Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application

Nomenclature

a

stretching rate

B 0

uniform magnetic field

C f

drag force facto

ϵ

hardness

E g Opt

energy bandgap

E H

HOMO

E L

LUMO

Er

local inertia

F

coefficient of variable inertia

F ′ , G

nondimensional speeds

K 1

permeability

κ f , κ p 1 , κ p 2

thermal conductivities

m

shape agent

Nu

local Nusselt number

p

pressure

Pr

Prandtl amounts

p y

fluid yield stress

p 1 , p 2

solid nanoparticles

q w

surface heat fluxing

S

suction/injection velocity

T

temperature of fluid

T 0

temperature at upwind wall

T h

temperature at down wall

u , v , w

velocity elements

U w

stretched surface speed

ν f

kinematic viscosity

ϑ

softness

λ

porosity

Y

similarity variable

σ f , σ p 1 , σ p 2

electrical conductivities

ρ f , ρ p 1 , ρ p 2

densities

μ B

plastic dynamic viscosity

Ω

angular velocity

μ f

dynamic viscosity

χ

electro-negativity

ς

chemical potentiality

ω

electrophilicity-index

1 Introduction

To bridge the gap between fossil fuels and clean energy systems, renewable energy technologies are now at the forefront of research and development efforts. Due to the fact that solar energy systems are associated with an unlimited energy source, a well-documented theory, simplicity, an environmentally friendly structure, and a noticeably greater energy and exergy efficiency range compared to other renewables, there is no doubt that solar energy systems play the preeminent position among the alternatives. But traditional working fluids with subpar thermophysical qualities are still used in solar energy systems. This is a significant drawback. To put it in another way, more enhancements can still be made to the aforementioned systems by the use of one-of-a-kind nanoparticles (NPs) that possess better thermal, electrical, optical, and mechanical capabilities. Sun thermal collectors that use NPs suspended in a liquid media to scatter and absorb sun energy are referred to as nanofluid-based direct solar collectors.

Nanofluids are solid–liquid composites made up of nanometer-sized solid molecules, fibers, rods, or tubes floating in various basic liquids, providing interesting technical possibilities for improving heat transmission despite its numerous benefits while causing peculiar thermal variations. The reproduction of nanofluids is mentioned in the evolutionary theory of adding solid particles to heat transfer fluids to increase thermal flexibility. This new idea was introduced by Maxwell in 1873. Because of the size impact and Brownian dispersion of NPs in fluids, nanofluids have more stability than normal liquids augmented with solid particles of micrometer or millimeter size. Nanofluids may operate easily in the microchannel heat sink without clogging with such ultra-fine nanomaterials, and the size of the heat transmission system can be lowered to employ nanofluids for effective heat transfer efficiency [1]. Nanofluids offer several advantages owing to their heat transfer stiffness and dispersion resilience. A significant quantity of space increases heat transmission between liquids and particulates [2]. The single-step technique is a practice that requires the manufacture of NPs as well as the fabrication of nanofluids, in which the nanomaterials are generated immediately using the physical vapor deposition (PVD) technique or the liquid chemical approach. As a result of avoiding the drying, storage, distribution, and dispersion of nanomolecules, the fusing of nanomolecules is minimized, and the liquid’s permanence is enhanced. The disadvantage of this strategy is that only the low-pressure vapor fluid is compatible with the procedure. This decreases the technique’s usage [3]. The method of electrospinning into basic liquids is a two-step procedure for producing nanoliquids. The nanomaterials, nanowires, or nanotubes utilized in this procedure are first created as a dry powder by evaporation gas, chemical evaporation, mechanical metal alloys, or other appropriate processes, and then dissolved in a liquid in the second stage. This method divides the preparation of nanofluids from the preparation of NPs. As a result, nanoscale agglomerates may happen at both phases, notably during the setup, storage, and transportation of the nanoscale. Aggregation not only causes micro-channels to break down and close but it also reduces heat conductance. To minimize particle bonding and increase the activities of different liquids, simple approaches such as supersonic combining or the inclusion of surfactants in liquids are frequently utilized. Because numerous businesses have indeed advanced nanopowder synthesis processes for industrial production levels, there may be cost benefits in adopting two strategies that rely on the usage of such powders. However, one critical issue that must be addressed is the robustness of the prepared suspension [4,5]. Peng et al. [4] investigated the parameters that determine nanofluid stability. The experimental findings revealed that the most critical elements influencing suspended stabilization were NPs concentricity, dispersion, liquid base viscidness, and pH value. The diversity, scope, NPs density, and ultrasonic vibration of nanofluids all contribute to their stability. Hwang et al. [6] used a UV-vis spectrophotometer to investigate the stability of nanoliquid. He felt that the features of fixed particulates and basic liquids, such as morphological particles, compositions of molecules, and basic liquids, had a significant impact on the stability of nanofluids. Furthermore, the inclusion of surfactant can increase the stabilization of the solution. Wang [7] also believes that the nanomolecules’ identical diameter and the varied viscidness of the nanoliquids are the most critical elements influencing the stability of the NPs suspension. The authors also found that the right pH value of nanofluids, as well as a high percentage of surfactants, had a substantial influence on nanofluid stabilization.

