presented, and the achievable modulation bandwidth is significantly increased.

This study demonstrates the use of fractional calculus in the field of epidemiology, specifically in relation to dengue illness. Using noninteger order integrals and derivatives, a novel model is created to examine the impact of temperature on the transmission of the vector–host disease, dengue. A comprehensive strategy is proposed and illustrated, drawing inspiration from the first dengue epidemic recorded in 2009 in Cape Verde. The model utilizes a fractional-order derivative, which has recently acquired popularity for its adaptability in addressing a wide variety of applicable problems and exponential kernel. A fixed point method of Krasnoselskii and Banach is used to determine the main findings. The semi-analytical results are then investigated using iterative techniques such as Laplace-Adomian decomposition method. Computational models are utilized to support analytical experiments and enhance the credibility of the results. These models are useful for simulating and validating the effect of temperature on the complex dynamics of the vector–host interaction during dengue outbreaks. It is essential to note that the research draws on dengue outbreak studies conducted in various geographic regions, thereby providing a broader perspective and validating the findings generally. This study not only demonstrates a novel application of fractional calculus in epidemiology but also casts light on the complex relationship between temperature and the dynamics of dengue transmission. The obtained results serve as a foundation for enhancing our understanding of the complex interaction between environmental factors and infectious diseases, leading the way for enhanced prevention and control strategies to combat global dengue outbreaks.

The main goal of this study is to analyze the nanofluid boundary layer as it flows over a bidirectional, exponentially extending sheet in both convective and magnetic field environments. The mathematical model considers the results of Brownian motion and particle movement caused by a temperature gradient. Using appropriate similarity transformations, governing partial differential equations are converted into ordinary differential systems, and the design of equations is then solved using the Haar wavelet collocation approach. The findings identify unique trends in the distribution of temperature and show relationships with particular sets of parametric values. These results emphasize how important it is to note temperature fluctuations associated with specific parametric settings. The findings are validated by contrasting the results with similar cases from earlier studies in the literature. The findings indicate that temperature distribution is reduced by increasing the Prandtl number. Additionally, the local Biot number has qualitatively similar effects on temperature and concentration profiles. For higher local Biot numbers, the profiles of concentration and temperature are better.

Magnetite and cobalt ferrite (CoFe 2 O 4 ) nanoparticles are frequently utilized in several applications, including magnetic drug delivery, hyperthermia, magnetic resonance imaging, etc . In the current investigation, the magnetohydrodynamic three-dimensional heat transfer (HT) flow induced by a non-Newtonian Eyring–Powell fluid is incorporated by a carrier sodium alginate (NAC 6 H 7 O 6 )-based CoFe 2 O 4 nanoparticles over a deformable (stretching/shrinking) horizontal plane surface with orthogonal shear stress and power-law velocity. The HT analysis along with the substantial effect of irregular heat source/sink as well as entropy generation is also performed. The similarity variables altered the posited leading equations into ordinary differential (similarity) equations. The function bvp4c in Matlab is then used to solve these equations numerically for various parameter values. Results indicate that, in general, there are two alternative solutions for the phenomenon of suction and deformable parameters. In addition, the essential thermal evaluation is enhanced owing to the significance of CoFe 2 O 4 nanoparticles, magnetic parameter, and irregular heat source/sink.

A metallic alloy is a combination of two or more elements, often called a compound or a solution. Steel is largely composed of carbon, a nonmetal, but alloys are often made up of metals. In this article, the authors have explored the electrically conducting water-based viscous nanofluids flow past a rotating disk surface. The nanofluids flow is composed of titanium and aluminum alloys where water is used as a base fluid. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. The impacts of viscous Joule heating, thermophoresis, Brownian motion, activation energy, nonlinear thermal radiation, and chemical reaction are investigated here. By employing an appropriate set of variables for shifting the leading equations to dimension-free form. The mathematical model is solved numerically by incorporating the bvp4c MATLAB scheme. Current work is validated with previous studies. The outcomes showed that the radial velocity increases when the disk surface stretches and reduces when the disk surface shrinks. On the other hand, the Azimuthal velocity increases when the disk surface shrinks and reduces when disk surface stretches. Both the radial and Azimuthal velocities are the diminishing functions of the magnetic factor, whereas temperature is the growing function of magnetic factor. In addition, the temperature is more influenced by the magnetic factor in the case of nonlinear radiation. The higher magnetic factor increases skin friction. In addition, the stretching case experiences more surface drag than the shrinking case. It is found that nanofluid flow containing titanium alloy has perceived the greater impacts of the embedded factors compared to the nanofluid flow containing aluminum alloy.

Sulphamic acid (SA) crystals supplemented with l -methionine (LM) were grown at moderate temperatures using a slow evaporation procedure. The powder XRD pattern showed that LM supplemented with SA (LMSA) crystals have an orthorhombic crystal structure. The FTIR studies confirmed the presence of various vibrational modes. Using a UV-Vis spectrometer, the transmittance of LMSA in the UV and visible range was observed, and the band gap of the LMSA was also calculated. The hardness value of LMSA was higher compared to that of pure SA. Photoluminescence emission studies of LMSA pointed out emissions at 491 and 542 nm, which were attributed to the transition from the 5 D 4 state to 7 F 6 and 7 F 5 ground, respectively. LMSA crystals were effective in killing pathogenic bacteria, according to the studies on their anti-bacterial activity.

The analysis of the fluid flow with the energy transfer across a stretching sheet has several applications in manufacturing developments such as wire drawing, hot rolling, metal extrusion, continuous casting, paper production, and glass fiber fabrication. The current examination presents the hybrid nanofluid flow past a convectively heated permeable sheet. The ferrous oxide (Fe 3 O 4 ) and Gold (Au) nanoparticles have been dispersed in the blood. The significances of thermal radiation, inclined magnetic field, and space-dependent heat source have been observed in this work. The modeled equations are presented in the form of partial differential equations and reformed into the set of ordinary differential equations (ODEs) by using the similarity substitution. The Matlab built-in package (bvp4c) is employed to resolve the transform nonlinear set of ODEs. The significance of flow constraints versus the velocity and temperature profiles is demonstrated in the form of Figures and Tables. The numerical outcomes for the physical interest quantities are presented in tables. It has been perceived from the results that raising the angle of inclination from 0° to 90° reduces both the velocity and energy profile. The escalating values of Eckert number, constant heat source, and space-dependent heat source factor accelerate the temperature profile. The velocity and temperature distributions are very effective in the cases of hybrid nanofluid (Au–Fe 3 O 4 /blood) when compared to nanofluid (Au/blood). The skin friction and rate of heat transfer are very effective in the cases of hybrid nanofluid (Au–Fe 3 O 4 /blood) when compared to nanofluid (Au/blood).

In this study, we investigated the effect of a rotation field and magnetic field on a homogeneous photo-thermoelastic nonlocal material and how its thermal conductivity changes as a result of a linearly distributed thermal load. The thermal conductivity of an interior particle is supposed to increase linearly with temperature under the impact of laser pulses. Microelastic (microelements distribution), non-local semiconductors are used to model the problem under optoelectronic procedures, as proposed by the thermoelasticity theory. According to the microelement transport processes, the micropolar-photo-thermoelasticity theory accounts for the medium’s microelongation properties. This mathematical model is solved in two dimensions using the harmonic wave analysis. Non-local semiconductor surfaces can generate completely dimensionless displacement, temperature, microelongation, carrier density, and stress components with the appropriate boundary conditions. The effects of thermal conductivity, thermal relaxation times, magnetic pressure effect, laser pulses, and rotation parameters on wave propagation in silicon (Si) material are investigated and graphically displayed for a range of values.

The ternary hybrid nanofluid leads to a significant enhancement in thermal performance applications like heat transfer in automotive engines, solar thermal energy storage, aerospace, and electronic cooling. The present study investigates the thermal characteristics of a ternary hybrid magnetized and radiated cross nanofluid comprising Al 2 O 3 , TiO 2 , and Ag nanoparticles in water subjected to combined convection flow around a vertical cylinder. Furthermore, innovative effects of the magnetic field, absorber surface of the cylinder, non-linear thermal radiations, and effective thermophysical characteristics of ternary nanofluid are taken, and a new model for heat transport is successfully achieved. The governing equations in the form of partial differential equations (PDEs) are obtained through Navier–Stokes and heat equations by applying current assumptions. The system of PDEs is converted into a set of ordinary differential equations (ODEs) via a similarity variable. The built-in code bvp4c in Matlab software further exercises the dimensionless ODE equations numerically. Adding multiple nanoparticles and the magnetic field effect enhances the heat transfer rate in the ternary hybrid cross nanofluid. The Weissenberg number reduces the velocity, the radiation parameter increases heat transport, and the increased volume friction of nanoparticles enhances thermal conductivity and rapid heat transport.

A mathematical model is envisaged that discusses the motion of 3D nanofluids (NFs) with anisotropic slip influence magnetic field past a stretching sheet. The heat transportation phenomenon is analysed by melting effect, heat generation, and chemical reaction. The main motivation of this study is to analyse the behaviour of liquid motion and heat transfer (HT) of NFs because this study has huge applications in boiling, solar energy, and micropower generation, which are used in the engineering process. The physical governing partial differential equation is transformed into a coupled non-linear system of ordinary differential equations using suitable appropriate transformations. The translated equations are calculated using Runge–Kutta–Fehlberg method via shooting procedure. The physical characteristics of various parameters on velocities, concentration, and thermal fields are explored in detail. The HT is high in NFs when compared to pure or regular liquids for ascending values of heat source parameter and slip factor. Also, the skin friction coefficients via coordinate axes and rate of Nusselt number were analysed.

The aim of this research is to provide a new computer-assisted approach for predicting thermophoresis particle decomposition on three-dimensional Casson nanofluid flow that passed over a stretched surface (thermophoresis particle decomposition on three-dimensional Casson nanofluid flow; TPD-CNF). In order to understand the flow behavior of nanofluid flow model, an optimized Levenberg–Marquardt learning algorithm with backpropagation neural network (LMLA-BPNN) has been designed. The mathematical model of TPD-CNF framed with appropriate assumptions and turned into ordinary differential equations via suitable similarity transformations are used. The bvp4c approach is used to collect the data for the LMLA-BPNN, which is used for parameters related with the TPD-CNF model controlling the velocity, temperature, and nanofluid concentration profiles. The proposed algorithm LMLA-BPNN is used to evaluate the obtained TDP-CNF model performance in various instances, and a correlation of the findings with a reference dataset is performed to check the validity and efficacy of the proposed algorithm for the analysis of nanofluids flow composed of sodium alginate nanoparticles dispersed in base fluid water. Statistical tools such as Mean square error, State transition dynamics, regression analysis, and error dynamic histogram investigations all successfully validate the suggested LMLA-BPNN for solving the TPD-CNF model. LMLA-BPNN networks have been used to numerically study the impact of different parameters of interest, such as Casson parameter, power-law index, thermophoretic parameter, and Schmidt number on flow profiles (axial and transverse), and energy and nanofluid concentration profiles. The range, i.e. , 10 −4 –10 −5 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks.

This article presents a new approach for solving the fuzzy fractional Degasperis–Procesi (FFDP) and Camassa–Holm equations using the iterative transform method (ITM). The fractional Degasperis–Procesi (DP) and Camassa–Holm equations are extended from the classical DP and Camassa–Holm equations by incorporating fuzzy sets and fractional derivatives. The ITM is a powerful technique widely used for solving nonlinear differential equations. This approach transforms the fuzzy fractional differential equations into a series of ordinary differential equations, which are then solved iteratively using a recursive algorithm. Numerical simulations demonstrate the proposed approach’s accuracy and effectiveness. The results show that the ITM provides an efficient and accurate method for solving the FFDP and Camassa–Holm equations. The proposed method can be extended to solve other fuzzy fractional differential equations.

The test of new equipment is usually carried out in multiple batches according to the task schedule and test results. Constrained by the test environment, cost, and other factors, the amount of reliability test data in each batch is relatively limited, which brings difficulties to the accurate equipment reliability estimation work. For the reliability simulation tests conducted before each batch tests, it is particularly important to make full use of each batch tests information and simulation tests information to estimate the reliability of the equipment for small sample tests. This study takes the common normal-type life distribution equipment as the research object, and selects the normal-inverse gamma distribution as the equipment life parameters prior distribution based on the Bayesian method. Combined with the system contribution, the fusion weights of each batch tests information are determined and all the batch tests information is fused. Finally, the estimation of equipment reliability based on multiple batch tests is completed. The research results show that this method can integrate the information of each batch test and simulation test, overcome the problem of insufficient information of single batch tests, and provide an effective analytical tool for equipment reliability estimation.

Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.

The heat and mass transportation for nanofluid across a swirling cylinder under the actions of magnetic effects and Cattaneo–Christov heat flux is reported in the current analysis. The objective of this study is to examine the energy and mass transmissions through hybrid nanofluid under the influence of heat source/sink and reactive species. The hybrid nanoliquid has been prepared by the dispersion of silver (Ag) and gold (Au) nanoparticles (NPs) in the base fluid ethylene glycol (C 2 H 6 O 2 ). The flow phenomena are expressed in the form of nonlinear partial differential equations and are converted to a nondimensional form, by employing the similarity substitution. For the computational estimation of the problem, the parametric continuation method is employed. The demonstration of velocity, mass, and energy outlines versus distinct physical factors is exposed in the form of figures. It has been perceived that the axial and swirling velocity outline drops with the influence of the Reynolds number, magnetic effect, and the insertion of Au and Ag NPs in C 2 H 6 O 2 . Furthermore, the hybrid nanofluid energy curve declines with the effect of the Reynolds number, thermal relaxation factor, and the volume friction of NPs.

We solve two numerical experiments described by 2D nonconstant coefficient advection–diffusion equations with specified initial and boundary conditions. Three finite difference methods, namely Lax–Wendroff, Du-Fort–Frankel and a nonstandard finite difference scheme, are derived and used to solve the two problems, whereby only the first problem has an exact solution. Stability analysis is performed to obtain a range of values of the time step size at a fixed spatial step size. We obtain the rate of convergence in space when the three methods are used to solve Problem 1. Computational times of the three algorithms are computed for Problem 1. Results are displayed for the two problems using the three methods at times T = 1.0 T=1.0 and T = 5.0 T=5.0 . The main novelty is the stability analysis, which is not straightforward as we are working with numerical methods discretising 2D nonconstant coefficient advection–diffusion equation where many parameters are involved. The second highlight is to determine the most efficient scheme from the three methods. Third, there are very few published studies on analysis and use of numerical methods to solve nonconstant coefficient advection–diffusion equations, and this is one of the very few rare articles treating such topics.

This research delves into dynamics of magnetohydrodynamic second-grade fluid flow influenced by the presence of gyrotactic microorganisms on a stretching sheet. The study takes into account various factors such as thermal radiation, chemical reactivity, and activation energy, all of which contribute to the complex behavior of fluid flow in this system. The interaction between the magnetic field and the fluid, combined with the biological aspect introduced by gyrotactic microorganisms, adds complexity to the overall analysis. The mathematical model is presented in the form of partial differential equations (PDE)s. Using the similarity variables, the modeled PDEs are transformed into ordinary differential equations. Homotopy analysis method is used for the solution of the modeled equations. After a detailed insight into this investigation, it is established that the velocity distribution declined for growth in magnetic factor and second-grade fluid parameter. The thermal characteristics are augmented for the greater values of radiation, thermophoretic and Brownian motion factors, while these profiles are weakened for upsurge in thermal relaxation time factor and Prandtl number. The concentration characteristics declined with the enhancement in Schmidt number, mass relaxation time, chemical reaction, and Brownian motion factors, while they amplified with enhancement in activation energy and thermophoresis factors. The microorganisms’ profiles are the declining functions of bioconvection Lewis and Peclet numbers. This study included a comparative analysis, which aligns closely with existing research, demonstrating a strong concordance with established findings.

This article presented micropolar hybrid nanofluid flow comprising copper and alumina nanoparticles over a flat sheet. The mixed convection phenomenon is studied under the effect of gravity. Some additional forces such as magnetic field, thermal radiation, Eckert number, heat source, and thermal slip condition are adopted in this analysis. The leading equations are transformed into dimensionless format by employing appropriate variables and then evaluated by homotopy analysis method (HAM). The obtained results are compared with published results and found a good agreement with those published results. Also, the results of HAM are compared with those of numerical method and found a good agreement as well. The fluctuations within the flow profiles are showcased utilizing figures and tables, followed by an in-depth discussion and analysis. The outcomes of this work show that the higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid viscosity, which results in the augmenting variation in the velocity profiles. The higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid thermal conductivity, which results in the augmenting variation in thermal distribution. The growing mixed convection factor amplifies the buoyancy force toward the stagnation point flow, which enlarges the velocity panel. The effects of hybrid nanoparticles (Cu-Al 2 O 3 /water) at the surface are smaller on friction force and larger in case of thermal flow rate when compared to the nanofluids (Cu/water and Al 2 O 3 /water).

