Volume 9, Issue 1

Solutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian decomposition method and the differential transformation method, for three practical engineering boundary value problems: (1) the deflection of a cantilevered beam with a concentrated load, (2) an adiabatic tubular chemical reactor which processes an irreversible exothermal reaction, and (3) the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylinder conduit. The accuracy and convergence of each method is investigated using the error remainder function. The method of variation of parameters is significantly more efficient than both the semi-analytical methods and traditional numerical methods while maintaining comparable accuracy. Unlike the semi-analytical methods, the efficiency of variation of parameters is independent of the nonlinearity. Variation of parameters is shown to be an attractive alternative to semi-analytical methods and traditional numerical methods for solving boundary value problems encountered in engineering applications in which solution efficiency is important.

The article proposes a nonlinear H-infinity control method for switched reluctance machines. The dynamic model of the switched reluctance machine undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the reluctance machine’s state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the reluctance machine’s dynamics, Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the reluctance machine an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each time-step of the control method. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. The stability of the control loop is proven through Lyapunov analysis.

In the last few years, the different teams have dramatically improved the directly injected, electrically assisted turbocharged, internal combustion engine of FIA F1 hybrid electric cars. With limited fuel flow rate, but unlimited boost, the engine is now delivering peak power at fuel conversion efficiencies about 45% running lean stratified with the help of some sort of jet ignition. The paper analyses the energy flow of a FIA F1 hybrid electric car covering one lap of the Monte Carlo race track of length 3.370 km. The amount of energy recovered is minimal, at the most 2 of the 9.77 MJ of braking energy, or 20.6%. The fuel consumption per lap, 1.16 kg of fuel, or 50.34 MJ of fuel energy, needed to deliver the 16.28-18.28 MJ of propulsive energy, at an outstanding average efficiency of 32 to 36%, may still be dramatically reduced. New rules are thus proposed to promote the development of technical features that could be beneficial to passenger car applications, from advanced turbo-compounding, to enhanced thermal and mechanical energy recovery, and better hybridization.

In this work, a risk index to monitor an anaerobic digestion process is established. The index is derived from the dynamical analysis of the system and it is composed by two conditions ensuring an optimum operating conditions inside bioreactor. The analysis is performed using bifurcation theory in order to study the effects of dilution rate, temperature and pH parameters at behavior system. For these purpose an extended version of the mathematical model proposed by Bernard [1] involving the dependence of growth kinetics on temperature and pH is used. The analysis shows both microbial growth and the performance of the bioprocess, when is highly affected by these parameters, indeed the washout condition occurs by combining a fold bifurcation and a transcritical bifurcation. From bifurcation diagrams both safety and optimal operation regions of the bioreactor are defined. Consequently, based on two conditions of stability a risk index to monitor the bioprocess on-line is proposed. The index is evaluated via numerical simulations allowing to detect system destabilization. The results obtained in this work may provide a useful methodology to monitor an anaerobic process and to guarantee the optimal performance of the bioreactor given that the model is sufficiently accurate.

MHD peristaltic transport of copper-water nanofluid in an artery with mild stenosis for different shapes of nanoparticles is studied in this paper. The exact solution is obtained for velocity, temperature and pressure gradient. The influence of all the parameters on velocity, temperature and pressure gradient is observed. The effect of stenosis plays a vital role in this paper, as it finds its application in the field of medicine. It is observed that the nanofluid flows rapidly in the presence of stenosis, which helps in destroying of the stencils soon. The shape of the nanoparticle is another important point to be concentrated due to based on the shape of the nanoparticle the fluid flow depends. The shape of the nanoparticle should be considered as bricks to increase the velocity, temperature and the pressure gradient. But a reversed behavior is observed if the shape of the nanoparticle is chosen as platelets. Streamlines are also concentrated and it is observed that there are more number of boluses if the shape of the nanoparticle is chosen as bricks. The effect of volume of the solid nanoparticle and stenosis warrants further study of the flow of nanofluids in tube and channel.

We apply homotopy perturbation transformation method (combination of homotopy perturbation method and Laplace transformation) and homotopy perturbation Elzaki transformation method on nonlinear fractional partial differential equation (fpde) to obtain a series solution of the equation. In this case, the fractional derivative is described in Caputo sense. To avow the adequacy and authenticity of the technique, we have applied both the techniques to Fractional Fisher’s equation, time-fractional Fornberg-Whitham equation and time fractional Inviscid Burgers’ equation. Finally, we compare the results obtained from homotopy perturbation transformation technique with homotopy perturbation Elzaki transformation.