Hybrid NPs are described as NPs composed of two or more diverse nano-meter dimensions. The liquid arranged by compound NPs is identified as hybrid nanofluid (HNF). A recent review of the nanofluid layer, the hybrid nanofluid, which combines complex particles with a complex composite of many NPs, aims to correct the degradation of mono nanofluid compounds by synthesizing any damage to mono nanofluid [8]. Hybrid nanoliquids work very well in terms of cooling when temperatures are high and cover a wide range of thermal materials. HNFs are usually prepared by dissolving two different types of NPs in basic liquids and are emerging as new nanotechnology [9]. HNF gains a higher rate of heat transfer compared to pure liquid as evidenced by experiments and numbers by many scientists. Choi [10]. were the earliest to apply a nanofluid that improved heat transmission rate compared to normal liquid. In 1995, she revealed her results at the Argonne National Laboratory. At the time, nanofluid was thought to be the next generation of heat transmission fluid because it offered exhilarating prospects to increase thermal efficiency above standard liquid [11]. This study has opened a new method for engineering systems due to the beneficial effects of manipulating nanofluids. Numerous tests have been performed and two categories of molecules have been suspended in basic fluids, namely “Hybrid nanofluid”. In the examination of Sidik et al. [11] HNF increases the heat transfer rate compared to nanofluid and light liquid. A mixture of multiwall sphere-shaped silica nanotubes mixture nanostructures and a thermal performance study of the corresponding nanofluid was probed by Choi and Eastman [12]. HNFs are very effective in terms of cooling when temperatures are high and include many thermal systems. HNFs are usually prepared by dissolving two different types of NPs in basic liquid and are emerging as new nanotechnology. Different types of synthetic nanofluids were prepared and studied by previous researchers under the requirements essential for their studies. Based on literature reviews, the HNF exhibits greater thermal transfer and rheological properties compared to the base fluid and mono nanofluid [13].

Non-Newtonian nanofluids are complex due to the indirect relationship between stress and stress rate, and this is because many phenomena in the real world are non-linear and are often described in non-linear expressions. A line problem is simple to answer but finding solutions to indirect difficulties is more challenging. Despite the availability of increasingly efficient processors, finding a clear exact solution to a given indirect issue is sometimes more difficult than obtaining a cost-effective solution [14]. However, when the findings of numerical approaches are sorted otherwise, they produce unstable spots; acquiring a thorough knowledge of the indirect issue is also challenging. If an indirect problem includes unity or has several solutions, the numbers get more complicated. While computational and mathematical approaches for handling indirect issues have limitations, they do offer benefits. As a result, we cannot dismiss any of these techniques, yet it is typically enjoyable to address an indirect issue through research [15]. Casson liquid is categorized as a non-Newtonian liquid and results in its rheologic properties related to shearing stress–strain relationships. It acts as elasticity in the lower shear strain and in addition to the critical amount of stress it behaves like a Newtonian liquid. Mustafa et al. [16] used a solution for homotopy analysis to investigate the flowing of this type of liquid boundary near the vertical position and presented the results of a limited case where the Casson factor manages to be infinite. Wang et al. [17] studied the development and formation of a hot boundary layer in Casson liquid motion over a solid surface in which both the surrounding liquid and the flat plate were maintained simultaneously and the heating of the flat plate abruptly surged in that surrounding liquid. They discovered parabolic partial variations that were resolved using the homotopy analysis approach. Makanda et al. [18] examined the 2-dimensional flowing and distribution of a specific type of chemical in the Casson fluid from an unstable expandable area where there is a magnetic field. It has often been observed that increasing magnetic and input parameters reduces velocity profiles, heat transmission coefficient, and concentricity outlines while drag tension increases. Hayat et al. [19] presented the Soret and Dufour effects on the two-dimensional flow of Casson fluid created by an expandable electric field. They used a homotopy analysis method to solve an incorrect system of different standardized calculations. Mukhopadhyay [20] investigated the consequences of thermal radiative on Casson liquid flowing and heat transference to a non-volatile stretchy region under absorbance/pulse and found that the Prandtl quantity may be employed to boost the cooling rate in Casson liquid flowing and temperature. An increment in the radiative parameter reinforces the profile, while the Casson variable decreases the boundary density and boosts the temperature boundary layer thickening. Rajan et al. [21] investigated the thermal characteristics and the flowing of Casson fluid via a stretchable surface in the existence of thermal radiative fluxing, magnetized force, viscous dissipative, heat generating, and chemical reactions influences. They discovered that the swelling heat generating factor decreased the temperature outlines in the boundary layer. Casson nanofluid unstable flowing has received little attention so far.