The microscopic pore-fracture structure and wettability have a significant influence on the two-phase seepage of shale gas and water. Due to the limitation of experimental conditions, the seepage patterns of gas and water in shale pores and slits under different wetting conditions have not been clarified yet. In this study, the three-dimensional digital rock models of shale inorganic pores, organic pores, and microfractures are established by focused ion beam-scanning electron microscopy scanning, and gas-driven water seepage simulation in shale microscopic pore-fracture structure under different wetting conditions is carried out based on volume of fluid method. The simulation results show that the gas–water relative permeability curves of microfractures are up-concave, and the gas–water relative permeability curves of inorganic and organic pores are up-convex; the gas–water two-phase percolation in microfractures is least affected by the change of wettability, the gas–water two-phase percolation in inorganic pores is most affected by the change of wettability, and the organic pores are in between; the gas–water two-phase percolation zone of microfractures is the largest, and the isotonic saturation is the highest; under the water-wet conditions, the critical gas saturation of microfractures, inorganic pores, and organic pores are 0.13, 0.315, and 0.34, respectively, and the critical gas saturation of organic pores under non-water-wet conditions is 0.525, indicating that under water-bearing conditions, the shale gas flow capacity in water-wet microfractures is the strongest, followed by water-wet inorganic pores, water-wet organic pores, and hydrophobic organic pores, respectively.

This work deals with the conversion of flow from confined to unconfined aquifers, a real-world problem that has attracted the attention of several authors. We have introduced a piecewise modified mathematical model where the first part deals with the flow within a confined system, and the second part deals with the flow within an unconfined system. In the unconfined part, we added the randomness to capture stochastic behaviours that could occur due to the geological formation. Moreover, we used a numerical method to solve the stochastic differential equations. The obtained model was evaluated numerically using some numerical scheme, and the stability analysis was performed using the von Neumann approach and the numerical simulations were presented.

Variable-order derivatives are the natural extension of ordinary as well as of fractional-order differentiations and integration, respectively. Numerous suggestions for fractional variable-order operators have been made in the literature over time. Therefore, this is the moment to shine a light on the variable-order fractional calculus, due to the fact that it accurately describes the mathematical underpinnings and emphasizing the modeling utility via using contemporary numerical techniques. This study focuses on investigating a fractional variable-order model of lymphatic filariasis infection using with Atangana–Beleanue–Caputo derivative. Our investigations have led to the development of newly refined results, focusing on both qualitative and numerical aspects of analysis. To achieve our research objectives, we employ the fixed point theorems of Banach and Krasnoselskii. These theorems serve as powerful tools, allowing us to establish results regarding the existence of solutions to the model. Additionally, for precise numerical simulations, we employ the fractional Euler’s method, a sophisticated computational technique that allows us to effectively simulate and interpret the results both numerically and graphically. These graphs illustrate distinct variable-orders, providing a comprehensive understanding of the model’s behavior under different conditions. Here, it should be kept in mind that we have select various continuous functions for variable to present our graphical illustration.

The ZK–mZK–BBM equation plays a crucial role in actually depicting the gravity water waves with the long wave region. In this article, the bilinear forms of the (2 + 1)-dimensional ZK–mZK–BBM equation were derived using variable transformation. Then, the multiple soliton solutions of the ZK–mZK–BBM equation are obtained by bilinear forms and symbolic computation. Under complex conjugate transformations, quasi-soliton solutions and mixed solutions composed of one-soliton and one-quasi-soliton are derived from soliton solutions. These solutions are further studied graphically to observe the propagation characteristics of gravity water waves. The results enrich the research of gravity water wave in fluid mechanics.

This research article analytically investigates a soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences and engineering. The soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences along with engineering, is examined with a view to securing various pertinent results of interest. For the first time, the conserved currents of an integrodifferential equation (especially those of higher dimensions) are calculated using a detailed optimal system of one-dimensional subalgebras. Infinitesimal generators of diverse structures ascribed to Lie point symmetries of the understudy model are first calculated via Lie group analysis technique. Additionally, we construct various commutations along Lie-adjoint representation tables connected to the nine-dimensional Lie algebra achieved. Further to that, detailed and comprehensive computation of the optimal system of one-dimensional subalgebras linked to the algebra is also unveiled for the under-investigated model. This, in consequence, engenders the calculation of abundant conserved currents for the soliton equation through Ibragimov’s conserved vector theorem by utilizing its formal Lagrangian. Later, the applications of our results are highlighted.

The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp ( − Φ ( ξ ) ) (-\Phi (\xi )) expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.

This study investigates the complex dynamics of a viscoelastic fluid subjected to magneto-hydrodynamics over a stretching sheet, incorporating the Cattaneo–Christov heat flux model. This model is especially advantageous for explaining heat transfer in materials possessing significant thermal conductivity, where the conventional Fourier’s law might not be precise. The investigation revolves around evaluating how the thermal relaxation time affects the boundary layer and how both thermal radiation and viscous dissipation influence the thermal field. The significance of this research lies in its contribution to understanding the intricate behavior of such fluids in the presence of magnetic fields and non-Fourier heat conduction. The primary objective is to analyze the impact of viscoelasticity, magnetohydrodynamics, and Cattaneo–Christov heat flux on the flow and heat transfer characteristics over the stretching sheet. The research methodology involves the application of mathematical models and numerical techniques, particularly the use of the shifted Chebyshev polynomials of the sixth-order approximation and spectral collocation technique. The major conclusion of the study underscores the significant influence of viscoelasticity, magnetic field, and Cattaneo–Christov heat flux on the transport properties of the fluid, providing valuable insights for applications in various engineering and industrial contexts. Certain notable results arising from the current issue indicate that heat transfer is more pronounced for the viscoelastic factor and magnetic parameter, whereas the thermal relaxation parameter exhibits the opposite trend. In addition, the inclusion of the Cattaneo–Christov term enhances our comprehension of thermal behavior.

There are several problems in physics, such as kinetic energy equation, wave equation, anomalous diffusion process, and viscoelasticity that are described well in the fractional differential equation form. Therefore, the solutions with elementary solution method cannot be solved and described deliberately with detailed physics of the problems, so these problems are solved with the help of special operators such as Mittag–Leffler (M–L) functions equipped with Riemann–Liouville (R–L) fractional operators. Hence, keeping in view the above-mentioned problems in physics in the current study, the generalized properties are derived M–L functions connected with R–L fractional operators that are investigated in the generalized form. These extended special operators will be used for the solutions of generalized kinetic energy equation. The M–L function is a fundamental special function with a wide range of applications in mathematics, physics, engineering, and various scientific disciplines. Ayub et al. gave the definition of newly extended M–L ( p , s , k ) \left(p,s,k) function. Also, they gave its convergence condition and found several results relevant to that. The purpose of this study is to investigate newly extended M–L function and study its elementary properties and integral transforms such as Whittaker transform and fractional Fourier transform. The R–L fractional operator is a fundamental concept in fractional calculus, a branch of mathematics that generalizes differentiation and integration to non-integer orders. In this study, we discuss the relation of M–L ( p , s , k ) \left(p,s,k) -function and R–L fractional operators. In some cases, fractional calculus is used to describe kinetic energy equations, particularly in systems where fractional derivatives are more appropriate than classical integer-order derivatives. The M–L function can appear as a solution or as a part of the solution to these fractional kinetic energy equations. Also, we gave the generalization of kinetic energy equation and its solution in terms of newly extended M–L function.

Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles ( i.e. , velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x -direction converges in the region − 0.8 ≤ ℏ f ≤ 0.5 -0.8\le {\hslash }_{\text{f}}\le 0.5 , in y -direction velocity is convergent in the zone − 0.6 ≤ ℏ g ≤ 0.35 -0.6\le {\hslash }_{\text{g}}\le 0.35 , while temperature converges in the region − 0.6 ≤ ℏ θ ≤ 0.4 -0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region − 0.5 ≤ ℏ φ ≤ 0.4 -0.5\le {\hslash }_{\text{φ}}\le 0.4 .

In order to solve the contradiction between large aperture elements and high-resolution images, in this study, we propose an improved image-resolution method based on generative adversarial network (GAN). First, we analyze the imaging principle of the optical synthetic aperture. Further, we improve a super-resolution GAN; especially, this network uses a multi-scale convolutional cascade to obtain global features of the image, and a multi-scale receptive field block and residual in residual dense block are built to obtain image details. In addition, this study uses the Mish function as the activation function of the discriminator to solve the problems of neuron extreme, gradient explosion, and poor generalization ability of the model. Through simulation, the results show that the proposed method can achieve a peak signal-to-noise ratio (PSNR) of 30 dB compared with traditional image super-resolution reconstruction methods for synthetic aperture image. The method proposed has an improvement of 2 dB in the PSNR and 0.016 in structure similarity index measure compared with the original super-resolution GAN. Therefore, this method can effectively reduce the image distortion and improve the quality of image reconstruction.

The traditional prediction of remaining useful life (RUL) for bearings cannot be calculated in parallel and requires manual feature extraction and artificial label construction. Therefore, this article proposes a two-stage framework for predicting the RUL of bearings. In the first stage, an unsupervised approach using a temporal convolutional network (TCN) is employed to construct a health indicator (HI). This helps reduce human interference and the reliance on expert knowledge. In the second stage, a prediction framework based on a convolutional neural network (CNN)–transformer is developed to address the limitations of traditional neural networks, specifically their inability to perform parallel calculations and their low prediction accuracy. The life prediction framework primarily maps the complete life data of bearings onto the HI vector. Based on the HI constructed through TCN, the known HI is input into the CNN–transformer network, which sequentially predicts the remaining unknown HI. Finally, the effectiveness and superiority of the proposed method are verified using two bearing datasets, providing validation of its capabilities.

The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.

The combined heat and mass transfer phenomenon is a significant aspect of engineering and industrial processes. This phenomenon finds applications in various areas such as air conditioning, cooling and heating control of electronic devices, reactors, chemical systems, and emission processes. This research model focuses on the analysis of mixed convection flow of a viscous fluid with heat and mass transfer on an inclined surface with porous medium characteristics. The study also considers external heat transfer effects, radiation, Soret influence, and chemical reactions. A perturbation solution is derived in closed form, and the impact of various parameters on the thermal behavior is investigated. A comparative analysis of the heating and cooling regimes in plate flow is conducted, revealing a reduction in velocity in the heated plate regime with changes in the permeability parameter and an increase in concentration phase due to the Soret number.

Closed-form expressions for the dimensionless velocity, shear stresses, and the flow vorticity fields corresponding to the isothermal unsteady Poiseuille flows of a fractional incompressible viscous fluid over an infinite flat plate are established. The fluid motion induced by a pressure gradient in the flow direction is also influenced by the flat plate that oscillates in its plane. The vorticity field is dependent on two spatial coordinate and time, and it is an arbitrary trigonometric polynomial in the horizontal coordinate. The exact solutions, obtained by generalized separation of variables and Laplace transform technique, are presented in terms of the Wright function and complementary error function of Gauss. Their advantage consists in the fact that the values of the fractional parameter can be chosen so that the predicted material properties by them to be in agreement with the corresponding experimental results. In addition, they describe motions for which the nontrivial shear stresses are influenced by history of the shear rates. It is found that the flow vorticity is stronger near the plate, but it could be attenuated in the case of fractional model.

A binary blend of rosuvastatin (ROS) and teneligliptin (TEN) used for the management of cardiovascular complications require a simple, analytical process for the quality assurance of this formulation. UV absorption spectra of ROS and TEN showed overlapping spectra. Hence, the overlapped spectra of ROS and TEN were separated by ratio difference, ratio first derivative; constant extraction coupled with exponentiation with division spectrum, and induced dual-wavelength methods. The proposed methods were authenticated by following the international council for harmonization criteria. A good linear relationship was demonstrated by all four methods, in 2–15 and 2–30 µg/mL for ROS and TEN, respectively. The high percentage retrieval of 98.96–100.22 and 98.72–99.73% for ROS and TEN, respectively, with small relative error, assured the correctness of the techniques. The validated techniques were employed for concurrent evaluation of ROS and TEN from binary formulation and laboratory-prepared mixture. The standard addition process verified the reliability of the projected procedures. The developed methods showed same accuracy and precision when compared to the HPLC methods along with safer solvent. Finally, the environmental sustainability of the presented UV spectroscopic procedures was found to be better than the reported HPLC method. Hence, eco-friendly, simple, and accurate mathematically processed UV spectroscopic procedures can be employed for simultaneous quantification of ROS and TEN for routine quality control study.

In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.

This work explores six newly designed compounds obtained by several substitutions in 2,5-di(2-thienyl) pyrrole molecule. For this series of compounds, the electronic and optical properties were investigated using density functional theory and time-dependent density functional theory (TD-DFT). The new compounds were characterized by calculating the chemical parameters that correlated with their optical and electrical properties. The lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) energies are calculated using the B3LYP functional with the 6-311G (d, p) basis set. The most low-lying energy level of the LUMO was found for Perr-NO 2 , indicating its effective electron injection capabilities and oxidation resistance. The HOMO and LUMO distributions of Perr-Cl and Perr-NO 2 displayed a remarkable complementarity throughout each component of the two compounds, indicating an effective intermolecular charge transfer. The molecular electrostatic potential analysis demonstrated that the proposed compounds have a broad distribution of electrophilic and nucleophilic sites, which predict a high degree of chemical reactivity. The electron density analysis at the bonding and anti-bonding sites of the title compounds was performed using the electron localization function and local orbital locator techniques. Non-covalent interaction analysis using the reduced density gradient approach classified all types of interaction: repulsive, weak, and attractive interactions within compound fragments. All compounds exhibited a robust repulsive interaction, as proved by the red spikes at 0.038 a.u. The ultraviolet/visible (UV/vis) spectrum was obtained by TD-DFT using CAM-B3LYP models in conjunction with 6-311G (d, p) basis set and methanol as a solvent, the absorption bands were found within the UV range, and the maximum wavelength showed red-shifted increases. These compounds could serve as a base material for developing selective gas sensors with considerable UV/vis absorption (180–400 nm). According to the research results, the designed compounds are good candidates for use as precursors in polymer designs for optoelectronic and sensor applications due to their high electrical conductivity and photochemical properties.

Nuclear waste control and related equipment play a vital role in safeguarding human health and the environment from the potential dangers of radioactive waste. This study addresses the critical challenge of enhancing the shielding effectiveness of container materials for nuclear waste management, with a focus on comparing the attenuation properties of glass and concrete composites. Our analysis revealed that the copper oxide-reinforced borosilicate glass container demonstrated a significant transmission factor (TF) value decrease by approximately 15% compared to steel–magnetite concrete at 1.3325 MeV, with a standard deviation of ±1.5%, indicating its lower protective characteristics. Nonetheless, it exhibited a 10% higher TF reduction compared to the cement–bitumen mix at the same energy level, with a precision error of ±1.2%. In addition, the half-value layer for this glass was determined to be 2.5 cm for 1.3325 MeV gamma rays, showing moderate shielding capacity. The study demonstrates that optimizing the oxide content in the borosilicate glass matrix significantly enhances its shielding effectiveness. This advancement in nuclear waste management materials is justified by our comprehensive evaluation, highlighting the potential of optimized glass materials to outperform traditional concrete in certain scenarios, thus contributing to the development of more effective nuclear waste containment solutions.

In the current study, we delve into examining the movement of a nanofluid within a Williamson boundary layer, focusing on the analysis of heat and mass transfer (HMT) processes. This particular flow occurs over a sheet that undergoes nonlinear stretching. A significant facet of this investigation involves the incorporation of both the magnetic field and the influence of viscous dissipation within the model. The sheet is situated within a porous medium, and this medium conforms to the Darcy model. Since more precise outcomes are still required, the model assumes that both fluid conductivity and viscosity change with temperature. In this research, we encounter a system of extremely nonlinear ordinary differential equations that are treated through a numerical technique, specifically by employing the spectral collocation method. Graphical representations are used to illustrate how the relevant parameters impact the nanoparticle volume fraction, velocity, and temperature profiles. The study involves the computation and analysis of the effect of physical parameters on the local Sherwood number, skin friction coefficient, and local Nusselt number. Specific significant findings emerging from the present study highlight that the rate of mass transfer is particularly influenced by the thermophoresis factor, porous parameter, and Williamson parameter, showing heightened effects, while conversely, the Brownian motion parameter demonstrates an opposing pattern. The results were computed and subjected to a comparison with earlier research, indicating a notable degree of conformity and accord.