In this research work, we have shown that it is possible to use fuzzy transform method (FTM) for approximate solution of strongly fractional nonlinear problems. In numerical methods, in order to approximate a function on a particular interval, only a restricted number of points are employed. However, what makes the F -transform preferable to other methods is that it makes use of all points in this interval. The comparison of the time used in minutes is given for two derivatives Caputo derivative and Caputo-Fabrizio derivative.

In the present study the flow of power-law fluid, due to a stretching sheet embedded in a saturated porous medium, is considered. This study also accounts for the variable thermal conductivity in the process of heat transfer along with dissipation due to Joule heating. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert nonlinear partial differential equations to non linear ordinary equations. The numerical method, Runge-Kutta method with shooting technique has been applied to solve the resulting equations. The power-law fluid exhibits a dual property in the presence of magnetic field. The limiting cases n → 0 and n → ∞ have been discussed. For large n the solution becomes unstable which leads to flow instability(Shown in the graph).

The present work is concerned with an analytical study of entropy generation in viscous, incompressible fluid in an inclined channel with porous walls. The solution of the governing equations were obtained in closed form. The expression for the irreversibility ratio was also obtained and the results were presented graphically and extensively discussed for different values of the dimensionless parameters. The result indicates that wall inclination enhance entropy generation.

In this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.

Equipment performance improvement in a wide range of working conditions is one of the major goals of aerodynamics. This goal can be achieved by the deformation of the object being examined or by using flow control techniques in active or inactive modes. In different researches, how to change the development ratio on the semi-confined space with input jet system is surveyed. In this study, two-dimensional simulation of the flow has been investigated in three-jet laminar flow in a semi-confined space. To determine the effective and optimal mixing in a laminar flow, critical Reynolds numbers were determined to distinguish when the flow in the channel from a steady-state symmetric flowformed downstream recirculation and ultimately transient flow. To better understand the flow characteristics, the simulations were changed at a fixed jet spacing (input jets distance to height of space ratio). Also, in this paper, for comparison, four jets were considered. Based on the results, it was observed that in all cases, mixing occurred in the space between three jets. Placing the jet along the walls of the semi-confined space allows the best combination, and increase in the distance between the first and third jets and reduction of the particle coefficient caused to reach the critical Reynolds number faster and, as a result, mixing in a laminar flow with geometric changes of the semi-confined space.

A numerical investigation into the effect of temperature-dependent fluid properties on the thin film flow along an inclined heated plate is presented. The equations governing the coupled flow and heat transfer are formulated based on couple stress non-Newtonian model. Solutions of the coupled nonlinear differential equations are tackled numerically by using the combination of shooting method and the Fehlberg-Runge-Kutta method. Findings are presented graphically and discussed precisely.

Train safety and operational efficiency can be improved by investigating the dynamics of the train under varying conditions. Longitudinal train dynamics (LTD) simulations performed for such purposes, usually by utilising a nonlinear time-domain model. This paper covers two modes of LTD results corresponding to the time domain and frequency domain analysis. Time-domain solutions are essential to evaluate the full response used for parameter optimisation and controller design studies while frequency domain solutions can provide significant but straightforward clues regarding system dynamics. An advanced draft gear model, which works under a four-stage process is constructed considering all structural components, geometric relationships, friction modelling and dynamic characteristics such as hysteresis, stiffening, state transition, locked unloading, softening. Then, this model is parametrically reduced and implemented into an LTD simulation. The simulation in the time domain is conducted assuming a locomotive connected with a nine wagon via “ode3” fixed-step solver. The transfer function among the first wagon acceleration (output) and the locomotive force (input) estimated through system identification methodology. Then, the identification results interpreted by investigating step-response characteristic and best response giving parameter set is selected. Next, the modal and spectral analysis performed to reveal the behaviour of the in-train forces and the effects of vibration. This paper discusses a reliable methodology for the longitudinal dynamic analysis of the multi-bodied train in time and frequency domain and clarifies in-train vibration behaviour under the existence of sophisticated draft gear.