Magnetohydrodynamics (MHD) describes the extreme behavior of electromagnetic liquids in a magnetic field. MHD estimates that the electric field disappears into the moving water frame, without the potential effects of resistance [22]. MHD is about the interaction between moving fluids and the magnetism force. Ionization of the gas occurs at a rate that changes with increasing temperature due to the effective magnetic force that is created by the electrical force of the flow of this gas around a metal rod. Many fields in industry, engineering, and technology may benefit from models based on nanofluids and their behavior, such as those using heating or cooling systems. There has been a lot of research on MHD convection flowing of nanoliquids during the last decade. Two types of models have been used for the nanofluid flow, one-phase and two-phase approaches. In the two-phase approach, the basic fluid is considered a continuous phase, and the fixed particles are considered a continuous/clear phase, and the old Euler and Euler-Lagrange procedures are employed to mimic the flow [24]. Joule heating is a physical impact when the transfer of electrical energy to an electric electrode produces thermal energy. This thermal energy is demonstrated by the increase in the temperature of the conductor, hence the term “heat.” Joule heating is the process by which electrical energy is converted into thermal energy, in accordance with the principle of energy conservation [25]. Over the past few years, synthetic nanofluids have emerged as extensions of nanofluids and are believed to enhance their thermophysical and rheological properties and heat transfer properties. HNF was developed by combining basic liquids with a mixture of a composite type of distinctly formed NPs [26].

A source of heating system where heat is lost to the heat sink for example, in a built environment, a radiator may be considered a source of heat, while the surrounding space, which heats up through the process of radiation and convection, may be considered a hot spot [27]. Some items may serve as unintentional heat sources, which may not be desirable as they may cause excessive heat, such as people, computers, ovens, and other appliances. These heat sources are sometimes called heat loads. Heat sinks may include air conditioning systems, refrigeration equipment, heat weight, etc. A heat sink, in the context of thermodynamics, refers to a heat reservoir that has the ability to absorb a limitless quantity of heat while experiencing little changes in temperature. To facilitate the transmission of heat by convection, radiation, and conduction, heat sinks for electronics equipment need to maintain a temperature that is higher than the ambient environment. Due to the inherent inefficiency of power supply in electronics, excess heat is generated, which may have a negative impact on the device’s performance. Consequently, the construction incorporates a heat sinking to dissipate heat [28]. The temperature change will usually be accompanied by an increase in the pressure of the hole. If the soil is compacted enough these hole pressures will disappear. This study develops an analytical solution to the basic problem of the point heat source buried deep in the ground [29].