The current study theoretically and computationally analyses the viscoelastic Sisko fluids during the non-isothermal rollover web phenomenon. The mathematical modeling produces a system of partial differential equations, which we further simplify into ordinary differential equations through appropriate transformations. We have formulated the problem based on the lubrication approximation theory. The solution has been obtained with the perturbation method, and the outcomes are found in mathematical, tabular, and graphical forms that highlight the influence of pertinent parameters on velocity profiles, pressure gradients, flow rates per unit width, Nusselt number, pressure profile, temperature distributions, and other significant engineering quantities. Further, A comparative analysis between analytic and numerical solutions, utilizing the middefer method in the Maple environment, demonstrates reasonable agreement. Also, we observe that the fluid parameter significantly influences both velocity and temperature profiles. Moreover, the determination of a separation point 2.5000, accompanied by the observation of a maximum coating thickness of 0.6960. The enhancement in fluid heat transfer rate is approximately 5% compared to non-Newtonian fluid parameter values, with potential for further improvement by increasing the non-Newtonian parameter values. This comprehensive investigation offers valuable insights for practical implementation and future scholarly endeavors, with zero-order findings showcasing enhanced precision.

The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ \mu , and a parameter η \eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.

In this article, the solution to the time-fractional Fisher equation is determined using two well-known analytical techniques. The suggested approaches are the new iterative method and the optimal auxiliary function method, with the fractional derivative handled in the Caputo sense. The obtained results demonstrate that the suggested approaches are efficient and simple to use for solving fractional-order differential equations. The approximate and exact solutions of the partial fractional differential equations for integer order were compared. Additionally, the fractional-order and integer-order results are contrasted using simple tables. It has been confirmed that the solution produced using the provided methods converges to the exact solution at the appropriate rate. The primary advantage of the suggested method is the small number of computations needed. Moreover, it may be used to address fractional-order physical problems in a number of fields.

To evaluate the plan quality and robustness of volumetric modulated arc therapy (VMAT) and intensity modulated radiation therapy (IMRT) for breast cancer, 50 patients, including 25 patients who received radiotherapy after breast-conserving surgery (BCR) and 25 patients who received postmastectomy radiotherapy (PRT), were selected for this study. Nominal VMAT and IMRT plans were generated for each patient on Eclipse treatment planning system (version 15.6). The dosimetric metrics, dose distribution, gamma passing rate, and delivery time were compared. In addition, 12 uncertainty plans with plan isocenter uncertainty and CT density uncertainty were recalculated based on the nominal plans for each patient. The dose volume histogram (DVH) band width (DVHBW) was adopted to quantify the plan robustness of the nominal plans for the perturbed scenarios in this study. For BCR, the dosimetric metrics except planning target volume (PTV) conformal index (CI) and ipsilateral lung V 5 were not statistically different for IMRT and VMAT plans. PTV CI of VMAT plans was better than that of IMRT plans (VMAT: 0.923 ± 0.024, IMRT: 0.855 ± 0.032, p = 0.003). The ipsilateral lung V 5 of VMAT plan was higher than that of IMRT plan (VMAT: 42.4% ± 2.8%, IMRT: 40.5% ± 4.0%, p = 0.045). The VMAT plans save more than 1.20 min compared to the IMRT plans (VMAT: 0.87 min, IMRT: 2.08 min, p < 0.001). The gamma passing rates of VMAT plans were better than those of IMRT plans (3 mm/3%, VMAT: 99.7% ± 0.2%, IMRT: 99.4% ± 0.4%, p < 0.001; 2 mm/2%, VMAT: 97.2% ± 1.0%, IMRT: 96.9% ± 0.6%, p = 0.108). For PRT, the dosimetric metrics of VMAT plans, including PTV D mean , homogeneity index (HI), CI, and D max of spinal cord, were significantly better than those of IMRT plans. The VMAT plans save more than 45% time compared with IMRT plans (VMAT: 1.54 min, IMRT: 2.81 min, p < 0.001). The difference in gamma passing rates between VMAT plans and IMRT plans was not statistically significant. For the plan robustness, the DVHBW of VMAT plans and IMRT plans for BCR were 2.09% ± 0.23% and 2.98% ± 0.40%, respectively ( p < 0.05). For PRT, the DVHBW of VMAT plans was significantly better than those of IMRT plans (VMAT: 3.05% ± 0.26%, IMRT: 3.57% ± 0.27%, p < 0.05). The results show that the dosimetric metrics of VMAT plans were comparable to those of IMRT plans. More importantly, the VMAT plans had excited dose distribution and fast execution efficiency. The plan robustness of VMAT plans were superior.

Recognizing the flow behaviours across a Riga plate can reveal information about the aerodynamic efficiency of aircraft, heat propagation, vehicles, and other structures. These data are critical for optimizing design and lowering drag. Therefore, the purpose of the current analysis is to examine the energy and mass transfer across the mixed convective nanofluid flows over an extending Riga plate. The fluid flow is deliberated under the influences of viscous dissipation, exponential heat source/sink, activation energy, and thermal radiation. The Buongiorno’s concept is utilized for the thermophoretic effect and Brownian motion along with the convective conditions. The modelled are simplified into the lowest order by using similarity transformation. The obtained set of non-dimensional ordinary differential equations is then numerically solved through the parametric continuation method. For accuracy and validation of the outcomes, the results are compared to the existing studies. From the graphical analysis, it can be observed that the fluid velocity boosts with the rising values of the divider thickness parameter. The fluid temperature also improves with the effect of Biot number, Eckert number, and heat source factor. Furthermore, the effect of heat source sink factor drops the fluid temperature.

Acoustic streaming has a significant effect on accelerating material mixing and flow field disturbance. To explore the characteristics of acoustic streaming in the cylindrical tube array field under the action of an acoustic wave, we derive the dimensionless acoustic streaming control equation and establish a numerical calculation model of acoustic streaming. The effects of acoustic incidence angle, acoustic Reynolds number, and Strouhal number on the acoustic streaming vortex flow field in the tube array were investigated. The numerical results show that with the change in acoustic parameters, the acoustic streaming in the tube array presents rich changes in the vortex flow field, and there are flow field phenomena such as shrinking, merging, tearing, and splitting of the vortex structure. Toward the walls of each tube, there is a strong acoustic streaming flow velocity. Besides, there is also a large streaming velocity on the interface of the adjacent acoustic streaming vortices. The inner streaming vortex structure in the acoustic boundary layer decreases with the increase in the acoustic Reynolds number, but the intensity of the inner streaming vortex and outer streaming vortex increases rapidly, and the disturbance effect of the flow field is enhanced. With the increase in the dimensionless acoustic frequency (or Strouhal number), although the structure and intensity of the inner streaming vortex decrease, the velocity gradient on the wall of the cylindrical tube increases, which is beneficial to destroy the flow boundary layer of the cylindrical tube wall and accelerate the instability of the wall flow field.

Modern heat transport processes such as fuel cells, hybrid engines, microelectronics, refrigerators, heat exchangers, grinding, coolers, machining, and pharmaceutical operations may benefit from the unique properties of nanoliquids. By considering Al 2 O 3 {{\rm{Al}}}_{2}{{\rm{O}}}_{3} nanoparticles as a solo model and Al 2 O 3 – Cu {{\rm{Al}}}_{2}{{\rm{O}}}_{3}{\rm{\mbox{--}}}{\rm{Cu}} as hybrid nanocomposites in a hyperbolic tangent fluid, numerical simulations for heat and mass transfer have been established. To compare the thermal acts of the nanofluid and hybrid nanofluid, bvp4c computes the solution for the created mathematical equations with the help of MATLAB software. The impacts of thermal radiation, such as altering thermal conductivity and cross-diffusion, as well as flow and thermal facts, including a stretchy surface with hydromagnetic, and Joule heating, were also included. Furthermore, the hybrid nanofluid generates heat faster than a nanofluid. The temperature and concentration profiles increase with the Dufour and the Soret numbers, respectively. The upsurge permeability and Weissenberg parameter decline to the velocity. An upsurge variable of the thermal conductivity grows to the temperature profile. Compared to the nanofluids, the hybrid nanofluids have higher thermal efficiency, making them a more effective working fluid. The magnetic field strength significantly reduces the movement and has a striking effect on the width of the momentum boundary layer.

In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxiliary function method and the Laplace iterative transform method, we approximate these equations. These formulas are used to characterize plasma waves in oceans and ion acoustic waves in shallow water. The results discovered have important ramifications for our comprehension of many physical events. Our results show that both methods are robust, easy to use, and successful. Both methods yield results that are satisfactory to each other. With the use of tables and graphs, we compared the two suggested approaches. The findings suggest that the suggested methods can be widely applied to explore other real-world problems.

Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

Many scholars performed the analysis by using the non-Newtonian fluids based on the nano and hybrid nano particles in blood arteries to investigate the heat transport for cure in several diseases. These performances are presented to investigate the blood flow behaviour with extended form of the novel tetra hybrid Das and Tiwari nanofluid system attached by the Carreau fluid. The assessment of energy transport has been achieved based on the thermal radiation, heat source/sink, Joule heating, and viscous dissipation. The obtained partial differential equation from physical problem is transformed into ordinary differential equations (ODEs) by using the similarity variables. Furthermore, system of nonlinear ODEs attached with boundary conditions are transported into the system of first-order ODEs with initial conditions. For the numerical solution of obtained ODEs, the numerical solutions have been performed based on the RK method. The numerical results are plotted through figures, tables, and statistical graphs. Magnetic forces and inclined magnetic effects are caused to reduce velocity of blood. Temperature of blood within the arteries is increased by increasing the parameter of thermal radiation.

In many physical situations, it is reasonable to assume that the α -quantile of past life functions is increasing. In this study, we propose a new estimator for an increasing α -quantile of the past life function for right-censored data. We investigate the asymptotic properties of the new estimator and explore its weak and strong convergence. The simulation results show that the new estimator is consistent and outperforms the usual estimator from the literature. As an illustrative example, a time event from a data set of the Mayo Clinic study on primary biliary cirrhosis was analyzed.

The growing fascination with nanofluid flow is motivated by its potential applications in a variety of industries. Therefore, the objective of this research article is to conduct a numerical simulation of the Darcy porous medium flow of Newtonian nanofluids over a vertically permeable stretched surface, considering magnetohydrodynamic mixed convection. Various attributes, such as the impacts of slip, thermal radiation, viscous dissipation, and nonuniform heat sources, are integrated to explore the behavior of the flow. The utilization of the boundary layer theory helps to describe the physical problem as a system of partial differential equations (PDEs). These derived PDEs are then converted to a system of ordinary differential equations (ODEs) through the application of suitable conversions. The outcomes are obtained using the finite difference method, and the effects of parameters on nanofluid flow are compared and visualized through both tabular and graphical representations. The outcomes have been computed and subjected to a comparative analysis with previously published research, revealing a remarkable degree of agreement and consistency. Consequently, these innovative discoveries in heat transfer could prove beneficial in addressing energy storage challenges within the contemporary technological landscape. The noteworthy main findings indicate that when the porous parameter, magnetic number, velocity slip parameter, viscosity parameter, and Brownian motion parameter are assigned higher values, there is an observable expansion in the temperature field. Due to these discoveries, we can enhance the management of temperature in diverse settings by effectively modulating the heat flow.

The iterative Shehu transform homotopy perturbation method (HPM) is used in the present research to address fractional telegraph equations in different dimensions, respectively. Considered equations particularly stand out in the field of material science and certain other significant fields. A graphic comparison of estimated and actual results is used to assess the validity and efficacy of the suggested technique. Graphs show a match of approximate to exact findings. Without any linearization or discretization, the iterative Shehu HPM offers a reliable and efficient way to deliver approximations and accurate outcomes that is also error-free. The development of numerical regimes based on discretization is difficult and expensive computationally. Additionally, discretization error is produced as a result of discretization in purely numerical regimes. The present regime has produced robust results and is time-efficient. Also, no discretization error was produced.

This article investigates the unsteady mixed convention two-dimensional flow of magnetohydrodynamic Casson hybrid nanofluids (alumina oxide and titanium oxide nanoparticles with base fluid water) flow through porous media over a linearly stretched sheet. We analyzed the heat and mass transfer in mixed convection, thermal radiation, variable thermal conductivity, variable mass diffusivity, and chemical reaction in the presence of thermophoresis and Brownian motion. A system of partial differential equations is reduced to a solvable system of ordinary differential equations by applying a suitable similarity transformation. We used the Runga–Kutta method along with the shooting procedure to solve the flow, heat, and mass transfer equations along with boundary conditions. The results obtained from MATLAB codes are compared with previously published results of the same type in a limiting case. The results of the velocity, temperature, and concentration profile of the hybrid nanofluid for varying different flow parameters are obtained in the form of graphs, while the rate of shear stress, rate of heat, and mass transfer are expressed in tables. We noticed that velocity and temperature diminish as an unsteady parameter increases; however, the reverse trend was observed in the nanoparticle concentration profile. With an increase in the thermal radiation parameter, the resultant velocity and temperature profile improves, while the concentration of nanoparticle profiles decreases. The velocity and temperature increase with higher Brownian motion, while the velocity increases and temperature decreases with higher thermophoresis.

This article develops and investigates the behavior of soliton solutions for the spatiotemporal conformable Klein–Gordon equation (CKGE), a well-known mathematical physics model that accounts for spinless pion and de-Broglie waves. To accomplish this task, we deploy an effective analytical method, namely, the modified extended direct algebraic method (mEDAM). This method first develops a nonlinear ordinary differential equation (NODE) through the use of a wave transformation. With the help of generalized Riccati NODE and balancing nonlinearity with the highest derivative term, it then assumes a finite series-form solution for the resulting NODE, from which four clusters of soliton solutions – generalized rational, trigonometric, exponential, and hyperbolic functions – are derived. Using contour and three-dimensional visuals, the behaviors of the soliton solutions – which are prominently described as dark kink, bright kink, breather, and other N N -soliton waves – are examined and analyzed. These results have applications in solid-state physics, nonlinear optics, quantum field theory, and a more thorough knowledge of the dynamics of the CKGE.

In order to solve the problems of low transmission rate and large device size of electro-optical modulator, an electro-optic half subtractor based on silicon-based hybrid surface plasmon polariton waveguide is proposed in this study. The proposed device utilizes three units metal-oxide-semiconductor capacitor structure to achieve the half subtractor logic function of electro-optic control, improving the transmission rate of the electro-optic half subtractor while also reducing the device size using surface plasmon polariton technology, with a size of only 32 μm × 4.3 μm. At the same time, the use of hybrid silicon waveguides reduces the sharp Ohmic attenuation caused by surface plasmon polaritons and reduces optical insertion losses (ILs). The simulation results show that when the electro-optic half subtractor operates at the wavelength of 1,550 nm, the IL difference is 1.0 dB in each state, the transmission rate of the device is 0.75 Tbit/s, and the energy consumption is 12.69 fj/bit.

Various nanoparticles have been used to increase the heat transfer characteristics (HTC) of nanofluids in the heated tube. The use of various shapes of the same nanoparticle can have major impact on the HTC. In this study, computational fluid dynamics (CFD) analysis of the impact of particle shape (Brick and Platelet) and Reynolds (Re) number (4,500, 6,000, 7,500, and 9,000) on the HTC of nanofluid in the heated tube was carried out in accordance with Taguchi method. Heat transfer coefficient, Nusselt (Nu) number, performance evaluation criteria, and average static pressure drop were chosen as HTC. CFD analyses for 1% Fe 3 O 4 nanofluids in ANSYS Fluent software were performed in accordance with L8 orthogonal array. Particle shape and Re number were selected as the first and second factors, respectively. Signal/noise analysis was used to decide optimum levels and impact direction on HTC for each factor, whereas analysis of variance was implemented to define the importance levels and percentage impact ratios of the factors. According to the results obtained from the study, the nanofluids with platelet nanoparticles have a higher impact on the heat transfer coefficient compared to Brick nanoparticles. Although the increase in the Re number causes an increase in the heat transfer coefficient, Nu number, and average static pressure drop, it does not have any effect on the performance evaluation criteria. The results obtained from this study can be used as a guidance for experimental studies.

In this work, the exact solutions of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation are reported by adopting the He’s variational direct technique (HVDT). The analytic findings of solutions were obtained by semi-inverse scheme, and six form of supposed studies reveal that the solutions belong to soliton groups. The modulation instability is considered. The tan ( Π ( ξ ) ) \tan \left(\Pi \left(\xi )) scheme on the suggested model is employed to study new rational solutions. The investigated properties of solutions were determined by graphic studies, which shows significantly values of the parameters and susceptibility of abundant solutions. The obtained results in this work are expected to open new perspectives for the traveling wave theory. For the aforementioned wave solutions, we graphically describe their dynamical properties. It is worth mentioning that our results not only enable us to understand the dynamic properties of such equations more intuitively but also provide some ideas for researchers to facilitate more in depth exploration. It is important to mention that our proposed method is highly effective, consistent, and impacting and can be utilized to solve different physical models.

This study calls attention to the current state of the probability ( P ) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper noticed how fundamental issues raised in quantum mechanics (QM) directly derive from unresolved probabilistic questions. Endless philosophical debates create more problems than solutions, so the author of this research suggests going directly to the root of the issues and searching for the probability theory which formalizes the multifold nature of P . This study offers a brief overview of the structural theory of probability , recently published in a book, and applies it to QM in order to show its completeness. The whole probability-based interpretation of QM goes beyond the limits of a paper and these pages condense a few aspects of this theoretical scheme. The double slit experiment is used to corroborate the theorems presented here.

Hydrodynamic cavitation is widely used in many fields such as water treatment, impact rock breaking, and food preparation. The performance of hydrodynamic cavitation is closely related to its internal flow field. In the present study, cavitation flow field was analyzed by computational fluid dynamics in the reactor. The cavitation performance of the rotor is evaluated under different operating conditions. The time frequency distribution of pressure pulsation is studied. The pressure increases at the connection point between the local low-pressure area and the mainstream low-pressure area. Cavitation bubbles collapsed at the tail end of the cavity to form a local void area. The blade frequency amplitude of pressure pulsation shows the significant periodic change. The blade frequency amplitude decreases along the flow direction. The effect of the fluid outlet led to the increase in the second-order harmonic frequency amplitude. The research results could provide theoretical support for the research of cavitation mechanism of cavitation equipment.

This study examines the influence of wall velocity ratio on mixed convective heat transport in a permeable cavity containing an isothermal solid block at its center. The analysis considers the characteristics of various flow variables, i.e ., Darcy number, wall velocity ratio, Richardson number, and volume fraction of suspended nanoparticles, on heat transport and material flow characteristics. The principal equations are solved implementing the semi-implicit method for pressure linked equations algorithm, and the outcomes are compared with existing literature. The study shows that rising estimations of Darcy number, velocity ratio, Richardson number, and nanoparticles volume fraction lead to improved heat transfer rates. For example, at high Richardson number (100) and solid volume fraction (0.05), increasing the velocity ratio from 0.5 to 1.5 results in a 6% (5%) upsurge in heat transport rate. Conversely, at smaller Richardson number (0.01), the heat transport rate upsurges by 29% (28%). Similarly, at high Darcy numbers and low wall velocity ratios, a 3% (4%) escalate in heat transport rate is observed with an increase in nanoparticles concentration from 0 to 0.05, while a 9% (8%) increase in thermal performance is achieved at low Darcy numbers. The study emphasizes the importance of optimizing the combination of nanoparticles volume fraction, Darcy number, velocity ratio, and Richardson number to maximize thermal performance in the porous cavity.

The present study investigates the thermal convection of a power-law fluid in a horizontal porous layer that is heated from below. The study of flow in a porous medium is important because of its applications in various fields such as agriculture, geothermal sciences, and engineering. Linear instability analysis is performed using the normal mode method to solve the governing equations after non-dimensionalization. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for linear instability. The impact of gravity parameter, Peclet number, and power-law index on linear instability has been investigated. Linear and quadratic variations of gravity field are considered. From the results, it is evident that the critical Rayleigh number exhibits a non-monotonic relationship with the Peclet number. Increasing the gravity variation parameter leads to a more stable system, particularly in the case of linear gravity variation.

The aim of this study is to investigate the heat and mass transfer characteristics of Burgers nanofluid in the presence of thermo-diffusion effects. The analysis considers higher-order slip effects to study the transport phenomena. Additionally, the study examines the impact of thermal radiation and chemical reactions on the flow. Variable thermal conductivity assumptions are made for heat transfer analysis. The Cattaneo–Christov model, an extension of Fourier heat and mass theories, is employed for the analysis. Heat transfer evaluation is conducted using convective thermal constraints, and numerical computations are carried out using the Runge–Kutta method. The study visually represents the impact of flow parameters through graphical analysis. It is suggested that heat transfer can be significantly improved through the interaction of slip effects, and the concentration phenomenon is enhanced by the Soret number.

This article aims to provide a novel image paradigm for camouflaged object detection, i.e. , RGB-D images. To promote the development of camouflaged object detection tasks based on RGB-D images, we construct an RGB-D camouflaged object detection dataset, dubbed CODD. This dataset is obtained by converting the existing salient object detection RGB-D datasets by image-to-image translation techniques, which is comparable to the current widely used camouflaged object detection dataset in terms of diversity and complexity. In particular, in order to obtain high-quality translated images, we design a selection strategy that takes into account the structural similarity between pre- and post-conversion images, the similarity between the appearance of objects and their surroundings, as well as the ambiguity of object boundaries. In addition, we extensively evaluate the CODD dataset using existing RGB-D-based salient object detection methods to validate the challenge and usability of the dataset. The CODD dataset will be available at: https://github.com/zcc0616/CODD-Dateset.git.

This work presents a numerical analysis by zero-dimensional global model of the influence of electron temperature and concentration on production of OH and NO for helium plasma jet propagating in the atmosphere of humid air. The calculations are done for the constant electron temperatures (1–4 eV) and concentrations (10 10  cm −3 to 10 14  cm −3 ). The mole fractions of air and water vapor vary from 100 to 10,000 ppm. The presented analysis reveals that at low electron temperature and H 2 O contents, the dissociative electron attachment to O 2 dominates over attachment to H 2 O in production of OH. At higher amount, H 2 O modifies the high-energy tail of electron distribution function and increases rate coefficients for electron impact processes. Dissociative electron attachment to H 2 O dominates in the production of OH at 1 eV and remains important at higher energies when processes with O( 1 D), O( 1 S), O 2 ( 1 ∆) produce OH. Impact dissociation of H 2 O dominates over the dissociative attachment at 3 and 4 eV. NO comes mainly from air effluent in the plasma and O + NO 2 at 100 ppm of H 2 O. Above 2 eV, the conversion process between OH and NO dominates in NO production at higher amount of H 2 O. Regarding dependencies on electron concentration, at low electron temperatures, electron distribution function is affected only at 10 14  cm −3 . But in the case of higher temperature, electron concentration and water vapor have negligible influence. The best agreement with measured data is obtained for electron concentration 10 10  cm −3 and at temperature of 2 eV for OH and 10 12  cm −3 and 3 eV for NO.

The convection stability of Maxwell–Cattaneo fluids in a vertical double-diffusive layer is investigated. Maxwell–Cattaneo fluids mean that the response of the heat flux with respect to the temperature gradient satisfies a relaxation time law rather than the classical Fourier one. The Chebyshev collocation method is used to resolve the linearized forms of perturbation equations, leading to the formulation of stability eigenvalue problem. By numerically solving the eigenvalue problem, the neutral stability curves in the a –Gr plane for the different values of solute Rayleigh number Ra S are obtained. Results show that increasing the double diffusion effect and Louis number Le can suppress the convective instability. Furthermore, compared with Fourier fluid, the Maxwell–Cattaneo fluids in a vertical slot cause an oscillation on the neutral stability curve. The appearance of Maxwell–Cattaneo effect enhances the convection instability. Meanwhile, it is interesting to find that the Maxwell–Cattaneo effect for convective instability becomes stronger as the Prandtl number rises. That means Prandtl number (Pr) also has a significant effect on convective instability. Moreover, the occurrence of two minima on the neutral curve can be found when Pr reaches 12.

The complexity of thermal analysis in practical systems has emerged as a subject of interest in various fields of science and engineering. Extended surfaces, commonly called fins, are crucial cooling and heating mechanisms in many applications, such as refrigerators and power plants. In this study, by using a deterministic approach, we discuss the thermal analysis of conduction, convection, and radiation in the presence of a magnetic force within an extended surface. The present study develops a deep neural network to analyze the mathematical model and to estimate the contributions of each dimensionless model parameter to the thermal dynamics of fins. The deep neural network used in this study makes use of a feedforward architecture in which the weights and biases are updated through backward propagation. The accuracy of the neural network model is validated using results obtained from a spectral-based linearization method. The efficiency rate of the extended surfaces is computed using the neural network and spectral methods. The results obtained demonstrate the accuracy of the neural network-based technique. The findings of this study in relation to the novel mathematical model reveal that utilizing materials with variable thermal conductivity enhances the efficiency rate of the extended surface.

The present study formulates and further examines a steady-state heat diffusion process in a generalized multilayered heterogeneous circular composite. Sufficient boundary and interfacial data are assumed at the endpoints of the circumferential length, and the interfaces, cutting across the respective perfectly welded cylinders. A well-known classical method for solving linear partial differential equations has been sought to derive a compacted solution for the diffusion process in governing heterogeneous cylinders. Certainly, among the significant novel findings of the current study is the acquisition of a generalized series solution for m m -body multilayered heterogeneous circular composites, in addition to the portrayal of simple, yet an efficient method for solution; away from sophisticated numerical methods or integral transform methods that are not always invertible analytically. Moreover, three prototype situations of the structure have been profoundly examined, which are then found to satisfy all imposed structural assumptions. Moreover, the current examination finds relevance in the study and the analysis and design of multilayered bodies in engineering, material science, thermodynamics, and solid mechanics.

The implementation of three-dimensional (3D) printing technology has culminated in a notable rise in productivity and operational effectiveness for manufacturers. Additive manufacturing (AM) is a manufacturing technology that implies an alteration from the conventional approach of material removal. The fundamental idea underlying the AM technique is the gradual buildup of layers (layer-on-layer accumulation). In conventional approaches, every component can have detrimental implications due to the direct interaction between the tool and the workpiece, leading to the loss of heat through friction. The utilisation of 3D printing as a way to surpass conventional processing methods signifies a novel development in several sectors. This method involves the utilisation of unconventional techniques for the fabrication of components. The primary objective of this research is to investigate the chemical vapour jet drilling technique specifically applied to acrylonitrile butadiene styrene (ABS) materials. The intent is to enhance the surface characteristics, or surface finish (SF), and the dimensional accuracy (DA) of ABS workpieces. An evaluation regarding the reliability, repeatability, as well as preciseness of the vapour jet drilling (VJD) process is conducted via the utilisation of experiment and data analysis. The study employed a Taguchi L9 design of experiments to carry out a series of tests aimed at analysing the implications of three independent variables: pressure, flow rate, and standoff distance. The researchers employed a multiresponse optimisation approach to attain an optimal combination of parameters that resulted in a superior SF with DA. Consequently, the overall appeal of the outcome was reached. The process’s capabilities and dependability were assessed by conducting tests on the substrates at their optimal settings. Surface roughness and circularity were measured at numerous locations on the substrates. The study determined that the process capability indices ( C p and C pk ) had values over 1.33 for each of the response parameters, with C pk values also exceeding 1. The analysis of histograms and capability indices demonstrates that the VJD method, when conducted under optimised conditions, may be categorised as statistically controlled for the processing of ABS materials.

Monkeypox is a highly infectious disease and spreads very easily, hence posing several health concerns or risks as it may lead to outbreak. This article proposes a new mathematical model to simulate the transmission rate of the monkeypox virus-infected fractional-order differential equations using the Caputo–Fabrizio derivative. The existence, uniqueness, and stability under contraction mapping of the fixed point of the model are discussed using Krasnoselskii’s and Banach’s fixed point theorems. To verify the model proposed, we employ data that record the actual dynamics, and based on these data, the model can capture the observed transmission patterns in Ghana. Also, the analytic algorithm is used to find the result applying the Laplace Adomian decomposition method (LADM). Performance analysis of LADM is made regarding Runge-Kutta fourth order, which is the most commonly employed method for solving second-order ordinary differential equations. This comparison therefore offers information on the truth and reliability of the two techniques toward modeling the transmission pattern of the monkey pox virus. The information obtained through this study provides a better understanding of the antibodies linked to monkeypox virus spreading and provides effective strategies to doctors and politicians. This article helps shape better strategies about combating the impact of monkeypox virus in public health since it makes it easy to predict and prevent the occurrence of the disease.

Due to the nonlocality of fractional derivatives, the numerical methods for solving nonlinear fractional Whitham–Broer–Kaup (WBK) equations are time-consuming and tedious. Therefore, it is a research hotspot to explore the numerical solution of fractional-order WBK equation. The main goal of this study is to provide an efficient method for the fractional-in-space coupled WBK equations on unbounded domain and discover some novel anomalous transmission behaviors. First, the numerical solution is compared with the exact solution to determine the validity of the proposed method on large time-spatial domain. Then, anomalous transmission of waves propagation of the fractional WBK equation is numerically simulated, and the influence of different fractional-order derivatives on wave propagation of the WBK equation is researched. Some novel anomalous transmission behaviors of wave propagation of the fractional WBK equation on unbounded domain are shown.

In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the conformable extended Korteweg–de-Vries (KdV) model are investigated. First, the conformal fractional order extended KdV model is transformed into ordinary differential equation through traveling wave transformation. Second, two-dimensional (2D) planar dynamical system is presented and its chaotic behavior is studied by using the planar dynamical system method. Moreover, some three-dimensional (3D), 2D phase portraits and the Lyapunov exponent diagram are drawn. Finally, many meaningful solutions are constructed by using the complete discriminant system method, which include rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. In order to facilitate readers to see the impact of fractional order changes more intuitively, Maple software is used to draw 2D graphics, 3D graphics, density plots, contour plots, and comparison charts of some obtained solutions.

The flow and heat transfer characteristics of the fluid in the combustor were investigated using numerical simulation in this study. The physical properties of the cooling airflow were fully utilized, and the structure of the combustor was improved. Film hole with novel structure (arc-shaped slot hole) was proposed and compared with cylindrical hole. The optimization schemes for the combustor liner structure were established, in the meanwhile, the influence of different inclinations and slot depths on the temperature distribution of the combustor liner wall was investigated. Compared with the original structure, the average temperature of the target cooling zones in these optimized schemes are reduced by a minimum of 15.12% (227.1 K) and a maximum of 20.65% (351.6 K). A new assessment model (weighted average temperature assessment model) was proposed to provide an effective assessment of the overall cooling effect. The following conclusions were arrived at: high temperature in localized areas is an important reason for the damage of combustor liner wall. Compared to cylindrical hole, the cooling performance of arc-shaped slot hole is better. When the hole type is the same, the larger inclination has higher jet height than the smaller inclination, and the cooling effect is worse. Increasing the slot depth h can improve the cooling efficiency.

This study examines the effects of various M-shaped water wave shapes on coastal environments for the modified regularized long-wave equation (MRLWE). This work explores the complex dynamics of sediment transport, erosion, and coastal stability influenced by different wave structures using the Hirota bilinear transformation as a basic analytical tool. By providing insightful information about how these wave patterns impact coastal stability, it seeks to broaden our knowledge of dynamic coastlines. As we explore the intricate interactions between water waves and beaches, the knowledge gained from this research could help direct sustainable coastal management and preservation initiatives. For convenience, a range of M-shaped wave structures are depicted, demonstrating the adaptability of the Hirota bilinear transformation approach in recognizing novel wave patterns. Overall, this work contributes to a better understanding of the dynamics of the coastal environment, highlights the wide range of applications for mathematical models in science and engineering, and helps to develop more sensible and practical coastal management and conservation strategies for the protection of coastal areas against changing water wave patterns. Finally, as far as the authors could verify, this is the first work in the literature in which M-shaped soliton solutions are derived for the MRLWE using any method.

Microwave ablation is becoming an increasingly important minimally invasive procedure that uses dielectric hysteresis to generate heat and destroy cancer cells. Tissue damage depends on the input power, procedure duration, and antenna position. Therefore, one of the essential problems is determining parameters that ensure the destruction of the tumor with the desired margins and minimal damage to the healthy tissue. In addition to experimental methods, computer modeling has been proven to be an effective approach for improving the performance of microwave ablation (MWA). Moreover, since the thermal spread in biological tissue is difficult to measure, the development of a predictive model from procedural planning to execution may have a great impact on patient care. This study focuses on determining the optimal parameters for MWA treatment of liver tumors using two identical parallel-positioned multi-slot coaxial antennas. The simulation results suggest that an input power of 20 W or 15 W per antenna suffices for complete tumor ablation with a sufficient safety margin for 600 and 900 s, respectively. In both cases, the created ablation zones were similar. The ablation zones for 15 W per antenna were more spherical, invading a smaller amount of healthy tissue than those for 20 W per antenna. This study may represent a step forward in planning MWA treatment for individual patients.

This research explores new soliton solutions to the Atangana–Baleanu derivative (ABD) fractional system of equations for ion sound and Langmuir waves (FISLW). We utilize the fractional ABD operator to convert our system into an ordinary differential equations. In recent years, machine learning (ML) evolves significantly in the context of data analysis and computing different solutions, which typically enables systems to operate wisely. Now, we are going to use numerous ML tools including matplotlib. pyplot as plt , scipy.integrate , mpl toolkits.mplot3d , and Axes3D to generate various types of optical solutions by using complete discriminant of the polynomial method. We will also analyze solutions for the hyperbolic function, trigonometric function, Jacobian elliptic function (JEF), and other solitary wave solutions. Solitons have extensive uses in pure and applied mathematics, including nonlinear partial differential equations: the Boussinesq equation, the nonlinear Schrödinger equation, and the sine-Gordon equation, Lie groups, Lie algebras, and differential and algebraic geometry. In addition, we study the chaotic behaviour, i.e. , 2D, 3D, time series, Poincarè maps, and sensitivity analysis of our governing model. Sensitivity analysis explores how changes in a system’s variables affects its behaviour.

A numerical framework is established for a two-dimensional steady flow of the magnetized Jeffery fluid model over elongated/shrinking sheets, with potential applications such as coating sheets, food products, fiber optics, drilling fluids, and the manufacturing processes of thermoplastic polymers. The model also demonstrates the influence of chemical reaction, magnetic field, and stability analysis which provide a novel contribution to this study. To ensure the ease and effectiveness of this analysis, we transform the set of difference equations governing the system into ordinary equations using the similarity transformation. The reliability of the solution is examined by using stability analysis. The Navier–Stokes equations have been transformed into self-similar equations by adopting appropriate similarity transformations and subsequently solved numerically using the bvp4c (three-stage Labatto-three-A formula) approach. The comparison between the derived asymptotic solutions and previously documented numerical results is quite remarkable. The self-similar equations display a duality of solutions within a limited range of the shrinking parameter, as observed from the data. For each stretching scenario, there is a unique solution. Hence, an examination of temporal stability has been conducted through linear analysis to establish the most fundamentally viable solution. The determination of stability in the analysis is based on the sign of the smallest eigenvalue, which indicates whether a solution is unstable or stable. The analysis of stability reveals that the first solution, which describes the primary flow, remains stable. Through the utilization of graphs, we thoroughly examine and discuss the influence of emerging factors. The numerical results obtained from this analysis demonstrate multiple solutions within a certain range of M 1 ≥ M ci {M}_{1}\ge {M}_{{ci}} , i = 1 , 2 , 3 i=1,2,3 , and no solution in the range M 1 < M ci {M}_{1}\lt {M}_{{ci}} . M ci {M}_{{ci}} denotes the critical values, which increase as the quantities of Sc {\rm{Sc}} increase from 0.3 to 0.9. Similarly, multiple solutions exist for λ ≥ λ ci \lambda \ge {\lambda }_{{ci}} , i = 1 , 2 , 3 i=1,2,3 , and no solution in the range λ < λ ci \lambda \lt {\lambda }_{{ci}} is observed.

This study proposes a comprehensive heat conduction model that incorporates fractional time derivatives and two-phase lags to describe the behavior of non-simple thermoelastic materials accurately. Generalized fractional differential operators with non-singular kernels are introduced. This type of fractional derivative includes the Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. The model also consists of the two-temperature idea, which considers the effect of microstructure through a two-stage delay approach. Interactions of a thermoelastic nature caused by the rapid heating of an isotropic substance under the influence of an external body force were studied as a practical application of the new concept. There has been some discussion about the effect of the discrepancy index and fractional differential operators. Finally, the graphical representations obtained from the numerical simulations were used to explain the behavior of the studied physical fields. The generalized fractional heat transfer model is demonstrated to be capable of producing a temperature forecast that is in close agreement with experimental data. As a result, the proposed model may be useful for solving difficulties in heat transfer, anomalous transport, and other branches of engineering analysis.

In this study, we examine the movement of two hard spheres aligned in a straight line within an incompressible couple stress fluid under the impact of the magnetic field. Both objects have distinct shapes and move along an axis connecting their centers with varying velocities. As a first step, an incompressible analytical analysis is performed on a fluid with couple stress properties around an axially symmetric particle. Using the superposition principle, a general solution is developed for couple stress fluid flows over two moving objects. In order to achieve the boundary conditions, the boundary collocation strategy is applied to the surfaces of the two spheres. A set of tables and graphs illustrates numerical estimates of the dimensionless drag forces acting on two spherical objects. In addition, a drop in Hartmann number or an increase in couple stress viscosity will increase the dimensionless drag force on each spherical particle.

This study has established the radiation shielding efficacy of zircaloy-2 and zircaloy-4 over a wide spectrum of energy levels. Using the Monte Carlo method, the gamma and neutron transmission factors (TF and nTF) were calculated for various energy levels. Zircaloy-2 demonstrated the highest gamma-ray absorption capacity and the lowest neutron absorption capacity among the investigated alloys. The results indicate that zircaloy-2 and zircaloy-4 have nearly the same neutron transmission characteristics. Although many studies have examined the structure and physical characteristics of these materials, there has been a lack of Monte Carlo simulations to comprehensively investigate the correlation between gamma absorption, neutron absorption parameters, and mechanical qualities. This research aims to examine the ability of zirconium and its zircaloy-2 and zircaloy-4 alloys, which are critical materials used in the nuclear industry, to absorb gamma and neutron radiation over a broad spectrum of frequencies. According to the results, zircaloy-2 has the best ability to absorb secondary gamma rays and the highest level of resistance to them. Despite the minimal disparity in the nTF between the two alloys, simulation results have shown that zircaloy-2 has a higher level of neutron transmittance. These results have the potential to expedite the development of novel materials with enhanced attributes for various applications.

In this article, we take into consideration the stochastic Schrödinger equation (SSE) perturbed in the Itô sense by the multiplicative Wiener process. We employ an appropriate transformation to turn the SSE into another Schrödinger equation with random variable coefficients (SE-RVCs). We used the generalizing Riccati equation mapping method and the Jacobi elliptic function method to find novel hyperbolic, trigonometric, rational, and elliptic functions solutions for SE-RVCs. After that, we can acquire the SSE solutions. For the first time, in this work, we assume that the solution to the wave equation for the Schrödinger equation is stochastic, whereas all earlier studies assumed it to be deterministic. Furthermore, we give various graphs to display the effect of multiplicative Wiener process on the exact solutions to the SSE. We deduce that the multiplicative Wiener process stabilizes the solutions of the SSE.

The modeling of count data is found in many fields, such as statistical physics, public health, medicine, epidemiology, applied science, sociology, and agriculture. In many physical situations, it has been observed that many times in the real world, the original variables may be continuous in nature, but discrete by observation. In this study, the α {\rm{\alpha }} -quantile residual life function for discrete lifetime models is defined and some attributes are investigated. The relation between this measure and the hazard rate function is studied. We discuss how this measure could be useful for finding the burn-in time of a lifetime dataset. Then, a new stochastic order based on the α {\rm{\alpha }} -quantile residual life is proposed and studied.

Improving coating technology and thin film formation by optimizing the experimental parameters has become essential for various industrial and technological fields. This work aims to study the influence of the precursor materials on the physical and electro-optical properties of Cr 2 O 3 thin films. The solutions were prepared using the sol–gel route and deposited on glass slides using the spin coating technique. The structure and morphology of the films were studied using XRD, FT-infrared (IR), and field-emission scan-electron microscope. The results indicated the formation of a high-purity Cr 2 O 3 (Eskolaite) phase in the form of spherical nanoparticles with sizes of 17–25 nm. Three bands appear at 490, 765, and 889 cm − 1 {{\rm{cm}}}^{-1} in the FTIR spectra, which are attributed to Cr – O {\rm{Cr}}{\rm{\mbox{--}}}{\rm{O}} / Cr ═ O {\rm{Cr}}{\rm{&#x2550;}}{\rm{O}} vibrations. The I – V curves showed linear behavior and good ohmic features. Ultraviolet-visible-near infrared spectra showed that the films are highly transparent, with band gaps in the range of 2.60–2.90 eV, and refractive indices in the range of 1.92–2.25. The sheet resistances, the new figure of merit, the real and fictional dielectric constants, and the optical conductivity were discussed. The Cr 2 O 3 thin films are the best candidates for various utilizations, including solar cells, sensors in the IR region, and energy storage.

Valsartan and rosuvastatin together in a binary form have been utilized to reduce hypertension and hyperlipidemia to control cardiovascular complications. This study depicts the simple three mathematically manipulated UV spectroscopic techniques for the estimation of rosuvastatin and valsartan in the formulation. The first method is simple UV absorption at 310 nm by RST and the first derivatization method for VTN. Determining the magnitude difference of a ratio spectrum at two identified wavelengths is the second approach, and determination of the magnitude of the first derivatives of the ratio spectra of RST and VTN constitute the third technique. The selection of wavelengths, divisor concentrations, and peak amplitudes were optimized and validated. The straight line was constructed in the range of 1–30 and 2–25 µg/ml for RST and VST by the normal and first derivatization method. By using the magnitude difference and magnitude of first derivative ratio spectra approaches, the concentrations of 1–12 and 2–25 µg/ml for RST and VTN, respectively, displayed a straight line. The limit of quantification was less than 1 µg/ml for RST and less than 2 µg/ml for VTN. It was eventually found that the accuracy, expressed as a percentage recovery, ranged between 98.94 and 99.55% for RST and 100.36 and 101.08% for VTN. The % RSD did not exceed 1.82 and 1.91 for RST and VTN, respectively. The three techniques were used to accurately measure RST and VTN in their binary formulations and physically mixed solutions, and the results were statistically compared to the previously published HPLC technique. The outstanding recovery achieved by using the authentic standard addition approach validated the methods’ supplemental accurateness. The Analytical Greenness and Red Green Blue procedures verified the eco-friendliness of the suggested UV spectroscopic approaches, which were also found to be superior to the documented HPLC methods.

This investigation explores the analytical solutions to the time-fractional multi-dimensional Navier–Stokes (NS) problem using advanced approaches, namely the Aboodh residual power series method and the Aboodh transform iteration method, within the context of the Caputo operator. The NS equation governs the motion of fluid flow and is essential in fluid dynamics, engineering, and atmospheric sciences. Given the equation’s extensive and diverse applicability across several disciplines, we are motivated to conduct a thorough analysis to understand the complex dynamics associated with the nonlinear events it describes. For this purpose, we effectively handle the challenges posed by fractional derivatives by utilizing the Aboodh approach. This will enable us to obtain accurate analytical approximations for the time fractional multi-dimensional NS equation. By conducting thorough analysis and computational simulations, we provide evidence of the efficiency and dependability of the suggested methodologies in accurately representing the dynamic behavior of fractional fluid flow systems. This work enhances our comprehension of the utilization of fractional calculus in fluid dynamics and provides valuable analytical instruments for examining intricate flow phenomena. Its interdisciplinary nature ensures that the findings are applicable to various scientific and engineering fields, making the research highly versatile and impactful.

The purpose of this work is to investigate the effect of thermal radiation on convective heat transfer for an electrically conducting hybrid nanofluid moving perpendicularly through a microchannel with parallel plates heated under isothermal conditions, while subjected to a transverse magnetic field. In this case, one surface exhibited a superhydrophobic slip and temperature jump, whereas the others did not. The objective of the study was to determine the impacts of thermal radiation, heat generation, and magnetism on the volume flow rate, velocity, and bulk temperature when either surface is heated by a constant wall temperature. Our findings reveal that the radiation parameter significantly influences both the Nusselt number and skin friction differently depending on the surface conditions, while also reducing flow rate and bulk temperature. The heat generation parameter similarly affects these variables but varies with the type of surface being heated. Additionally, both the velocity and temperature profiles increase with the porosity parameter and heat generation coefficient, regardless of the heated surface. Statistical analysis confirms the significance of magnetic and heat generation parameters in determining skin friction and the Nusselt number, and streamlines and isotherms illustrating the effects of thermal radiation and magnetism on two different hybrid nanofluids when heated on nonslip and superhydrophobic surfaces were provided. These insights provide valuable information for the design and maintenance of mini- and microdevices in the fields of nanoscience and nanotechnology.

For treating and diagnosing cardiovascular diseases, the field of biomedical engineering is significant because it develops new ways and techniques. Stenosis is the narrowing of an artery, and it leads reduction in the flow rate of blood. This study investigates the blood flow mechanism in an artery using a mathematical model of Carreau nanofluid with four distinct nanoparticles. Tetra nanofluid model produces significant advancement in the simulation of blood flow through the stenosed arteries. The model is capable of predicting the pressure drop and velocity distribution for diagnosing and treating stenosis. The spectral relaxation approach is used to present the model's efficiency and effectiveness, which makes it a suitable method for solving the governing equations of this study. The findings of this study have important implications for the development of new treatments and diagnostic techniques for stenosis and other cardiovascular diseases.

This study focuses on the propagation behavior of traveling wave solution in microcrystalline materials using the polynomial complete discriminant system method. By establishing a complete discriminant system, we systematically analyze the formation and evolution process of traveling wave solution in microcrystalline materials. Specifically, we apply the cubic polynomial extension to the strain wave equation to obtain more accurate analytical solutions. Additionally, two-dimensional, three-dimensional, and contour plots are generated to visually illustrate the characteristics of the obtained solutions, facilitating a more intuitive understanding of their physical significance. These findings not only help reveal the propagation mechanism of traveling wave solution but also provide a theoretical foundation for the application of microcrystalline materials.

In this study, we introduce an efficient analysis of a new equation, termed the time-fractional q q -deformed tanh-Gordon equation (TGE), which is the fractional form of the q q -deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field of mathematical physics, which is due to its applications in many fields including superconductivity and fiber optics. It has many applications in condensed matter physics and in modeling physical systems that exhibit violated symmetries. We investigate the q q -deformed TGE in fractional form using Caputo fractional derivative to capture non-local and memory effects, which means they can take into account the entire history of a function rather than just its current value. Notably, this equation has not been previously solved in fractional form, making our approach pioneering in its analysis. We solve this equation utilizing the modified double Laplace transform method, which is considered a semi-analytical technique that combines the double Laplace transform with Adomian polynomials to enable us to extract nonlinear terms. This method renowned for its efficacy in handling fractional differential equations; this is evident from the results obtained in the tables by comparing the analytical solution with the approximate solution we obtained, as well as by calculating the absolute error between them. We examine the existence and the uniqueness of the solution utilizing Schaefer’s fixed-point theorem. Different graphs in 2D and 3D are presented to clarify the effect of different parameters on the behavior of the solution, specially the fractional operator and the deformation parameter q q .

Soliton solutions play a crucial role in modeling stable phenomena across optical communications, fluid dynamics, and plasma physics, owing to their stability and persistence in solving nonlinear equations. This study centers on the extended Sakovich equation, emphasizing the importance of soliton solutions in predicting and controlling localized wave behaviors, which advances nonlinear dynamics and its various applications due to its integrable properties and flexible soliton characteristics. This equation is applicable across diverse fields such as fluid dynamics, nonlinear optics, and plasma physics, where it effectively models nonlinear wave phenomena, including solitons and shock waves. Additionally, it provides crucial insights into wave propagation in biological systems and acoustics, making it a valuable tool for analyzing complex wave dynamics. Additionally, we investigate bifurcation and modulation instability within this equation, employing the improved Sardar subequation method and the ℛ ′ ℛ , 1 ℛ \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{{ {\mathcal R} }^{^{\prime} }}{ {\mathcal R} },\frac{1}{ {\mathcal R} }\right) method to derive solitary wave solutions. These methods yield a diverse range of waveforms – hyperbolic, trigonometric, and rational functions – validated rigorously using Mathematica software for accuracy. Graphical representations vividly display various soliton patterns, such as singular, multi-singular, periodic singular, kink, anti-kink, bell-shaped, Kuznetsov–Ma Breather, and parabolic-shaped, highlighting their effectiveness in revealing innovative solutions. Furthermore, a comparative analysis verified the novelty of our derived soliton solutions. This research significantly contributes to advancing soliton solutions for the Sakovich equation, promising diverse applications across scientific disciplines.

In this article, we mainly study new soliton solutions of the conformable time fractional Drinfel’d–Sokolov–Wilson (DSW) equation which has applications in a wide range of practical applications, including fluid dynamics problems. After fractional order travelling transformation, the partial differential equation studied in this article is transformed into ordinary differential equation and connected with a quadratic polynomial. By using the complete discriminant system of quadratic polynomial, we have achieved the classification of soliton solutions of the DSW equation and provided the precise expressions of their solutions, including hyperbolic function solutions, triangle function solutions and Jacobian elliptic function solutions. Some solutions obtained in this article are shown with 3D and 2D plots in order to investigate the propagation characteristics of soliton waves satisfying the conformable time fractional DSW equation. This method is not only fast and effective, but also can obtain new forms of solutions for DSW equation, which is beneficial for people to further understand fluid dynamics problems. This method is also applicable to studying the solutions of other types of partial differential equations.

Intraocular lenses (IOLs) based on a transparent hydrophilic acrylic polymer have been irradiated by a 365 nm UV lamp at a 200 mJ/cm 2 fluence and at different exposure times, from 1 h up to 19 h, in air and at room temperature. The macromolecular modifications induced in the lens have been investigated by attenuated total reflectance coupled to Fourier transform infrared spectroscopy and optical spectroscopy. Particular attention was devoted to the study of chemical modifications of the IOL by UV irradiation, which induced chain scissions, radical formation, and cross-links in the more superficial polymer layers. The experimental results at long exposures demonstrate that the IOL transmission decreases in the UV and NIR ranges, remaining nearly constant in the visible range.

A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance – and reality – of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann–Lemaître–Robertson–Walker (FLRW) lapse function, g tt {g}_{{\rm{tt}}} . Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum.

In this article, we report the application of a commercial supercontinuum light source for testing fiber optics components in a broad optical range. We demonstrate that this kind of light can be successfully used to measure the parameters of a number of passive fiber components, such as fiber Bragg gratings, fiber couplers, wavelength division multiplexers, and fibered isolators. We also show that near the double wavelength of the pulsed laser used to pump the nonlinear fiber generating the supercontinuum, the standard optical spectrum analyzers demonstrate the false spectral peak that affects the test results and that using a simple low-cost monochromator placed at the supercontinuum source output permits the elimination of this peak. The results of experiments related to the characterization of passive fiber devices in the broad optical range, from 1 μm to more than 2 μm, are discussed in detail as possible applications of the proposed technique.

In this article, we take into account the fractional space Kundu–Mukherjee–Naskar model with time-dependent coefficients (FSKMNE-TDCs). By incorporating time-dependent coefficients (TDCs) into the equation, researchers can better model systems that exhibit nonconstant or nonlinear behavior over time. This has important implications for understanding complex phenomena such as turbulence in fluid flow, quantum tunneling in particle physics, and time-varying electromagnetic fields. We apply the mapping method to obtain hyperbolic, elliptic, trigonometric and rational fractional solutions. These solutions are vital for understanding some fundamentally complicated phenomena. The obtained solutions will be very helpful for applications such as optical fiber wave propagation in a magnetized plasma, oceanic rogue waves, and ion-acoustic waves. Finally, we show how the M-truncated derivative order and TDCs affect the exact solution of the FSKMNE-TDCs.

A novel photocathode has shown promise for generating green hydrogen from sanitation water at a rate of 50 µmol/h per 10 cm², using waste water as an electrolyte in a three-electrode cell. This photocathode is composed of two layers: a poly(1 H -pyrrole) seeding layer topped with a silver-silver oxide/poly(1 H -pyrrole) (Ag-Ag 2 O-P1HP) dendritic nanocomposite. The nanocomposite exhibits broad light absorption up to 660 nm and possesses a bandgap of 1.8 eV. SEM images reveal that the Ag-Ag 2 O-P1HP nanocomposite consists of well-ordered semi-spherical nanoparticles, with an average size between 80 and 100 nm. These spherical nanoparticles offer a large surface area, which enhances photon absorption and trapping efficiency. Additionally, the crystalline structure is characterized by a small crystal size of 32 nm, further contributing to the material’s efficiency. Hydrogen generation performance was evaluated by measuring the current density ( J ph ) under white light and monochromatic light, compared to the dark current ( J o ). The photocathode’s sensitivity was tested using four different monochromatic wavelengths: 540, 440, 340, and 730 nm. The first three wavelengths – 540, 440, and 340 nm – resulted in high J ph values of −0.19, −0.20, and −0.21 mA/cm², respectively, indicating significant hydrogen production. Conversely, the 730 nm wavelength produced a lower J ph value of −0.17 mA/cm², as the energy at this wavelength is insufficient to induce significant bond vibrations, resulting in limited hydrogen production. The high efficiency, combined with the straightforward fabrication of this photocathode, suggests that it could be scaled up as a prototype for industrial hydrogen generation applications.

In this article, we present the results of the numerical study related to the balance of photons in a fiber laser simulated by the traveling wave model (TWM). This study is essential since the balance of photons is closely related to the fundamental physical law of conservation of energy. For generality, we consider that active ions of the gain fiber present excited state absorption at both the laser and pump wavelengths and the fiber background loss. We compare the results of simulation based on the TWM, in which the radial distributions of the populations of the energy levels of the active ions are accounted for, with those obtained when these distributions are omitted. We show that, in the first case, the balance of photons is wholly preserved, while in the second case, the balance of photons is disturbed by tens of percent. The physics behind this result is discussed.

The present research explores nematicons in liquid crystals (LCs) with quadruple power law nonlinearity utilizing the modified extended Fan sub-equation technique as an analytical tool to investigate the optical spatial soliton solutions. For the inaugural time, a novel version of nonlinearity is investigated in relation to LCs. There are distinct applications for the several wave solutions that have been created in optical handling data. The aforementioned modified extended Fan subequation approach offers novel, comprehensive solutions that are relatively easy to deploy in comparison to earlier, regular methodologies. This approach translates a coupled non-linear partial differential equation into a coupled ordinary differential equation through implementing a traveling wave conversion. This approach indicates that a large variety of traveling and solitary solutions that rely upon five parameters can be incorporated by the nematicons in LCs. In addition, the investigation yields solutions of the single and mixed non-degenerate Jacobi elliptic function form. Novel solutions, such as the periodic pattern, kink and anti-kink patterns, N-pattern, W-pattern, anti-Z-pattern, M-pattern, V-pattern, complexion pattern and anti-bell pattern, or dark soliton solutions of nematic LCs, have been constructed by means of modified extended Fan subequation technique through granting suitable values for the parameters. The computer software Mathematica 14 is used to illustrate several modulus, real and imaginary solutions visually in the form of contour, 2D, and 3D visualizations that help understand the concrete importance of the nematicons in LCs. This research additionally offers a physical comprehension of the obtained solutions and applications of model. The imposed approach is ultimately thought to be more potent and effective than alternative approaches, and the solutions found in this work could be beneficial in our understanding of soliton structures in LCs.

In the current investigation, we propose the analytical and numerical solutions of the Navier–Stokes equation for the reverse roll coating process (RRCP) using a bath of the Sisko fluid model (SFM). A suitable transformation is applied to the partial differential equation-based mathematical model of SFM-RRCP, resulting in a set of nonlinear ordinary differential equations. The perturbation method has been employed to find the analytical solutions for velocity, flow rate, pressure gradient, pressure, and temperature distribution. The Newton–Raphson method has been used to find coating thickness. Furthermore, numerical integration has been applied to compute some mechanical quantities of interest, including power input and roll separation force. Sensitivity analysis is another approach implemented using response surface methods to examine the impacts of velocity ratio and non-Newtonian parameters on coating thickness, power input, and roll separating forces. The residual graphs and contour diagrams are also shown. It has been observed that as the value of non-Newtonian fluid parameters increases, the velocity profile decreases. However, the coating thickness on the web is a decreasing function. Further, it has been observed that separation points moved toward the nip region when the value of the velocity ratio was raised. Moreover, the sensitivity of roll separating forces and power input to input parameters is negative.

The present problem investigates 3D flow over an expanding wedge geometry of a tangent-hyperbolic Casson fluid. A two-phase approach considers a liquid phase and a dusty fluid, while a Darcy–Forchheimer law is used to model this fluid flow to capture motion and heat transfer. The several aspects are based on variable thermal radiation, heat sink effects, and slip conditions applied. A tri-hybrid nanofluid comprising silicon dioxide, copper, and aluminum oxide nanoparticles suspended in ethylene glycol, the base fluid, is incorporated into the analysis. The derivation of nonlinear ordinary differential equations (ODEs) is used to characterize momentum, thermal behavior, and fluid motion under these circumstances. ODEs are formulated using similarity transformations and slip conditions. The finite element approach is employed. It is estimated that the fluid phase on the heat transfer rate and skin friction coefficient is higher than the dusty phase on the Nusselt number and skin friction coefficient. The heat transfer rate for ternary hybrid nanofluid is larger than that for hybrid nanofluid.

A novel photocathode has been developed for H 2 gas generation from sewage water, utilizing a bismuthyl chloride–poly m -toluidine (BiOCl–PMT) nanocomposite supported on poly-1 H pyrrole (P1HP). X-Ray photoelectron spectroscopy analysis confirms the formation of bismuth oxide intercalated within the polymer network through a chemical reaction, resulting in the creation of bismuth oxide chloride (BiOCl). This photocathode exhibits strong absorption in the UV region, extending into the visible spectrum, with a bandgap of 2.75 eV, enabling effective interaction with photons and efficient energy transfer to the photocatalyst nanomaterials. The material’s crystalline size is limited to 39 nm, and it features a highly porous polymer structure with a pore size of 20 nm, aggregating into larger structures approximately 300 nm thick. When employed as the working electrode in a three-electrode cell, the BiOCl/PMT/P1HP photocathode shows a measured photocurrent density ( J ph ) of −0.046 mA/cm² under illumination, which drops to −0.032 mA/cm² when the light is turned off. The resulting photocurrent of 0.012 mA/cm² reflects the photocathode’s efficient photoelectrochemical behavior. The performance of the photocathode during sewage water splitting can be adjusted by varying the photon energies between 3.6 and 1.7 eV, using filters to control photon wavelengths. This variation is evident in the linear sweep voltammetry curves, with J ph values ranging from −0.045 mA/cm² at 3.4 eV to about −0.042 mA/cm² at 1.7 eV under an applied bias voltage of −0.7 V. The photocathode’s high efficiency is further demonstrated by its ability to produce 15 µmol/h of H 2 gas for a 10 cm² area. This promising performance, combined with cost-effectiveness, makes the BiOCl/PMT/P1HP photocathode an attractive option for green chemistry and industrial applications.

Diesel engines find extensive application in various production sectors, including industry and agriculture. Strengthening the condition monitoring and fault diagnosis of diesel engines is of paramount importance in ensuring the smooth operation of production systems. Timely detection and elimination of defects play a crucial role in maintaining the normal functioning of these systems. Significant temperature fluctuations during the operation of diesel engines are often associated with malfunctions, including ignition failure, abnormal intake, and exhaust processes. Hence, the application of infrared thermography (IRT) for collecting infrared images of diesel engines and conducting quantitative analysis of the temperature distribution in these images has proven to be a faster and more efficient method for recognizing the health status of diesel engines, compared to other fault diagnosis methods. In recent years, there has been a growing interest in deep learning (DL) for fault diagnosis in various industries. This emerging trend has attracted significant attention from researchers. Convolutional neural network (CNN) has garnered significant attention owing to the exceptional capability in extracting image features. Therefore, the article presents a new fault diagnosis method for diesel engines using IRT and CNN. The proposed method involves conducting adaptive histogram equalization for image enhancement, followed by employing Softmax regression for pattern recognition. Finally, two sets of self-made experimental data are used to investigate the impact of temperature variations on fault diagnosis performance and to validate the efficacy of the proposed method in comparison with three DL methods. The findings indicate that this method exhibits superior performance in the realm of diesel engine fault diagnosis.

In this study, a generalization of the Estevez–Mansfield–Clarkson (EMC) equation that considers the presence of conformable time-fractional derivatives is investigated analytically. The integer-order model finds applications in mathematical physics, optics, and the investigation of shape developing in liquid drops. In this study, the Sardar sub-equation method, is employed to solve the generalized EMC equation. From the Sardar sub-equation method a broad range of soliton solutions, including dark-bright, combined dark-singular and periodic singular solitons, have been obtained. Some of the results derived in this study are plotted to illustrate that the solutions are solitary waves, indeed.

This study elucidates the axisymmetric rotation of two eccentric spheres immersed in an incompressible couple stress fluid within a porous annular region. The investigation incorporates boundary conditions applied to the surfaces of both spheres, which rotate axially at differing angular velocities. Utilizing a collocation scheme alongside a semi-analytical approach under the assumption of low Reynolds numbers, this research delves into the hydrodynamic couple force (torque) exerted by the Brinkman couple stress fluid on the interior sphere. The analysis reveals that the dimensionless torque becomes increasingly significant as permeability enhances the size ratio, couple stress fluid parameters, and separation distance. The computed torque values due to stress and couple stress are presented graphically, providing visual clarity to the findings. Additionally, all the results align closely with the numerical analysis of two eccentric rigid spheres in conventional couple stress fluids, devoid of permeability effects or slip conditions, as demonstrated in previous studies (Al-Hanaya and El-Sapa (Effects of slippage and permeability of couple stress fluid squeezed between two concentric rotating spheres. Phys Fluids. 2023;35:103112); Al-Hanaya et al . (Axisymmetric motion of an incompressible couple stress fluid between two eccentric rotating spheres. J Appl Mech Tech Phys. 2022;63(5):1–9)).

Transformer is extensively employed in natural language processing, and computer vision (CV), with the self-attention structure. Due to its outstanding long-range dependency modeling and parallel computing capability, some leading researchers have recently attempted to apply Transformer to intelligent fault diagnosis tasks for mechanical equipment, and have achieved remarkable results. Physical phenomena such as changes in vibration, sound, and heat play a crucial role in the research of mechanical equipment fault diagnosis, which directly reflects the operational status and potential faults of mechanical equipment. Currently, intelligent fault diagnosis of mechanical equipment based on monitoring signals such as vibration, sound, and temperature using Transformer-based models remains a popular research topic. While some review literature has explored the related principles and application scenarios of Transformer, there is still a lack of research on its application in intelligent fault diagnosis tasks for mechanical equipment. Therefore, this work begins by examining the current research status of fault diagnosis methods for mechanical equipment. This study first provides a brief overview of the development history of Transformer, outlines its basic structure and principles, and analyzes the characteristics and advantages of its model structure. Next it focuses on three model variants of Transformer that have generated a significant impact in the field of CV. Following that, the research progress and current challenges of Transformer-based intelligent fault diagnosis methods for mechanical equipment are discussed. Finally, the future development direction of Transformer in the field of mechanical equipment fault diagnosis is proposed.

Modeling several physical events leads to the Bagley–Torvik equation (BTE). In this study, we have taken into account the BTE, including the Caputo–Fabrizio and Atangana–Baleanu derivatives. It becomes challenging to find the analytical solution to these kinds of problems using standard methods in many circumstances. Therefore, to arrive at the required outcome, numerical techniques are used. The Laplace transform is a promising method that has been utilized in the literature to address a variety of issues that come up when modeling real-world data. For complicated functions, the Laplace transform approach can make the analytical inversion of the Laplace transform excessively laborious. As a result, numerical techniques are utilized to invert the Laplace transform. The numerical inverse Laplace transform is generally an ill-posed problem. Numerous numerical techniques for inverting the Laplace transform have been developed as a result of this challenge. In this article, we use the Weeks method, which is one of the most efficient numerical methods for inverting the Laplace transform. In our proposed methodology, first the BTE is transformed into an algebraic equation using Laplace transform. Then the reduced equation solved the Laplace domain. Finally, the Weeks method is used to convert the obtained solution from the Laplace domain into the real domain. Three test problems with Caputo–Fabrizio and Atangana–Baleanu derivatives are considered to demonstrate the accuracy, effectiveness, and feasibility of the proposed numerical method.

A model describing the transmission dynamics of cholera is considered in this article. The concerned model is investigated under the Caputo-Fabrizio fractal fractional derivative. The objective of this article is to study theoretical and numerical results for the model under our consideration. Classical fixed point approach is used to obtain sufficient conditions for the existence of solution to the proposed model. Adam’s Bashforth numerical method is utilized for the numerical interpretation of the suggested model. The considered technique is a powerful mathematical tool, that provides a numerical solution for the concerned problem. To discuss the transmission dynamics of the considered model, several graphical presentations are given.

The generalization of the classical FitzHugh–Nagumo model provides a more accurate description of the physical phenomena of neurons by incorporating both nonlinearity and fractional derivatives. In this article, we present a numerical method for solving the time-fractional FitzHugh–Nagumo equation (TFFNE) in the sense of the Atangana–Baleanu fractional derivative using B-spline functions. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while θ \theta -weighted scheme is used to discretize the space directions. The efficiency of the scheme is demonstrated through numerical results and rate of convergence. The convergence order and error norms are studied at different values of the noninteger parameter, temporal directions, and spatial directions. Finally, the effectiveness of the proposed methodology is examined through the analysis of three applications.

Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional S E 1 E 2 I R {\mathsf{S}}{{\mathsf{E}}}_{1}{{\mathsf{E}}}_{2}{\mathsf{I}}{\mathsf{R}} model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.

This study deals with a mathematical model that examines the spread of Coronavirus disease (COVID-19). This model has been handled with different processes such as deterministic, stochastic, and deterministic–stochastic. First of all, a detailed analysis is presented for the deterministic model, which includes the positivity of the solution, the basic reproduction number, the disease, and endemic equilibrium points. Then, for the stochastic model, we investigate under which conditions, the solution exists and is unique. Later, model is reconsidered with the help of the piecewise derivative, which can combine deterministic and stochastic processes. Numerical simulations are presented for all these processes. Finally, the model has been modified with the rate indicator function. The model presenting these four different situations is compared with the real data in Russia. According to the results obtained from these situations, the model that is obtained by adding the rate indicator function predicts the COVID-19 outbreak in Russia more accurately. Thus, it is concluded that the model with the rate indicator function presents more realistic approach than the previous ones.

This research work is devoted to investigate myeloid leukemia mathematical model. We give some details about the existence of trivial and nontrivial equilibrium points and their stability. Also, local asymptotical stability of disease-free and endemic equilibrium points is discussed. Also, positivity of the solution has been discussed. Some sufficient results are achieved to study the local existence and uniqueness of solution to the considered model for Mittag–Leffler kernel using the Banach contraction theorem. Three numerical algorithms are derived in obtaining the numerical solution of suggested model under three different kernels using Adams–Basforth technique. Numerical results have been presented for different fractals and fractional orders to show the behavior of the proposed model.

In last decades, there have been drastic environmental transformations and mutations happening all around the world. Due to the continuous mass transfer process, for example, CO 2 {{\rm{CO}}}_{2} mass transfer, which in this case, takes the form of greenhouse gas emissions, unusual and extreme kinds of phenomena have been occurring here and there, disturbing our ecosystems and causing damage and chaos on their paths. Reducing or stopping these gas emissions has become one of the major topics in our planet. We investigate the solvability of a mathematical model describing the mass transport process in nature and where additional perturbations parameters have been considered. Besides addressing the stability of the model, its convergence analysis is also given with the use of Crank–Nicholson numerical method, in order to assess its efficiency and perform some numerical simulations. The results obtained show that the model’s dynamic is characterized by many grouping (accumulation) zones, where mass (of CO 2 {{\rm{CO}}}_{2} , for instance) accumulates in an increasing way. This result is important in controlling how CO 2 {{\rm{CO}}}_{2} can be stored in this growingly perturbed environment that surrounds us.

Fractional stochastic differential equations (FSDEs) with fractional derivatives describe the anomalous diffusion processes by incorporating the memory effects and spatial heterogeneities of the porous medium. The stochastic component addresses the random nature of the fluid flow due to the variability in pore sizes and connectivity. The first objective of this research is to prove the well-posedness of a class of generalized proportional FSDEs, and we acquire the global existence and uniqueness of findings under certain settings that are coherent with the classic SDEs. The secondary purpose is to evaluate the continuity of findings in fractional-order formulations. The Carathéodory approximation is taken into account for a class of generalized proportional FSDEs, which is pivotal and provides well-known bounds on the norm of the solutions. Carathéodory’s approximation aids in approximating the FSDEs governing turbulent flows, ensuring the solutions are mathematically robust and physically meaningful. As is widely documented, the existence and uniqueness of solutions to certain types of differential equations can be formed under Lipschitz and linear growth conditions. Furthermore, a class of generalized proportional FSDEs with time delays is considered according to certain new requirements. With the aid of well-known inequalities and Itô isometry technique, the Ulam–Hyers stability of the analyzed framework is addressed utilizing Lipschitz and non-Lipschitz characteristics, respectively. Additionally, we provide two illustrative examples as applications to demonstrate the authenticity of our interpretations. The demonstrated outcomes will generalize some previously published findings. Finally, this deviation from fractional Brownian motion necessitates a model that can capture the subdiffusive or superdiffusive behavior.

The spiral-wound heat exchanger is a key equipment in the liquefied natural gas application, but the flow and heat transfer mechanisms remain unclarified. In this study, a three-dimensional numerical model is created, focusing on exploring the impact of four crucial structural parameters on the flow and heat transfer performance of natural gas, including the external diameter of tubes, the diameter of the core cylinder, the longitudinal pitch of tubes in the same layer, and the radial pitch of tube bundles between the adjacent layer. It was found that the tube diameter, core cylinder diameter, and radial pitch had significant effects on Nu and Δ p m . The optimal Nu on the shell side was obtained at medium core cylinder size. The longitudinal pitch had a weak effect on the performance of both sides, and the longitudinal pitch corresponding to the maximum values of Nu and Δ p m on both sides increased with the increase in the inlet Reynolds number. Under the effect of centrifugal force, a shifted tendency was shown by the velocity and temperature fields.

In this study, ultrasonic technology is combined with twisted belts to explore the comprehensive performance, and this study also investigated the effect of different Reynolds numbers, ultrasonic frequencies, and number of transducers on the performance of circular and twisted band tubes. It was found that ultrasonic waves applied on the tube plate enhanced the heat transfer performance of the heat exchanger tubes, reduced the flow resistance, and improved the overall performance, and the lower the ultrasonic frequency, the better the heat transfer and resistance reduction ability, and at the experimental condition frequency of 21 kHz, the maximum increase of Nu is 19.06%. With the increase of Reynolds number, the better the ultrasonic enhancement heat transfer performance, but the worse the resistance reduction performance. For different heat exchanger tube structures, the synergistic enhanced heat transfer effect of ultrasonic waves with the twisted belt is better than round tubes, and the synergistic drag reduction effect with the round tube is better than the twisted tape round tube. When the installed ultrasonic transducers are two, the heat transfer performance of the heat exchanger tube is the best, and the maximum increase in the value of Nu was 28.06%.

Airfoil printed circuit heat exchangers (PCHEs) possess exceptional comprehensive performance. In recent years, extensive research has been conducted on the layout and structure optimization of airfoil fins. As biomimetic technologies gradually mature, bionics has achieved numerous outcomes in optimizing airfoil aerodynamic characteristic. Inspired by the sailfish geometry, four types of bionic airfoils are proposed based on the NACA 0015 airfoil, to enhance the thermal-hydraulic performance of the airfoil PCHEs. The results show that while the four types of sailfish airfoils are effective in terms of drag reduction, their overall performance at the same pumping power is suboptimal, with only one type providing an advantage at the low Re region. Moreover, airfoils with concave head curves further increase the weakening of heat transfer by the velocity boundary layer.

The study aims to investigate the heat transfer efficiency in a hybrid nanofluid flow consisting of silver–molybdenum tetra sulphide (Ag–MoS 4 ) with variable magnetism. The Yamada–Ota model is incorporated to account for viscous dissipation and heat source/sink effects, providing a comprehensive understanding of the fluid flow characteristics. However, the dissipative heat along with thermal radiation combined with the hybrid particles enriches the flow properties. The proposed model is simplified to its corresponding non-dimensional form for using proper similarity rules, and the set of transformed problems is handled numerically by employing the in-house MATLAB function bvp5c. The research utilizes a new statistical approach based on response surface methodology (RSM) and sensitivity evaluation to enhance the overall heat transmission performance. The work is conducted to obtain the relevant data on heat transfer rate. The concentration of nanoparticles, thermal radiation, and heat source are selected as the key parameters affecting the heat transfer efficiency. RSM is employed to optimize these parameters and determine the optimal conditions for enhanced heat transfer rate. Furthermore, the sensitivity analysis is performed to evaluate the efficiency of individual parameters on heat transportation. The findings of this study demonstrate that the hybrid nanofluid flow of Ag–MoS 4 exhibits improved heat transfer efficiency compared to conventional fluids. Further, the Yamada–Ota conductivity model is also influential in enhancing the heat transfer properties.

Nanofluid, a significant branch of fluid mechanics, plays a pivotal role in thermal management, optics, biomedical engineering, energy harvesting, and other fields. The nanoparticles present in the fluid render the continuum mechanics ineffective, necessitating the adoption of fractional calculus to elucidate the effects of nanoparticles on the motion properties of the nanofluid. This article applies the modified extended tanh-function technique to solve two classical Schrödinger equations, the fractional Phi-4 model and the conformable fractional Boussinesq model, for nanofluids. Multiple exact solutions are obtained, and the corresponding graphical representations are provided to elucidate the basic properties of the nanofluid. This article provides new research perspectives for the development of nanofluids.

Primary goal of this research is to enhance stability of nanofluids which is vital for maintaining consistent thermophysical properties during various applications. Nanofluid stability is essential for obtaining the uniform thermophysical properties during its application. X-ray diffraction and zeta potential were performed to characterize three nanoparticles, namely TiO 2 , Al 2 O 3 , and ZnO. Experimental work was carried out under several trials to enhance the stability of nanofluids. Initially, deionized water was used as base fluid for stability analysis, but nanoparticles agglomerate within after 5 h. Second, alkaline water was selected as base fluid at different pHs ranging from 7 to 14 to analyze the stability of the nanofluids. Finally, the effect of surfactant addition on the stability of prepared nanofluids was also investigated. Observations revealed that at pH 11, nanoparticles exhibited enhanced stability compared to other pH levels. This stability can be attributed to the high zeta potential, fostering electrostatic repulsion between individual particles. It was concluded from the results that zeta potential increases in cases of (TiO 2 + ZnO) and (Al 2 O 3 + ZnO) from −44.2 to −47.8 mV and −42.4 to −44.1 mV with the addition of surfactant, respectively. In the case of (Al 2 O 3 + TiO 2 ), zeta potential decreases slightly from −47.7 to −44.9 mV with the addition of surfactant. Graphical abstract

The primary heat source from the sunlight is solar energy (SE), which is used in photovoltaic (PV) panels, solar power plates, PV, streetlights, and solar-based hybrid nanocomposites. Currently, research is focused on analyzing and improving the efficiency of SE, particularly for powering aircraft, by combining solar power with nanotechnology advancements. As such, this study focuses on examining concentrated solar power and proposes a method to improve the performance of solar airplanes by employing nanotechnology. Furthermore, the work is based on the investigation of the flow rate, thermal distribution, and entropy generation of the magnetized tangent hyperbolic hybrid nanofluid (HNF) along the interior parabolic solar trough collector of an aircraft wing. This work utilizes similarity variables to simplify the partial derivative model into ordinary differential equations. These equations are then solved using the Galerkin weighted residual approach with the help of MATHEMATICA 11.3 software. From the obtained outcomes, it is reflected that the HNFs have high thermal conductivity than the NF. Intensification of Weissenberg number improves the performance of airplane wings subjected to heat transmission. Therefore, this research contributes to improved thermal management in advanced nanotechnology and solar aircraft.

Periodic behaviour analysis of nano/microelectromechanical systems (N/MEMS) is an important area due to its numerous prospective applications in micro instruments. The intriguing and unique qualities of these systems, notably their tiny size, batch manufacturing, low power consumption, and great dependability have piqued the attention of academics and enterprises in using these structures to manufacture various microdevices. This article presents the parameter expansion method (PEM) to obtain the approximate solutions of N/MEMS. The present approach, as well as its speed and simplicity in providing analytical solutions that converge quickly to the exact numerical ones, distinguishes this study. The PEM has the benefit of immediately providing analytical solutions to nonlinear differential equations while avoiding costly calculations. Furthermore, in terms of establishing numerous terms of semi-analytic solutions, this approach is very faster and superior to other established analytical techniques in the literature.

Casson fluids containing carbon nanotubes of various lengths and radii on a moving permeable plate reduce friction and improve equipment efficiency. They improve plate flow dynamics to improve heat transfer, particularly in electronic cooling and heat exchangers. The core objective of this study is to investigate the heat transmission mechanism and identify the prerequisites for achieving high cooling speeds within a two-dimensional, stable, axisymmetric boundary layer. This study considers a sodium alginate-based nanofluid containing single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) and Casson nanofluid flow on a permeable moving plate with varying length, radius, and nonlinear thermal radiation effects. The plate has the capacity to move either parallel to or perpendicular to the free stream. The governing partial differential equations for the boundary layer, which are interconnected, are transformed into standard differential equations. These equations are then numerically solved using the Runge–Kutta fourth-order scheme incorporated in the shooting method. This research analyses and graphically displays the effects of factors including mass suction, nanoparticle volume fraction, Casson parameter, thermal radiation, and temperature ratio. Additionally, a comparison is made between the present result and the previous finding, which presented in a tabular format. The coefficient of skin friction decreases in correlation with an increase in Casson fluid parameters and Prandtl number. Heat transfer rate decreases with a variation in viscosity parameter, while it is increasing with an increase in Prandtl number. In addition, this study demonstrates that heat transfer rate for MWCNT is significantly higher than that of SWCNT nanoparticles. Thermal radiation and temperature ratio reduce the heat transfer rate, whereas nanoparticle volume fraction and Casson parameter enhance it over a shrinking surface.

Non-uniform heat sources and sinks are used to control the temperature of the reaction and ensure that it proceeds at the desired rate. It is worldwide in nature and may be found in all engineering applications such as nuclear reactors, electronic devices, chemical reactors, etc . In food processing, heat is used to cook such as microwave ovens, pasteurize infrared heaters, and sterilize food products. Non-uniform heat sources are mainly used in biomedical applications, such as hyperthermia cancer treatment, to target and kill cancer cells. Because of its ubiquitous nature, the idea is taken as our subject of study. Heat and species transfer analysis of a non-Newtonian fluid flow model under magnetic effects past an extensible moving sheet is modelled and examined. Homogeneous chemical reaction inside the fluid medium is also investigated. This natural phenomenon is framed as a set of Prandtl boundary layer equations under the assumed convective surface boundary constraint. Self-similarity transformation is employed to convert framed boundary layer equations to ordinary differential equations. The resultant system is solved using the efficient finite difference utilized Keller box method with the help of MATLAB programming. The influence of various fluid-affecting parameters on fluid momentum, energy, species diffusion and wall drag, heat, and mass transfer coefficients is studied. Accelerating the Weissenberg number decelerates the fluid velocity. The temperature of the fluid rises due to variations in the non-uniform heat source and sink parameters. Ohmic dissipation affects the temperature profile significantly. Species diffusion reduces when thermophoresis parameter and non-uniform heat source and sink parameters vary. The Eckert number enhances the heat and diffusion transfer rate. Increasing the chemical reaction parameter decreases the shear wall stress and energy transmission rate while improving the diffusion rate. The wall drag coefficient and Sherwood number decrease as the thermophoretic parameter increases whereas the Nusselt number increases. We hope that this work will act as a reference for future scholars who will have to deal with urgent problems related to industrial and technical enclosures.

The purpose of the current research is to inspect the free convection of the nanofluid (Cu–water) within a hexagonal cavity containing a square obstacle with isothermal vertical walls at T h {T}_{{\rm{h}}} and T c {T}_{{\rm{c}}} , and insulated horizontal walls. The aim of this study is to analyze the interaction between the Rayleigh number ( 10 3 < Ra < 10 5 {10}^{3}\lt {\rm{Ra}}\lt {10}^{5} ), obstacle’s position (top, bottom, and center), and volume fraction of the nanoparticles ( 0 < Ø < 0.2 0\lt \O \lt 0.2 ) on the thermal behavior within the enclosure. Simulations were performed using COMSOL Multiphysics software based on the finite element method. The obtained results were demonstrated using streamlines, isotherms, and average Nusselt numbers. It is concluded that the increase in the Rayleigh quantity Ra {\rm{Ra}} and nanoparticle concentration Ø \O increases the average Nusselt N u av {\rm{N}}{{\rm{u}}}_{{\rm{av}}} , which expresses the rate of heat flow in the studied enclosure. Furthermore, the position of the inner obstacle in the middle of the cavity has a more significant thermal efficiency than the other cases.

This research article delves into the intricate domain of nonlinear wave dynamics within the framework of a Murnaghan hyperelastic circular pipe. Thus, the current study makes use of some powerful analytical approaches to examine the propagation of nonlinear elastic waves on a Murnaghan hyperelastic circular pipe. The work is exceptional since it allows for the incorporation of double dispersion terms and material nonlinearity in the controlling nonlinear mode. The study entails a thorough examination of the propagation and interaction of solitons within the Murnaghan hyperelastic medium, providing insights into the distinctive nonlinear wave phenomena manifested by circular pipe configurations. Theoretical insights are substantiated by numerical simulations, presenting a comprehensive understanding of the dynamic responses within these elastic structures. In the end, graphical representations of some of the derived solutions have been provided for clarification. In addition, the reported solutions in the study help researchers working in modern fields of engineering and materials science to obtain valuable insights that can inform the design, analysis, and optimization of materials and structures in contemporary applications.

In this article, the plane Poiseuille flow of couple stress fluid of Vogel’s model between two parallel plates under the influence of non-isothermal effects have been investigated using Optimal homotopy asymptotic method (OHAM) and New iterative method (NIM). The governing continuity and momentum equations are transformed to ordinary differential equations and the coupled system of differential equations is then explored using the said methods. The expressions for velocity profile, temperature distribution, average velocity, volume flux, and shear stress have been obtained employing the said methods. Various essential flow properties have been presented and discussed. The results acquired via these techniques are in the form of infinite series; thus, the results can be effortlessly calculated. Comparison of both techniques are illustrated with the help of different tables and graphs and found both methods to be in a good agreement. Consequently, it will be more appealing for the investigators to apply the proposed methods to diverse problems arising in fluid dynamics.

This investigation takes into account the flow of a hybrid copper–molybdenum disulfide ( Cu – MoS 2 ) \left({\rm{Cu}}{\rm{\mbox{--}}}{{\rm{MoS}}}_{2}) /water nanofluid across a plane flat surface that has been nonlinearly extended in lateral directions. Suitable boundary conditions are used to characterize the nonlinear variants in the velocity and temperature profile of the sheet. The innovative aspect of this work is to examine the impact of thermal conductivity on temperature and entropy across an extended surface using hybrid nanofluids. We obtain numerical techniques of modified boundary layer ordinary differential equations using the effective and reliable optimal homotopy analysis technique (OHAM). A graphic depiction of the influence of several parameters is shown. In this case, the hybrid model takes into account 0.01 0.01 of copper ( Cu ) \left({\rm{Cu}}) and 0.01 0.01 of molybdenum disulfide ( MoS 2 ) {({\rm{MoS}}}_{2}) nanoparticles within base fluid water. The second principle of thermodynamics is used to compute the irreversibility factor. The performance of nanofluid and hybrid nanofluid was compared for pivotal velocity, temperature profile, and entropy formation. The estimated skin friction and Nusselt number are the significant physical parameters. It can be observed that when the values of the stretching rate ratio and power index law increase, the skin friction increases, but it can have the opposite behavior compared to the Nusselt number.

The significance of the study comes in the fact that it investigates complex fluid dynamics and magnetohydrodynamics phenomena, which have the potential to be applied in a variety of domains, such as physics, engineering, and materials science. Their exceptional physical significance stems from their ability to combine the unique properties of multiple substances to provide the desired functions and performance characteristics. However, in this study, the numerical studies of slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over stretching/shrinking surface were investigated. The main objective of current research is to examine the influence of solid volume percentage of cobalt ferrite, the sharply oriented magnetic field, and velocity slip factors on the behaviour of skin friction and heat transfer subjected to suction effect. Moreover, the study included an analysis of the behaviour of velocity and temperature profiles in relation to the consideration of the magnetic parameter, the solid volume percentage of cobalt ferrite, the Prandtl number, and the thermal radiation parameter. The equations that regulate the system were converted partial differential equations into ordinary differential equations by making use of the relevant similarity variables, and then, it solved with bvp4c MATLAB software. The boundary requirements are satisfied in particular parameter ranges where dual solutions are achieved. Besides, dual solutions were obtained in shrinking zone. At critical points, the two dual solutions intersect; however, after these points, no further solutions are accessible. The heat transfer rate decreased the velocity slip factor, while it increased the thermal slip factor. In addition, the thickness of the thermal boundary layer increased thermal radiation, while simultaneously reducing the Prandtl number. Besides, the temperature profile improves when the value of cobalt ferrite is higher. In summary, according to stability analysis, he first solution is stable and the second solution is unstable.

This article aims to use passive flow control to analyze the transportation of heat, mass, and charged particles toward a 3D plate. The current problem offers a novel exploration of the flexible domain of non-Newtonian materials, which are well known for their wide range of applications in the engineering and industrial domains. The current study explores the complex dynamics of heat and mass transfer in a fluid that flows over an elongating sheet. The motion of the nanofluid on the surface is caused by the stretching of the 3D plate. The suspension of mixtures of tetra-hybrid nanoparticles can enhance thermal performance and cooling mechanism. Moreover, the 3D model includes modeling of multiple important parameters, such as heat source, thermal radiation, and Hall and Ion slip effects, in Cartesian coordinates for a three-dimensional stretched plate. This comprehensive analysis of various effects offers a new perspective to the field. Partial differential equations represent the emergent phenomena in the problem formulation process. It was estimated that an enhancement of charged particles and motion regarding nanoparticles is enhanced versus an enhancement of charged particles. With the greater power law index, suction, and Weissenberg number, the acceleration of nanoparticles is enhanced.

Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.

This research endeavors to conduct an examination of the thermal characteristics within the duct filled with the copper nanoparticles and water as base fluid. In exhaust systems, like car exhausts, chimneys, and kitchen hoods, duct flows are crucial. These systems safely discharge odors, smoke, and contaminants into the atmosphere after removing them from enclosed places. The study focuses on a laminar flow regime that is both hydrodynamically and thermally developed, with a specified constraints at any cross-sectional plane. To address this, we employ the finite volume method as it stands as a judicious choice, offering a balance between computational efficiency and solution accuracy. Notably, we have observed that the deceleration of flow induced by elevated Rayleigh numbers can be effectively regulated by the application of an appropriately calibrated external magnetic field. The prime parameters of the problem with ranges are: pressure gradient ( 1 ≤ p 0 ≤ 100 ) (1\le {p}_{0}\le 100) , Hartmann number ( 0 ≤ Ha ≤ 50 ) (0\le \text{Ha}\le 50) , Rayleigh number ( 1 , 000 ≤ Ra ≤ 40 , 000 ) (1,000\le \text{Ra}\le 40,000) , and magnetic parameter ( 0 ≤ M ≤ 50 ) (0\le M\le 50) . Furthermore, our analysis reveals that the Nusselt number exhibits a nearly linear correlation with the nanoparticle volume fraction parameter, a trend observed across a range of Rayleigh numbers and magnetic parameter values. We have noted that a mere 20% nanoparticle volume fraction can result in up to 62% rise in the Nusselt number while causing an almost 50% decrease in the factor f Re . This research framework serves as a robust foundation for understanding the intricate interplay between magnetic influences and thermal-hydraulic behavior within the delineated system.

Shear thickening fluid (STF)-impregnated Kevlar fabric can be used as “Liquid armor” for the protection of weapons and equipment. The concentration of dispersed phase in STF and the fabric structure are important factors that affect the mechanical properties of composites. To obtain the mechanical properties of Kevlar fabric impregnated with STF, nano-sized silicon dioxide particles (SiO 2 ) and Polyethylene glycol were used as dispersing phase and dispersing medium, respectively, by impregnating Kevlar fabrics with 2D planar and three-dimensional (3D) angular interlock structure, fiber-reinforced composite fabrics impregnated with STF with different physical structures were obtained. The results show that the shear thickening behavior of STF is the most obvious when the concentration of STF is 60%. In addition, fabric structure and STF concentration play an active role in the mechanical properties of STF/Kevlar fiber reinforced composites. Compared with pure Kevlar fabric, the maximum tensile load and the maximum puncture load of the three-dimensional angular interlocking structure of STF/Kevlar fiber reinforced composites are increased by more than 13,000 N and 120 N, respectively. The research results can provide theoretical support for the mechanical properties of STF/Kevlar fiber-reinforced composites and individual protection research.

In this work, the Marangoni convective flow of magnetohydrodynamic tangent hyperbolic ( F e 3 O 4 − Cu / {{\rm{F}}{{\rm{e}}}_{3}{\rm{O}}}_{4}-{\rm{Cu}}/ ethylene glycol) hybrid nanofluids over a plate dipped in a permeable material with heat absorption/generation, heat radiation, elastic deformation and viscous dissipation is discussed. The impact of activation energy is also examined. Hybrid nanofluids are regarded as advanced nanofluids due to the thermal characteristics and emerging advantages that support the desire to augment the rate of heat transmission. The generalized Cattaneo–Christov theory, which takes into account the significance of relaxation times, is modified for the phenomena of mass and heat transfer. The fundamental governing partial differential equations are converted to ordinary differential equations (ODEs) by adopting similarity variables. The Runge–Kutta–Fehlberg-45 technique is utilized to solve nonlinear ODEs. Regarding the non-dimensional embedded parameters, a graphic investigation of the thermal field, concentration distribution, and velocity profile is performed. The results show that the increasing Marangoni ratio parameter enhances velocity and concentration distributions while decreases the temperature distribution. The velocity profile is decreased and the efficiency of heat transfer is improved as the porosity parameter is increased. Nusselt number is diminished with the rising values of the porosity variable.

Hybrid nanofluids (HNFs) have outstanding energy transfer capabilities that are comparable to mono-nanofluids. Materials had appliances in obvious fields such as heat generation, micropower generation, and solar collectors. The objective of this study is to investigate the new aspects of convective heat transfer in an electrically conducting Carreau HNF situated between two parallel discs. In addition to the presumed stretchability and rotation of the discs, physical phenomena like nonlinear radiation, viscous dissipation, Joule dissipation, and heat generation and absorption are considered. The Cu and TiO 2 nanoparticles dispersed in engine oil to understand the intricate phenomenon of hybridization. The Tiwari and Das nanofluid model is employed to model the governing partial differential equations (PDEs) and then simplified using boundary layer approximation. The suitable transformations of similarity variables are defined and implemented to change the set of formulated PDEs into ordinary differential equations. The reduced system is solved semi-analytically by the homotopy analysis method. The influences of involving physical parameters on the velocity and temperature are plotted with the help of graphical figures. This study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, our research provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers, and microelectronics.

In this study, a single cooling channel system is suggested for conductive double panel systems. The cooling channel for the vertical component uses perforated porous insert (PP-I) and porous insert (P-I), while cylinders are used in the PP-I case. The permeability of the porous channel (Da between 1 0 − 5 1{0}^{-5} and 1 0 − 1 1{0}^{-1} ), size of the cylinders (Rc between 0 and 0.25), and location of the PP plate (Yp between 1 and 4.5) are all taken into account when calculating the effectiveness of the cooling system using finite element method. It is found that PP-I can effectively control the vortex size and enhance cooling performance, particularly for vertical plate. Nusselt number is enhanced in the absence of cylinders in the vertical channel by 92% as contrasted to 51% in the presence of cylinders. When cylinders are used for the vertical channel, the temperature drop of 1 3 ° C 1{3}^{^\circ }{\rm{C}} is computed. The flow field noticeably changes when the permeability of the P-I and PP-I is altered. The equivalent temperature increases for P-I and PP-I with setups at Da = 1 0 − 5 {\rm{Da}}=1{0}^{-5} and Da = 1 0 − 2 {\rm{Da}}=1{0}^{-2} are 7.7 ° C {\text{7.7}}^{^\circ }{\rm{C}} and 4.4 ° C {\text{4.4}}^{^\circ }{\rm{C}} , respectively. The performance of cooling for the vertical plate is influenced favorably by the higher values of the porous plate’s vertical placement. By moving the porous object, it is possible to reduce the temperature by 8 ° C {8}^{^\circ }{\rm{C}} . For panel surface temperature, a proper orthogonal decomposition (POD)-based reconstruction model with 12 POD modes is used. The POD-based model accurately captures the effects of utilizing P-I and PP-I on the panel temperature.

This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.

Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser–plasma interactions. Second, we review analytical results concerning the Stark–Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha π-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures (“L-dips”) in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser–plasma interactions. We also review the rich physics behind the L-dips phenomenon – because there was a confusion in the literature in this regard.

The energy bound-state solutions of the spinless Salpeter equation (SSE) have been obtained under a spin-dependent Cornell potential function via the Wentzel–Kramers–Brillouin approximation. The energy levels were applied to predict the mass spectra for the charmonium, bottomonium, and bottom-charmed mesons. The relativistic corrections for the angular momentum quantum number l > 0 l\gt 0 , total angular momentum quantum numbers j = l , j = l ± 1 j=l,\hspace{.3em}j=l\pm 1 , and the radial quantum numbers n = 1–4 improve the mass spectra. The results agree fairly with experimental data and theoretic results reported in existing works, where the authors utilized different forms of the inter-quark potentials and methods. The deviation of the obtained masses for the charmonium and bottomonium from the observed data yields a total percentage error of 3.32 and 1.11%, respectively. The results indicate that the accuracy of the masses is correlated with the magnitude of masses for the charm and bottom quarks. The SSE together with the phenomenological spin-dependent Cornell potential provides an adequate account of the mass spectroscopy for the heavy mesons and may be used to predict other spectroscopic parameters.

The coherent manipulation and control of bright and dark solitons through sodium atomic medium have been investigated in this manuscript. Dark soliton is reported for reflection and bright soliton is reported for transmission pulses with variation in position and driving field parameters through sodium atomic medium. Further the transmission pulse is periodic dark and bright solitonic behaviors and reflection pulse is periodic bright solitonic behavior with variation in the incident angle and Rabi frequency of the control field. Elliptical dark and bright solitons as well as breather types solitons are also investigated for reflection and transmission pulses. The dark soliton in reflection is due to slow light propagation and bright soliton is obtained due to fast light propagation of transmission through the medium. The modified results of the dark and bright solitons are useful for telecommunication and ultra-fast signal routing system.

The magnitude of the rate of chemical reactions also depends on the position in the gravitational field where a chemical reaction is being carried out. The rate of chemical reaction conducted at a stronger gravitational field, i.e. , near the surface of some heavy planet, is slower than the rate of reaction conducted at a weaker gravitational field, i.e. , away from the surface of a heavy plant, provided temperature and pressure are kept constant at two positions in the gravitational field. The effect of gravity on the rates of reactions has been shown by formulating the rate constants from almost all types of reaction rate theories, i.e. , transition state theory, collision theory, Rice–Ramsperger–Kassel–Marcus, and Marcus’s theory, in the language of the general theory of relativity. The gravitational transformation of the Boltzmann constant and the energy quantum levels of molecules have been developed quantum mechanically. A gravitational transformation of thermodynamic state functions has been formulated that successfully explains the quasi-equilibrium existing between reactants and the activated complex at different gravitational fields. Gravitational mass dilation has been developed, which explains that at weaker gravitational fields, the transition states possess more kinetic energy to sweep translation on the reaction coordinate, resulting in the faster conversion of reactants into products. The gravitational transformation of the half-life equation shows gravitational time dilation for the half-life period of chemical reactions and thus renders the general theory of relativity and the present theory in accord with each other.

A question in physics is whether Special Relativity (SR) is the only theory that explains relativistic behavior. SR measures time dilation by a relative velocity between two frames. Laboratory experiments with a single moving body fit this concept. However, GPS satellites and their ground clocks measure time dilation by a velocity relative to a common non-rotating Earth inertial frame. To better understand the conceptual difference, an experimental survey was undertaken. The survey analysis showed that laboratory experiments also fit into the non-rotating Earth frame concept. The laboratory experiments only need to add the Earth rotational velocity to both the laboratory frame and the moving frame. The analysis also revealed that the relative velocity calculation was astonishingly close to the common Earth frame calculation. The common Earth frame then becomes the explanation for all experimental types. And it signifies that a gravity field – moving body interaction causes relativistic effects. The experimental record also contained enough data to draft an empirical kinetic theory different than SR. The “no preferred reference frame” of SR is replaced by “there is a preferred reference frame.” And the preferred frame is the nearby Earth gravity field.

The graphitic carbon nitride–poly(1H pyrrole) (g-C 3 N 4 -P1HP) composite, formed by seeding onto P1HP, is created through a two-step polymerization process of 1H-pyrrole. In the second stage, g-C 3 N 4 is incorporated, allowing it to blend within the P1HP matrix. The resulting nanocomposite, composed of nanoscale semi-spherical particles, exhibits remarkable efficiency in capturing photons and facilitating energy transfer between particles, making it an ideal candidate for hydrogen (H₂) gas production. This is particularly effective when using common electrolytes, such as natural seawater from the Red Sea or synthetic seawater produced in the lab. To assess its performance, a three-electrode cell was designed, and the H₂ gas output was measured against current density ( J ph ). The photocathode achieved a current density of −0.65 mA/cm² in natural seawater and −0.62 mA/cm² in synthetic seawater. The hydrogen generation rates were 16.8 µmol/h in natural seawater and 16.0 µmol/h in synthetic seawater per 10 cm², with the natural electrolyte yielding better results. The photocathode’s high sensitivity, efficiency, and environmentally friendly properties – both in materials and electrolytes – underscore the potential of using Red Sea water as a sustainable resource for hydrogen production. These encouraging findings open the door to industrial-scale applications, positioning seawater as a practical solution for renewable hydrogen generation.