This article investigates the time-dependent MHD heat transfer flow of Jeffrey fluid from a stretching sheet, the topic significance to non-Newtonian viscoelastic material processing. Using similarity transformations, the governing coupled non-linear PDE’s are remodel into ODE’s with suitable free stream and wall boundary conditions. The developed non-dimensional non-linear problem is revealed to be analysed by several key thermosphysical and rheological parameters, namely, Jeffrey fluid parameter ( λ ), Deborah number ( β ), Prandtl number (Pr), buoyancy parameter ( ξ ), magnetic parameter ( M ) and unsteadiness parameter ( A ). The semi-exact differential transform technique is applied to elucidate the coupled nonlinear governing equation of non-Newtonian Jeffrey fluid problem. Also, the solution is validated with numerical results attained via the MATLAB bvp4c function. Excellent accurateness is attained through the DTM approach. Further validation with available consequences from the existing literature is incorporated. The results indicate that fluid velocity and temperature are boosted with increasing Deborah number and stretching parameter however it shows a decreasing trend with Jeffrey fluid parameter and convection parameter. It also shows when augmenting the magnetic parameter which reduces the flow and increases the thickness of the boundary layer.

The unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

The initial-boundary value problem for a pseudo-parabolic equation exhibiting initial layer is considered. For solving this problem numerically independence of the perturbation parameter, we propose a difference scheme which consists of the implicit-Euler method for the time derivative and a central difference method for the spatial derivative on uniform mesh. The time domain is discretized with a nonuniform grid generated by equidistributing a positive monitor function. The performance of the numerical scheme is tested which confirms the expected behavior of the method. The existing method is compared with other methods available in the recent literature.

The relative and absolute sea-level patterns in the five LTT tide gauge stations of Oceania, Fremantle, and Sydney in Australia, Auckland, and Dunedin in New Zealand, and Honolulu in the Hawaii Islands, United States of America, are analyzed first based on tide gauge and GPS time series. The average relative rate of rise is +1.306 mm/yr., the average acceleration is +0.00490 mm/yr 2 , and the average absolute rate of rise is +0.125 mm/yr. This result is consistent with the result for Japan and the West Coast of the Americas. All the LTT tide gauges of the Pacific consistently show a small sea-level rise, with a significant contribution by subsidence, and negligible acceleration. This result is well-matched by the land increase, rather than shrinking, of the Pacific atolls’ islands recently highlighted by other researchers. Two case studies for locations where there are no LTT tide gauges are then provided. In Tuvalu, over the short time window 1977 to present, the relative rate of rise is +1.902 mm/yr., biased by low ESO water levels, and subsidence, but the absolute rate of rise is +0.157 mm/yr. In Adelaide, the relative rate of rise of the sea level is less than 2.3 mm/yr. with an overwhelming contribution by subsidence of 2.1 mm/yr. The thermosteric effect is thus less than 0.2 mm/yr. The sea-level acceleration is also small negative in Adelaide, −0.01936 mm/yr 2 .

The aim of this article is to derive new exact solutions of conformable time-fractional Cahn-Allen equation. We have achieved this aim by hyperbolic function and expa function methods with the aid of symbolic computation using Mathematica. This idea seems to be very easy to employ with reliable results. The time fractional Cahn-Allen equation is reduced to respective nonlinear ordinary differential equation of fractional order. Also, we have depicted graphically the constructed solutions.

Present research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

This study has been conducted to focus on natural convection flow of Casson fluid through an annular microchannel formed by two cylinders in the presence of magnetic field. The process of heat generation/absorption is taken into consideration. Combined effects of various parameters such as porous medium, velocity slip and temperature jump are considered. Solution of the present mathematical model is obtained numerically using fourth-fifth order Runge-Kutta-Fehlberg method. The flow velocity, thermal field, skin friction and Nusselt number are scrutinized with respect to the involved parameters of interest such as fluid wall interaction parameter, rarefaction parameter, Casson parameter and Darcy number with the aid of graphs. It is established that higher values of Casson parameter increases the skin friction coefficient. Further it is obtained that rate of heat transfer diminishes as fluid wall interaction parameter increases.