The applications that are most common for molybdenum disulfide NPs are in the realm of lubricants and greases. Examples of technology that are difficult to maintain include space vehicles and satellites, as well as some military fields. When utilized molybdenum disulfide NPs as an item in these composites. Mechanical exfoliation may be seen in things like photodetectors, optoelectronic devices, and sensors, among other things. In the case of liquid exfoliation, some examples include quantum dots, nanoplatelets, and energy storage devices. MoS₂ does not need surface treatments to avoid strong interactions with biomolecules, which opens a greater voltage range. This is one of the benefits of using this material. In this way, MoS₂ is used in biomedical technological endeavors such as single-molecule sequencing of DNA. Graphene oxide (GO), a graphene product that has been oxygenated is now being used in the fields of biotechnology and medical procedures for the treatment of cancer, the transport of drugs, and cellular visual storytelling. Utilizing decreased GO may be beneficial for a variety of applications, including those involving technological devices, storage of energy, (bio)sensors, applications in healthcare, tissues, catalysts, supercapacitors, and procedures for purifying water.

The purpose of this research is to integrate theoretical and experimental evaluations of the flow and thermal transmission analyses of Casson nanofluids (i.e., sodium alginate and molybdenum disulfide [Na-Alg/MoS₂]^m and sodium alginate and molybdenum disulfide and graphene oxide [Na-Alg/MoS₂ + GO]^h) within solar aircraft wings as two parallel sheets in a parabolic trough solar collector (PTSC). Different factors, such as heat production, flow rate, and thermal radiation, were included in an analysis of wings’ heat transfer ability. The kinetic and energy control formulae have been examined using the Keller-box method (KBM), a well-established numerical technique. We quickly examine and display in charts and tables how different variables affect the velocity, shear stress, and temperature fields, as well as the surface frictional factor and Nusselt number. Notably, [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h with a thickness of 150 ± 5 nm are fabricated using the PVD technology. The LUMO model, HOMO, and FTIR were used to analyze thin films that were created using DMOl³/TDDFT-DFT for both the [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h combinations. A schematic of the investigated flow model is shown in Figure 1.

Figure 1

Schematic of flow model.

2 Experimental work

2.2 Synthesis of [MoS₂]^NPs using sol–gel method

MoS₂ aerogel NPs produced using the polymerized sol–gel process are presented in Figure 2 as a flow chart [30].

Figure 2

Flow chart of the preparation process of [MoS2]^NPs using the sol–gel method.

2.4 Fabrication of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h thin films

[Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h powder at 25°C were mixed in a solution of C₂H₅OH/99 %. Various weights (20, 30, 40, and 50 mg) of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h were dissolved in 5 mL of C₂H₅OH solution. Thin films of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h (Figure 3) were deposited on quartz substrate utilizing the PVD method using a UNIVEX 250 Leybold (Cologne, Germany). Multiple instruments for measuring thin-film thickness ≅ 150 ± 5 nm here in UNIVEX units are available. The decision is dependent on appropriate evaluations and automation. The usage of crystal systems that oscillate is the norm. This may have one or more sensor heads, and it is designed for use in ultra-high-vacuum environments [32].

Figure 3

Fabrication process of thin films of nanofluids together with a technique for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h.

3 Mathematical modeling

A 3-dimensional, time-independent, MHD, and revolving flow of ([Na-Alg/MoS₂ + GO]^h) hybrid nanomaterial lying among two plates with angular velocity Ω [ 0 , Ω , 0 ] in the effect of heat transference has been examined in the present analysis. U w = ax ( a > 0 ) represents the stretched velocity regarding the lower plate while the upper surface is permeable. V = [ u , v , w ] is the flow field velocity. There is a constant magnetic field B 0 in the direction of y -axis. At low magnetism Reynolds quantity assumption, induced magnetism force is ignored. The physical flow model as well as the related coordinate system is specified in Figure 4. The constitutive model specifying Casson fluid is as follows [18]:

where μ B is the dynamical viscidness of liquid, p y is the yield stress, e ij is the deformation rate component, and π = e ij e ij .

Figure 4

Geometry of the problem.

Following is a component form of governing PDEs [18,37]:

where α hbnf = κ hbnf ( ρ C p ) hbnf is the thermal diffusion of HNF while p * * = p − Ω 2 x 2 2 is the varied pressure.

For [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂+GO]^h, the expressions are given in Tables 2 and 3. Thermal gradient is formulated on HNF. Temperature of the upper wall is T 0 while that of the lower wall is T h with T 0 < T h . Thermo-physical features of MoS₂, Na-Alg, as well as GO, are given in Table 4.

The endpoint constraints at the upstair and downstair walls are as [37] follows:

Similarity transformations are [18] as follows:

The resulting dimensionless system of ODEs is provided by

having subsequent nondimensional endpoint constraints as follows:

Linkage between dimensionless parameters and non-dimensional equations are as follows:

The dimensional form of local Nusselt number N u x as well as the skin-friction coefficient C f is described below [32,38].

where τ w = μ hbnf 1 + 1 β u y is the shearing stress and q w = − k hbnf T y is the wall heat fluxing. Nondimensional form of equation (14) via similarity alterations of equation (8) is observed as follows:

where R e x = U x ν f represents the local Reynolds number.

4 Numerical implementations

For many values of factors, the Keller-box method scheme [39,40] using the algebraic program MATLAB is employed to resolve the non-linear system of Eqs. (9)–(11) and concerns the endpoint constraint (12). The KBM chart is represented by a flowing map (Figure 5).

Figure 5

Flowing map explaining KBM.

5 Code validity

To determine the precision of providing KBM solution, the comparison is made between some of our findings and those of Hussain et al. [41] for − θ ′ ( 0 ) in the condition of varied values of sucking parameter S with other factors held fixed. Obtained outcomes are extremely accurate as well as authentic, demonstrating that the present numerical technique is quite trustworthy because of numerical calculation (Table 5).

6 Outcomes and review

The fluidity and thermal transferring ability of an interesting concoction of molybdenum disulfide with sodium alginate ([Na-Alg/MoS₂]^m along with HNF combined with GO as [Na-Alg/MoS₂ + GO]^h have been investigated during its passage between parallel plates under magnetic effect and apart at height ( h ), which takes angular rotation in the vertical direction. Surprisingly, the upper plate has been thought of as permeable, whereas the bottom plate extends from the center on both sides. The goal of this investigation was achieved with the use of velocity charts in x and y directional velocities labeled F' and G , respectively. The thermal status of the system has also been studied using thermal dispersal maps. Skin resistance parameter ( C f ) and Nusselt number ( Nu ) were also computed and shown in tables as parameters of interest. β = 0.1 , Er = 0.1 , γ = 0.2 , δ = 0.1 , N r = 0.1 , ϕ a = ϕ b = 0.05 , B 1 = 5 , B 2 = 0.5 , B 3 = 0.5 , and S = 1 are the used values to get the numerical findings. Experiments constantly have been repeated to ensure that the results are consistent. In general, the findings do not differ by more than a modest percentage point (1 or 2%). In addition, the related several data have been checked regularly. We separated the data into two portions once it was gathered. The initial set of data has been used to build a mathematical model that connects the input and goal data. The second set of data was used to validate models, and we were able to get results that were close to the goal and accurate.

6.1 Raman spectra of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h

Figure 6(a) and (b) show Raman spectra and considered [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h thin films. Carboxylate groups are responsible for the inclination of the sodium alginate functional groups to build complex structures with [MoS₂]^NPs [42]. From Figure 6(a), the Raman spectra of [Na-Alg/MoS₂]^m film demonstrated the absorption band in 4,000–3,700 cm⁻¹ area because of the stretching vibration band of ν(OH) group. Two strong absorption bands that appear at the range of 3,000–2,600 cm⁻¹ can be attributed to stretching ν(–CH) [43]. Noted strips at 1,460 cm⁻¹ and 1,415 cm⁻¹ were assigned to two types of shrinking vibrations (asymmetric and symmetric) of ν(COO–), correspondingly, and are detailed to the ionic bonding. The cross-linkage of the [MoS²]^NPs with the sodium alginate emerges at the shoulder of 1,150 cm⁻¹ for the stretching of both ν(C–C) and ν(C–O) [44]. Stretch band ν(C–C) (1,070 cm⁻¹) shows a lower strength, indicating a greater O–H binding vibration or strongly binding [MoS₂]^NPs to sodium alginate guluronic acids which appeared at wave number 1,070 cm⁻¹ [45]. Furthermore, guluronic and mannuronic acids are linked to stretching vibration strips analyzed at 890 cm⁻¹ as well as 830 cm⁻¹. Ionic bundling of [MoS²]^NPs and sodium alginate chains has been inferred to be due to minor changes in the carboxyl groups [46]. The intermediate bands at 620 and 500 cm⁻¹ in the downfield area are featured to (–O–MoS₂–O–) that described the reaction of MoS₂ with Na-Alg. As shown in spectra Figure 6(b), the strong absorption bands appearing at the range of 2,000–1,600 cm⁻¹ wavenumber values for [Na-Alg/MoS₂ + GO]^h thin film can be attributed to the in-plane sp² domains of [GO]^NPs [47]. The 2D band at 1,777 and 1,678 cm⁻¹ is related to ν Sym and ν Unsym (COO–) in GO structure matrix, respectively. The band at 661 cm⁻¹ in the downfield area is attributed to the reaction of MoS₂ with Na-Alg and [GO]^NPs to form an ionic binding ((Na-Alg)–O–MoS₂–O–(GO)) [48].

Figure 6

Collective modeled and experimentation IR spectra of (a) [Na-Alg/MoS₂]^m and (b) [Na-Alg/MoS₂ + GO]^h nanofluids.

The simulated Raman spectra were estimated of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h isolated gaseous state. Minor variants among frequencies projected and calculated are seen in Figure 6(a) and (b). Since vibrational types of examined ligands are helpful in achieving minimal symmetry and torque, along with other modes about the plane, it is hard to point out because ring modes degrade, other than imitating. However, the obtained graph shows some clear motions [49]. Obtained experimental ( λ Exp . ) and computed ( λ Cal . ) data are demonstrated by the subsequent formula for [Na-Alg/MoS₂]^m nanocomposite: λ Cal . = 0.945 λ Exp . + 17.23 with correlation coefficient ( R 2 = 0.989 ). For [Na-Alg/MoS₂ + GO]^h: λ Cal . = 0.981 λ Exp . + 19.27 with correlated factors ( R 2 = 0.988 ).

6.2 Geometric study

Several data have been assessed and implemented of the positive and negative surface ratio effects in electron levels before modeling isolated molecules for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h nano-fluid. The results demonstrate that positive surface density is maintained until it reaches the nuclear components; however, the number of negative components decreases with Gaussian 09w/DFT [50]. While the proportion of positive areas is around 68% of the total at 0.002 au, at 0.01 au, the ratio is over 85%. Figures 7(a) and 8(a) indicate that the visual representations of the MEP iso area value of −15 kcal mol⁻¹ may be utilized in nanofluid pairs of fields. The 3 D min principles of ME P V max are −7.254 × 10⁻² and −1.460 × 10⁻¹kcal mol⁻¹ for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h required by MEP’s structure, correspondingly. Also, the calculated MEP V max and MEP V min should take special considerations as predicted based on the presence of alternate electron. The flourishing electron life of its unique pair depends on substituted energy provided by a nanofluid. MEP V min is a basic and straightforward technique to determine the pair power in the solitary pair area. Increasing electron density (ED) in a pair of oxygen atoms is the main feature of the negative MEP V min range. Pulling out an electron from the cluster helps minimize the unwanted life of MEP V min . MEP V min concentrated on electrical nanofluid impact estimates that rely on quantities of distinct types to be significantly practical and clearer than structures (OH). In the imagining data of [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h, respectively, the nanofluid matrix μ -donating strength is employed. [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h are exchanged for solely the quantity of MEP V min when nanofluid movement is not required [51]. Figures 7(b) and 8(b) shows ED for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h, correspondingly. The macrocyclic plane’s negative electrostatic potential [P] is symmetrically apparent in all computations [52] and the positive and negative portions vary according to a base group. The sources (DNP) are enlarged in DN to include irrelevant additional extensions with the base folder (4.4), SCF-lenience (0.0001), and maximum SCF-rooms (0.5–102), and multi-polar octupole, as shown in Figures 7(c) and 8(c).

Figure 7

(a) MEP, (b) ED, (c) [P], and (d) HOMO and LUMO computations of [Na-Alg/MoS₂]^m.

Figure 8

(a) MEP, (b) ED, (c) [P], and (d) HOMO and LUMO computations of [Na-Alg/MoS₂ + GO]^h.

In Figures 7(d) and 8(d), HOMO as well as LUMO are specifications in common reactive descriptors utilizing quantum estimations [53]. Molecular balance can be defined by energy differences among FMOs. This has a vital role in measuring electrical conductivity which is further helpful for understanding electrical transport. Negative E H and E L show the stability of the structural matrix. Observed FMOs provide estimations about electrophilic positions inside aromatic compounds. Increment in E H was obtained with the utilization of An enhancement in E H was achieved by using the Gutmannat variable approach on M-L sites via M-L augmentation while reducing the length of the strip [54]. The difference in the energy strip explains the relation of load transfer in a molecule. E g Opt was stated as chemically reactive as well as having kinetic stability. Softness and hardness are included in the stability and reactivity assessment. The greatest value of molecular orbital coefficients decides the location. The appearance of nucleophilic attack on H–O (2), –CH₂O (7), O–H (4), and –CH₂O (10) atoms is HOMO position. E g Opt are 1.641 and 0.158 eV which are shown in Figures 7(d) and 8(d) for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h, respectively. The E g Opt for [Na-Alg/MoS₂ + GO]^h is lesser than E g Opt for [Na-Alg/MoS₂]^m because of its soft-ability as well as being more polarizable. Because electrons can have an acceptor, soft particles are deemed responsive rather than hard particles. As the device uses an electrical external charge, it anticipates energy stability. The quentities of HOMO ( E H ), LUMO ( E L ), E g Opt , chemical potential ( ς ), electrophilicity-index ( ω ), softness ( ϑ ), electronegativity ( χ ), hardness ( ϵ ), ΔNmax, and ϱ are counted in Table 6.

Table 6

Geometry factors/computed DFT for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h

Compound	E H	E L	E H ‒ E L	χ	ς	ϵ	ϑ	ω	Δ N m ax	ϱ
[Na-Alg/MoS2]m	‒6.367	‒4.726	1.641	5.547	‒5.55	‒0.821	‒0.609	‒18.747	‒6.76	‒1.219
[Na-Alg/MoS2 + GO]h	‒4.853	‒4.695	0.158	4.774	‒4.77	‒0.079	‒6.329	‒144.25	‒60.43	‒12.66

6.3 Consequence of Casson constraint ( β )

Flow behaviour affected by Casson constraint ( β ) on any direction of “ x ” as well as “ y ” were described in terms of F ′ and G in Figure 9(a) and (b), respectively. β is a flow-influencing parameter, which can manipulate viscous conditions by exerting them. An increment in Casson resister ( β ) hinders fluidity of passing fluid which is seen in every direction. In horizontal conditions of flow, [Na-Alg/MoS₂]^m nanofluid moves slower than [Na-Alg/MoS₂ + GO]^h. However, in the flow of “ y ” -direction, NPs experience more added resistance of gravity inclusive of other significance, which leads [Na-Alg/MoS₂ + GO]^h to slow down more than [Na-Alg/MoS₂]^m. The presence of NPs fills the inter-molecular spaces of the fluid used, leading to this observed behavior. This means that the interfacial distances between the fluid molecules are filled with NPs that have been added, which makes us see that behavior occurring in the case of increasing the Casson constraint in the direction of the vertical axis, especially.

Figure 9

Impact of β on (a) F ′ ( Y ) and (b) G ( Y ) . Impact of δ on (c) θ ( Y ) and (d) θ ( Y ) .

6.5 Outcomes regarding local inertia ( Er ) and porosity ( γ ) constraints

Figure 10(a) and (b) represent the flow conditions for hiking values of the local inertia parameter ( Er ). In both displays, it can be noted that the flow gets slower for a certain range due to the force, then later it gets hiked. As a result of increasing the local inertia parameter, it physically slows the movement of molecules inside the nanofluid, and thus the fluid flow velocity decreases and its resistance increases. Porosity γ creates a notable impact on flow behaviors in any flowing situation. Figure 10(c) and (d) showcase such claims, that porosity can pull back the fluidity of both ([Na-Alg/MoS₂]^m) and ([Na-Alg/MoS₂ + GO]^h) in lateral and vertical directions. Flow velocity is not strongly dependent on porosity for porosities bigger than the critical porosity. For values below the critical porosity, velocity is strongly impacted by porosity, and a little reduction in porosity results in a large increase in velocity.

Figure 10

Impact of Er on (a) F ′ ( Y ) and (b) G ( η ) . Impact of γ on (c) F ′ ( Y ) and (d) G ( η ) .

6.6 Consequence of fractional volume of nano ( ϕ nf ) and hybrid ( ϕ hbnf ) nanofluids

Dominance of efficiency of mono and HNFs was influenced by the NPs proportion in the fluid levels. Fractional volume rate resists the flow speed which can be observed in Figure 11(a) and (b), respectively, in lateral and vertical flow directions. Figure 11(c) shows the thermal dispersion in interested surrounding for cumulative values of a fractional volume of both mono ϕ nf and hybrid ϕ hbnf . Because the NPs were designed for heat transmission, they must push and capture heat from the surface, reflecting an increase in the thermal state. Increasing the concentration of NPs inside the fluid reduces the movement resistance of the fluid flow as a result of reducing the interlayer distances between the molecules that are filled with NPs, and thus the stored thermal energy increases, which raises the temperature of the nanofluid.

Figure 11

Changes in (a) F ′ ( Y ) , (b) G ( Y ) , and (c) θ ( Y ) with ϕ and ϕ hbnf .

6.7 Outcomes about Reynolds number ( B 1 )

Variations in Reynolds number B 1 could directly affect the fluidity in the system and eventually, could influence the thermal constraints. Figure 12 clarifies the abovementioned assertions to be right. Interestingly, improvement in Reynolds number B 1 results in increasing the lateral velocity F ′ , while pulling down the vertical velocity G of [Na-Alg/MoS₂ + GO]^h and [Na-Alg/MoS₂]^m. This might be owing to the magnetic and gravitational parts of vertical fluidity being supported, as seen in Figure 12(a) and (b). Figure 12(c) represents the dwindling thermal dispersal for the Reynolds number B 1 , which swifts fluids due to the lack of time to grasp temperature from the sheet. The physical reason for this is that the Reynolds number is inversely proportional to the viscosity of the fluid, which creates the effects seen on the flow velocity and temperature of the nanofluid.

Figure 12

Changes in (a) F ′ ( Y ) , (b) G ( Y ) , and (c) θ ( Y ) with parameter B 1 .

7 Conclusion

Theoretical simulation and experimental inspection of the flow and heat transmission analysis of Casson nanofluids of a combination of molybdenum disulfide with sodium alginate in [Na-Alg/MoS₂ + GO]^h flows based on [Na-Alg/MoS₂]^m and GO were investigated inside solar aircraft wings as two parallel surfaces in a PTSC use. Mono [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h thin films have been formulated by using PVD method. DFT is calculated using the package DFT in Material Studio 7.0 software. The simulated analysis based on LUMO, HOMO as well as other active nanofluid variables. The main results are summarized as follows:

1. Regarding fluidity in the lateral “ x ” direction, as a standalone constraint, Reynolds number B 1 assists the flow while all other influencing constraints tend to suppress it.

2. Constraints of rotation B 2 and Hartman number B 3 tend to boost the upright fluidity in the “ y ” direction for both combinations of [Na-Alg/MoS₂ + GO]^h and [Na-Alg/MoS₂]^m. The rest of the constraints act against it.

3. Drag force is increased with the increase in the size of nanomolecules, especially in the downstairs wall than the upstairs.

4. Upper wall has a higher thermal transference rate than the lower wall. The Hartman number, other than the Reynolds number, had a role in improving the heat transference rate.

5. When GO is added, the hybrid combination [Na-Alg/MoS₂ + GO]^h is made, which shows an advance in major heat transfer compared to the mono mixture of [Na-Alg/MoS₂]^m.

6. The ratio percentage between energy bandgap E g Opt values for [Na-Alg/MoS₂]^m and [Na-Alg/MoS₂ + GO]^h decreased by 82.43%, leading to more efficiency of [Na-Alg/MoS₂ + GO]^h as a coolant in the solar energy applications.

There are many constructive studies with valuable ideas that can be worked on in future studies and transform the mathematical system into a system based on hybrid nanofluids so that they can be studied theoretically and experimentally for different fluids and different NPs as well. The important examples of these studies are available in previous literature [55–57]. It can be said that in the near future we are currently working on extending the current concept in this study to include the main ideas of previous literature [58,59,60,61,62,63].