The present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al 2 O 3 ), and titanium dioxide (TiO 2 ) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu -water nanoparticles is more than that of Al 2 O 3 - water nanofluid. On the other hand, the axial velocity of the fluid in case of Al 2 O 3 - water nanofluid is more than that of TiO 2 nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using Mathematica ® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To illustrate the accuracy and efficiency of the proposed methods, the maximum error remainder is calculated. The results shown that the proposed methods are accurate, reliable, time saving and effective. In addition, the approximate solutions are compared with the fourth order Runge-Kutta method (RK4) achieving good agreements.

This paper presents, numerical study of stress field in functionally graded material (FGM) hollow cylinder by using finite element method (FEM). The FGM cylinder is subjected to internal pressure and uniform heat generation. Thermoelastic material properties of FGM cylinder are assumed to vary along radius of cylinder as an exponential function of radius. The governing differential equation is solved numerically by FEM for isotropic and anistropic hollow cylinder. Additionally, the effect of material gradient index ( β ) on normalized radial stresses, normalized circumferential stress and normalized axial stress are evaluated and shown graphically. The behaviour of stress versus normalized radius of cylinder is plotted for different values of Poisson’s ratio and temperature. The graphical results shown that stress field in FGM cylinder is influenced by some of above mentioned parameters.

Some difference equations are generally studied by investigating their long behaviours rather than their exact solutions. The proposed equations cannot be solved analytically. Hence, this article discusses the main qualitative behaviours of two rational difference equations. Some appropriate hypotheses are examined and given to show the local and global attractivity. Special cases from the considered equations are solved analytically. The periodicity is also proved in this work. We also illustrate the achieved results in some 2D figures.

The primary target of this paper is to obtain the analytic solutions for the incompressible unsteady flow of fractionalized MHD Jeffrey fluid over an accelerating porous plate with linear slip effect is assumed between fluid and the plate. The governing equations of Jeffrey fluid are developed by fractional calculus approach. The velocity distribution and its corresponding shear stress both are obtained in terms of generalized M -function by using Laplace transform technique and considering all initial and boundary conditions. We have also discussed that obtained results of fractionalized MHD Jeffrey fluid for different cases for instance, with and without slip effects, with and without MHD and porosity effects. The influence of the different parameters affected on the flow characteristic is deliberated with the help of graphs. Finally, the analysis among different fluid models exhibits by graphical illustrations.

For quantitatively identifying the chaotic patterns in traffic flow prediction, certain types of Duffing systems can be used. The accuracy and reliability of numerical results of the system’s solution have significant influence on the traffic flow prediction. The nonlinear dynamic behavior of Duffing system used for the traffic flow prediction is investigated in this research. The solutions of the system are developed and solved numerically by using the P-T method. The regular and irregular responses of the system considered are graphically illustrated with the newly developed P-R method. Based on the results of the research, the frequency and amplitude of the external excitations applied on the system significantly affecting the nonlinear dynamic behavior therefore the traffic flow prediction in transferring the results by Wigner-Ville transform. Additionally, a comparison between the P-T and Runge-Kutta method is conducted in regarding the accuracy and reliability of the methods.

In this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method. In the case of nonlinear partial differential equations, the quasilinearisation method is used to linearize the equation. The multi-domain technique is applied in both space and time intervals, which are both decomposed into overlapping subintervals. The spectral collocation method is then employed in the discretization of the iterative scheme to give a matrix system to be solved simultaneously across the overlapping subintervals. Several test examples are considered to demonstrate the general performance of the numerical technique in terms of efficiency and accuracy. The numerical solutions are matched against exact solutions to confirm the accuracy and convergence of the method. The error bound theorems and proofs have been considered to emphasize on the benefits of the method. The use of an overlapping grid gives a matrix system with less dense matrices that can be inverted in a computationally efficient manner. Thus, implementing the spectral collocation method on overlapping grids improves the computational time and accuracy. Furthermore, few grid points in each subinterval are required to achieve stable and accurate results. The approximate solutions are established to be in excellent agreement with the exact analytical solutions.

The pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q -homotopy analysis transform method ( q -HATM). The considered technique is graceful amalgamations of Laplace transform technique with q -homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q -HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

In this paper a novel technique i.e. accelerated homotopy perturbation Sumudu transformation method (AHPSTM), which is a hybrid of accelerated homotopy perturbation method and Sumudu transformation to obtain an approximate analytic solution of nonlinear partial differential equation (PDE) with proportional delay, is used. This approach is based on the new form of calculating He’s polynomial, which accelerates the convergence of the series solution. The series solutions obtained from the proposed method are found to converge rapidly to exact solution. In order to affirm the effectiveness and legitimacy of proposed method, the proposed technique is implemented on nonlinear partial differential equation (PDE) with proportional delay. The condition of convergence of series solution is analyzed. Moreover, statistical analysis has been performed to analyze the outcome acquired by AHPSTM and other semi-analytic techniques.

A two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

Marine hydrokinetic turbines of MW-level capacity for harvesting oceanic currents are here reviewed. The best design is 3-blades, open rotor, axial flow turbines, of similar design philosophy to wind turbines, which are anchored to the ocean floor. The best locations are those with the oceanic current resource of higher intensity and stability, non-excessive depth of the ocean floor, proximity to shore, and favorable topography. In these locations, marine hydrokinetic turbines may become competitive with other renewable energy alternatives. It is expected that such turbines will be installed and will start producing electricity, within the next decade, working with power coefficients, the ratio of electric power from the turbine to wind power, around 0.45, similarly to wind turbines. This will pave the road for further progress and significant uptake of technology so far of no impact on the global energy mix.

In this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

The research issue of which are the present relative and absolute rates of rise and accelerations for North America is here addressed. The data of the 20 long-term-trend (LTT) tide stations of the West Coast of North America with more than 80 years of recorded data are shown. The absolute rates of rise are computed by considering the absolute vertical velocity of Global Navigation Satellite System (GNSS) antennas near the tide gauges, and the relative rate of sea-level rise from the tide gauge signals. The 20 LTT stations along the West Coast of North America show an average relative rate of rise of -0.38 mm/yr., an average acceleration of +0.0012 mm/yr 2 , and an average absolute rate of rise of +0.73 mm/yr. This is the first paper publishing a comprehensive survey of the absolute sea-level rates of rise along the West Coast of North America using the reliable information of relative sea-level rates of rise from LTT tide gauges plus the absolute subsidence rates from different GNSS antennas close to the tide gauge installations.

Casson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x -direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z -direction.

This study theoretically investigates the effects of variable viscosity, thermal conductivity and wall conduction on a steady mixed convection flow of heat generating/absorbing fluid passes through a vertical channel. One of the channel plates moves with a constant velocity while the other is stationary. The governing flow equations are solved analytically using homotopy perturbation method (HPM). The effects of the thermophysical and hydrodynamics parameters are captured in graphs and tables. It has been observed that, both the velocity and temperature distributions decrease with increase in viscosity and boundary plate thickness near the heated plate while a reverse cases were observed near the cold plate. Increase in thermal conductivity ε decreases the fluid flow near the heated plate. When the boundary plate thickness is increased, the critical value of Gre to onset the reverse flow increases while increase in thermal conductivity reduces the critical value of Gre . It’s also noticed that the skin friction and rate of heat transfer at the heated plate decrease with increase in boundary plate thickness d .

In this work, we introduce a new construct to the cubic B-spline collocation method in the three and four-dimensions. The cubic B-splines method format is displayed in one, two, three, and four-dimensions format. These constructions are of utmost importance in solving differential equations in their various dimensions, which have applications in many fields of science. The efficiency and accuracy of the proposed methods are demonstrated by its application to a few test problems in two, three, and four dimensions. Also, comparing the exact solutions and with the results obtained by using other numerical methods available in the literature as much as possible.

The prediction of oscillators is usually employed in various industrial and technological problems; such as car shock absorbers, bungee jumping, earthquake-proof buildings, musical instruments, metronome and the process of hearing. This manuscript investigates the effects of newly presented fractional operators on free and forced linear oscillators. The second order nonlinear classical governing differential equation of Duffing oscillator is reduced into second order linear classical governing differential equation of free and forced linear oscillators by invoking non-integer order differential operators namely Atangana-Baleanu and Caputo-Fabrizio. The fractionalized differential equation is solved by invoking Laplace transform method for finding the optimal solutions of displacement based on infinite series approach. The solutions of displacement are obtained via Atangana-Baleanu and Caputo-Fabrizio differential operators separately then expressed in terms of elementary and gamma functions. Finally the parametric analysis is depicted graphically on the basis of comparison of modern fractional operators subject to the emerging rheological parameters.

This work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

In this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs.