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Magnetohydrodynamic flow efficiency and irreversibility improvement research are multiple problems that arise when electroosmosis forces affect Buongiorno’s nanofluid in a complicated peristaltic tapered channel. Thermal energy and temperature gradients cause nanoparticles to migrate randomly, affecting flow efficiency and irreversibility. Sometimes the infected veins generate complex peristaltic waves on its walls. The mathematical model that characterizes the motion of Jeffrey magnetohydrodynamic Buongiorno’s nanofluid inside a complex tapered peristaltic channel, considering the effects of electroosmotic forces, is discussed. The long wavelength and low Reynolds numbers approximation is considered. The approximate solution of the nonlinear system of partial differential formulas is obtained using the Adomian decomposition method. Also, the irreversibility of the system and entropy generation are being studied. Flow characteristics with biophysical and thermal parameters are plotted and discussed. The improvement in the interstitial distances that make up the nanofluid in turn enhances the Bejan numbers. So, one of the important results is that when the increment of Brownian motion and thermophoresis of the nanoparticles, the Bejan numbers are raised significantly. Both the Jeffrey parameter and Debye–Huckel parameter work to upsurge the loss of kinetic energy within the molecules, which reduces the temperatures inside the nanofluid and thus reduces the entropy rate, in contrast to the rest of the parameters that raise the kinetic energy inside the molecules that make up the nanofluid.Graphical Abstract

•Novel technique is used for stability heating effects of photothermal theory.•Analysis is established stability processes at semiconductor medium boundaries.•Governing equations are established using 1D elastic-optoelectronic deformation.•Main physical quantities are obtained by HPM with various eigenvalues.

A theoretical study of velocity slippery, thermal jump, and mass slippery influences in three-dimensional (3D) hybrid nanofluid flowing via a biaxial extending surface is presented. In the present study, a hybrid nanofluid composed of nanoparticles of both magnesium oxide (MgO) and copper oxide (CuO) was formed homogeneously in methanol as a conventional fluid. The controlling boundary layer equations (continuity, impetus, heat, and concentration) are transmuted into nonlinear ordinary differential equations (ODEs) by employing suitable similarity transformations. The numerical solutions were done with the help of bvp4c code in the MATLAB software. Impact of emergent parameters is presented on velocity profile, temperature, and concentration. The physical interest of drag force, Nusselt, and Sherwood numbers are displayed with various parameters. Validation of computations has been performed with published results. Our results suggest that a linear biaxial stretching sheet has a greater significant impact on flow boundary. When the size of the nanoparticles boosts, the velocity outlines decreases, and the thermal and the concentration boundary layers increase. By the increment in the Brownian diffusion parameter, the heat transmission rate reduces while the mass transport rate upsurges. Incrementation thermophoresis parameters works to reduce the heat and mass transmission rate.

Within the most recent effort, a non-Newtonian inclination magnetized Carreau nanofluid that has such a cubed autocatalysis impact is detailed. When the flow behavior is moved via a magnetic field, the speed of the fluid is thoroughly investigated under these conditions. The findings about the temperature transparency of the Carreau nanofluid are obtained via the use of temperature-dependent heat transfer, and the measurement of the nanofluid’s amount is accomplished by the utilization of homogeneous heterogeneous chemical processes. The physical model is used to construct partial differential equations (PDEs), which are then processed via variables that are comparable in order to obtain ordinary differential equations (ODEs). Also offered for operation is bvp4c which generates their analytical data. A combination of charts and statistical diagrams is used to display the findings. The movement of nanoparticles from inside the fluid is represented by the uniform chemical process. Furthermore, due to the fact that these nanoparticles are buried in the fluid, the temperature rises in both shear and shear thickness situations. Additionally, the higher magnetic force decreases the Lorentz force, which in turn decreases the movement of the nanofluid at reduced rates.

The goal of this research is to provide a novel conceptual base for ternary hybridity nanofluids that will improve heat transmission. This model illustrates how to produce heat conduction that is superior to the hybridity nanofluid. The ternary hybridity nanofluid is made by suspending three distinct kinds of nanostructures (TiO2, Al2O3, and SiO2) in ethylene glycol with varying physical and chemical linkages. The combination of these nanoparticles aids in the decomposition of hazardous compounds, environment cleansing, and the cooling of other equipment. This article describes the ternary hybrid nanofluids such as the conductivity of thermal and electrical, specific heat capacitance, viscosity, and density. The ordinary differential equations for the liquid and temperature are solved utilizing the Keller box method (KBM). The main finding discovered that the tri-hybrid nanofluid transferred more heat compared to the hybrid nanofluid. The velocity and temperature field diminishes for these ranges of parameters: $0 \le \gamma \le 2$(velocity slip$\gamma $) and $0 \le {\gamma _1} \le 2\,\,$(temperature slip ${\gamma _1}).\,\,$The Darcy–Forchheimer $Fr$ranges between $0.5 \le Fr \le 1.4$diminishes the fluid velocity. The fluid moving subjected to a rotating cone has various applications in engineering like cone clutch, steam generators, loudspeaker cooling, lubricating grease for seals, hydrology, geosciences, etc.Graphical Abstract

•Two-dimensional boundary layer flow of williamson hybrid nanofluid over a stretching sheet is studied.•The influence of different nanoparticles is explored while using single phase model.•The impact of shape factor and heat source is investigated.•A numerical procedure namely keller box method is used for the solution.•(SiO2−Cu/EO)hybrid nanofluid is better transfer source as compared to (Cu/EO)nanofluid.

Heat transfer is critical due to its broad application in a variety of industries. New hybrid nanofluids are being used to improve the heat transfer competencies of ordinary fluids and have an enormous exponent heat than nanofluids. Hybrid nanofluids, a novel form of nanofluid, are being utilized to improve the heat transfer capacities of regular fluids and have a more outstanding heat exponent than nanofluids. Two-element nanoparticles submerged in a base fluid make up the hybrid nanofluids. Flow and heat transport properties of a hybrid nanofluid across a slick surface are studied in this study. Nanoparticle shape analysis, porous media, thermal conductance variations, and thermal radiative effects are all part of the process. A numerical approach called the Keller box method is used to solve the governing equations numerically. EO-Engine Oil has been used as a rich, viscous base fluid in this study, and a Cason hybrid nanofluid was examined. This fluid contains two diverse forms of nanoparticles: Copper (Cu) and Magnesium Zinc Zirconium alloy (MgZn6Zr). Compared to standard Cu-EO nanofluids, the heat transmission level of such a fluid (MgZn6Zr-Cu/EO) has steadily increased, which is an important finding from this study. The boundary-lamina-shaped layer's components have the highest thermal conductivity, while sphere-shaped nanoparticles have the lowest. When nanoparticles are assimilated, the entropy of the system increases by a factor of three: their ratio by fractional size, their radiative properties, and their thermal conductivity variations.

•Rotating Sutterby nanofluid flow in a slippery expandable sheet was investigated.•Tiwari–Das nanofluid model was employed in mathematical modelling.•Keller box method is adopted to find the approximate solutions.•Gold nanoparticles suspended in blood as base fluid were taken into account.•Heat transfer rate was enhanced between 17.2% and 62.1% with thermal radiative flow.

In this research work, we introduce the influences of the shape of nanoparticles and joule heating in the hydromagnetic flow of hybrid nanofluids between non-parallel plates. A mixture base fluid (H2O (50%)-C2H6O2(50%)), a hybrid nanofluid containing hybrid nanoparticles (graphene oxide-molybdenum disulfide, GO-MoS2) as nanoparticles, is considered. The non-linear governing equations are reduced into ordinary-differential equations (ODEs) by similarity transformations. The non-linear ordinary-differential equation (ODE) is solved numerically utilizing 4th–5thorder Runge-Kutta-Fehlberg (RKF-45) with a shooting method and analytically using the homotopy analysis method (HAM). The effect of the rarefaction parameter, Reynolds number, channel angle, Hartmann number, electric field parameter, and the shape of nanoparticles on fluid velocity and skin friction are discussed and presented in a graphical form. Also, the theoretical results and the effectiveness of the homotopy analysis method (HAM) are confirmed by numerical tests and presented graphically coupled with detailed discussions.

There are flow research centers on magnetohydrodynamic (MHD) emission of auxiliary liquid in an extended region. The prevailing model is constrained by attractions/infusion and gooey release. The administering model is based on the Koo–Kleinstreuer–Li nanofluid model in the existence of entropy generation. Final requirements of this model are addressed by implementing the shooting strategy, which incorporates a fourth approach for the Runge–Kutta strategy. Into the bargain, the last adds (in standard ordinary differential equations (ODE) divisions) are obtained from the measurable controls partial differential equations, which were represented toward the start of the overseeing model. The varieties for all boundaries are exhibited through graphical arrangements. It is noticed that expanding the substantial volume portion diminishes speed but builds nuclear power dispersion. Likewise, the classification of mathematical qualities on divider heat move rate and skin contact is introduced. Both Reynolds and Brinkman numbers improve the entropy rate of the thermal system resulting in the growth effects of inertial forces and the surface heat dissipation, respectively.

The heat transport and entropy formation of an unsteady Sutterby hybrid nanofluid (SBHNF) are investigated in this work. SBHNF’s flowing and thermal transport properties are investigated by exposing the nanofluid to a slippery hot surface. This analysis includes the influences of solid-shaped nanoparticles, porous materials, radiative flux, and viscous dissipative flow. The Galerkin finite element technique (G-FEM) is used to find self-similar solutions to equations that are then transformed into ODEs using appropriate transformations. This research considers two diverse kinds of nanosolid-particles, copper (Cu) and graphene oxide (GO), using non-Newtonian engine-oil (EO) as the working fluid. In the flowing, energy, skin friction, Nusselt number, and entropy production, important findings for the various variables are visually depicted. The most notable finding of the analysis is that when SBHNF (GO–Cu/EO) is compared to a typical nanofluid (Cu–EO), the thermal transmission rate of SBHNF (GO–Cu/EO) gradually increases. Furthermore, heat transfer is greatest for spherical-shaped nanoparticles and lowest for lamina-shaped nanoparticles. The entropy in the model is increased when the size of the nanoparticles ϕ\phi is increased. The comparable impact is noticed once the radiation flowing Nr{N}_{\text{r}}and Deborah number λ\lambda increase.

The mathematical modeling of hybrid nanofluid flow and heat transfer with entropy generation toward parabolic trough surface collector (PTSC) inside the solar-powered ship (SPS) is performed. The mathematical model used non-Newtonian Oldroyd-B model amidst a constant inclined magnetic field influence is being considered. The mathematical model is then reduced by adopting appropriate similarity transformation into a higher-order nonlinear differential equations system. The reduced model is computed using the well-known technique called the Keller Box scheme. Physical parameters effectiveness, for instance, thermal radiation, viscous dissipation, hybrid nanoparticles, and Joule heating, is displayed in graphs. The silver-ethylene glycol (Ag-EG) characteristic performance outperformed the silver-magnetite-ethylene glycol (Ag-Fe3O4/EG). The maximum efficiency of Ag-EG is about 26.3%, while the minimum is at least 5.6%.

•A mathematical model is developed for the parallel stretching rotating disk flow of ferrofluids.•Novel variable viscosity and thermal conductivity is studied for typical flow.•Chebyshev spectral numerical solutions have been achieved with an excellent correlation.•The variable thermal conductivity is improved with the considered nanoparticles.

The essence of the present investigation is to reveal the hydrothermal variations of viscoelastic nanofluid flow in a porous medium over a stretchable surface. A higher-order chemical reaction is incorporated with thermophoresis and Brownian motion. Similarity conversions reduce the resulting equations into their dimensionless form and then solved using Runge-Kutta-Fehlberg (RKF) based shooting procedure. The effects of underlying factors on the flow are discussed through various graphs and tables. Computational results for noteworthy skin friction and heat and mass transport are presented and reviewed with sensible judgment. The study reveals that the fluid velocity reduces with incremental values of the viscoelastic parameter k1*and magnetic strength. The temperature reduces for the suction parameter with the existence of stretchable but enhances with thermophoresis and Brownian motion effects. Heat transfer rate amplifies for Prbut declines for γ. Mass transfer rate increases with the increase in Brownian parameter and Schmidt number. A comparative analysis shows a better agreement with previous results in limiting scenarios.

The present analysis focuses on using Casson nanofluid in a porous solar collector flow on an infinite surface. Nanofluid flow is altered on stretched surface induction. Nonlinear ordinary differential equations (ODEs) are derived and impaired by reducing boundary conditions to suited similarity transformation. Set of ODEs were solved approximately using the Keller box technique. Results were analyzed and elaborated for Copper-engine oil (Cu-EO) nanofluid and Ferro oxide-engine oil Fe3O4-EO nanofluid as well. Skin friction coefficient increased significantly while the Nusselt number decreased with an induced magnetic parameter. Moreover, the net system entropy was higher along with the flow velocity and the non-dimensional Brinkman number. The study revealed a better collecting of heat with Casson-nanofluid. Heat transfer rate is a crucial parameter of Cu/Fe3O4-EO as a working fluid. Net thermal efficiency enhancement of Cu-EO over Fe3O4-EO is found to have a minimum of 2.7% and an optimum of 18.5%.

In this paper, very efficient, intelligent techniques have been used to solve the fourth-order nonlinear ordinary differential equations arising from squeezing unsteady nanofluid flow. The activation functions used to develop the three models are log-sigmoid, radial basis, and tan-sigmoid. The neural network of each scheme is optimized with the interior point method (IPM) to find the weights of the networks. The confrontation of the obtained results with the numerical solutions shows good accuracy of the three schemes. The obtained solutions by utilizing the neural network technique of our variables field (velocity and temperature) are continuous contrary to the discrete form obtained by the numerical scheme.

In this paper, the boundary layer analysis of three-dimensional Prandtl nanofluid flow over a convectively heated sheet in a porous material is addressed. Nonlinear radiation and high-order chemical reaction analysis are featured in this work. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. Features of Brownian motion and thermophoresis accounting for nanoparticle diffusion are taken into account. Then, a complete discussion of the influences of the flow regime on several thermofluidic parameters is presented. The outcome of the present study is that velocity field lines are grown due to the strengthening of Prandtl fluid numbers β1and β2while a reverse trend takes place for temperature profile. Furthermore, it is shown that when the magnetic strength is improved, the skin friction coefficient and heat transfer rate triggers considerable evolution. The obtained results of this model closely match with those available in the literature as a limiting situation.

Solar energy is the leading thermal source from the sun, with huge use of technology such as photovoltaic cells, solar power plates, photovoltaic lighting, and solar pumping water. The current effort deals with solar energy analysis and a technique to enhance solar aircraft effectiveness by using solar and nanotechnological energy. The work is based on the investigation of thermal transfer by utilizing hybrid nanofluid past an inside solar wings parabolic trough solar collector (PTSC) to rich the studies of the solar aircraft wings. The thermal source is titled solar radiative flow. For various properties such as porous media, Cattaneo Christov heat flux, viscous dissipation, play heating and thermal energy flow, the heat transfer efficiency of the wings is verified. In the case of the tangent hyperbolic fluid, the entropy generation analysis was applied. The modeled energy and momentum equations were managed using the well-established numerical plan known as the Keller box process. This paper is made up of double-different kinds of nano solid particles, Cu (copper) and ZrO2(zirconium dioxide) in EG (ethylene glycol) as standard fluid. Various control parameters are discussed and shown in figures and tables for velocity, shear stress, temperature outlines, frictional factor, and Nusselt number. The efficiency in the aircraft wings in the case of thermal radiation amplification and variable thermal conduction parameters is seen to be improved in terms of thermal transfer. In comparison to the traditional nanofluid, hybrid nanofluid is the ideal source of heat transfer. The thermal efficiency of ZrO2–Cu/EG compared to Cu-EG decreases to a low of 2.6% and peaks to 3.6%.

Thermal energy from the Sun comes mostly from sunlight. These energies might be used in photovoltaic cells, sustainable power systems, solar light poles, and water-collecting solar pumps. This age studies solar energy and how direct sunshine might improve solar panel efficiency. Solar energy, especially solar tiles, is widely used in manufacturing today. The literature includes a modified Buongiorno hybrid nanofluid prototype. There are no studies that have examined the impact of tri-hybrid and unique tetra hybridity nanomolecules integrated with the Buongiorno nanofluid prototype on liquid moving on a flexible surface. This study examines the effects of an improved Buongiorno tetra hybrid nanoliquid prototypical with Buongiorno and Tiwari–Das nanofluid on magnetized double-diffusive binary nanofluid with cross fluid and Maxwell liquid flowing with variant thermal conductance over a porous medium. Different profiles include diffusion thermo and thermo diffusion. The LobattoIIIA scheme’s convergence and stability are examined in terms of residual error, mesh points for ordinary differential equations (ODEs), and boundary conditions. Leading equations about liquid flow continuity, impetus, temperature, and concentricity are obtained using continuity, conservation of momentum, the second law of thermodynamics, Fick’s second law of diffusion, and boundary layer expectations. The system of partial differential equations obtained from the given assumption becomes a system of ODEs and well-established LobattoIII. Their numerical solution is obtained using a numerical technique. Statistical charts and tables provide numerical solutions. The heat transport rate of tetra-hybrid nanomolecules increases dramatically, unlike tri- and di-hybrid nanomolecules. The improved Buongiorno tetra hybrid nanofluid (BTHNF) model produces more heat when radiation Rd{\rm{Rd}}, Brownian diffusion Nb{\rm{Nb}}, and thermal conductivity are increased. The data show that the diffusion factor LL, Brinkman number Br{\rm{Br}}, and Reynolds number Re increase entropy production, but Bejan number reduces it owing to an increase in Be{\rm{Be}}and Re\mathrm{Re}. A statistical regression study shows that retaining the Maxwell fluid parameter constant and increasing the Weissenberg number We{\rm{We}}decrease the drag coefficient error. A BTHNF model containing tetra hybrid nanoparticles has not been utilized to examine heat and mass transferences in non-Newtonian fluids, considering diffusion, thermo, and thermo diffusion. Entropy generation in a binary fluid with tetra hybrid nanoparticles and BTHNF has not been studied. Tetra hybrid nanofluid is not mentioned in the literature. This effort aims to create a new tetra-hybrid nanofluid model. This article is novel because it investigates the effects of thermal radiation, thermal conductivity, porosity, Darcy–Forchheimer, and Buongiorno models on a tetra-hybrid nanofluid flow under an extensible sheet.

This examination explores the flow of a hybridized nanofluid (HyNf) containing silica and tin oxide nanoparticles mixed with engine oil (EO/SnO2-SiO2). The flowing occurs via a permeable material constrained by a semi-infinite flat plate. The study takes into account various factors such as convective heat and mass transference, chemical reactions, the Dufour effect, the Lorentz force, thermal radiative fluxing, and radiative absorbing. The research involves converting the managing formulas of the flowing model into a dimensionless form and applying the regular perturbation procedure to find solutions for the rate of fluid flow, temperature, and species diffusion. The surface frictional factor, Nusselt quantity, and Sherwood quantity reflect the shearing stress, rates of heat transference, and rates of mass transport at the plate, respectively. An analysis is conducted on the impact of several factors, including the suction variable, magnetic variable, radiation-absorbing factor, Casson parameter, and Dufour number, on the flow and related quantities. This analysis is based on an examination of graphs and tables. The findings suggest that the heat transference rate in the Casson hybridized nanofluid is better than that in the mono nanofluid. It is exposed that the temperature reduces at the plate having improved frequency of oscillation and also fluid velocity declines for improving values of aligned magnetized field M, but it shows the reverse phenomenon with Gr1and Gc1.

The current study investigates two-dimensional natural convective heat transference and entropy production in a tilted wavy-walled enclosure under the magnetic field and thermal radiation effect. The enclosure is filled with Cu–Al2O3/H2O hybrid nanofluid and subjected to a non-uniformly heated curved left wall, constant cold right curved side, uniformly heated bottom side, and insulated upper side. The regulating formulas in the non-dimensional form are reduced to streaming function-velocity expression and are numerically solved based on the Bi-CGStab method. The simulations are behaved with diverse Rayleigh amounts, Hartmann numbers, an incline angle of the enclosure, radiation parameters, diverse amplitude of the curved wall, and volume fraction of hybrid nanoparticles. Numerical code validation with other published results agrees well with the present outcomes. Heat and entropy generation were improved with the change in dimensionless parameters, and the findings have been clarified through discussion. The observations indicate that the Rayleigh numbers, nanoparticle fractional size, amplitude, and radiation parameter influence the convective effect and entropy production inside the enclosure. In contrast, the Hartmann number detracts from the convective effect. The findings suggest that a rise in the cavity angle may result in a corresponding boost or decline in heat transference. The minimum Nusselt numbers is obtained at δ=90°, as the angle of incline of the enclosure restraints the fluid rapidity and diminishes the heat transference rates. To design heat exchangers, this particular study may serve as a guide.

This study introduces a three-dimensional numerical analysis of the mixing yield stress fluid inside stirred vessels. The Bingham–Papanastasiou model predicts the yield stress behavior of the working fluid. The implications of a new anchor impeller design are investigated; it involves certain modifications to a typical anchor impeller’s blade. Different curved shapes replace the straight blade of a classical anchor. The flow pattern and energy consumed inside the stirred system for various geometrical configurations, Reynolds numbers (0.1, 1, 10, and 100), and Bingham numbers (1, 10, 100, and 500) have been investigated. According to the findings, introducing this new geometrical configuration gives a significant acceleration of flow pattern and extension of the well-mixed zone, as well as decreased power consumption (Np{\rm{Np}}). Three configurations were introduced to the mixing system: Case 1 is a standard anchor impeller, and Cases 2 and 3 are curved anchor impellers with two shapes different. Case 3 (helical design of blade) has been found to be the less power consumption case by five times, i.e., for Case 1 and Case 2, Np=5{\rm{Np}}=5, whereas for Case 3, Np=1{\rm{Np}}=1. Based on the results, it is evident that the configuration (Case 3) demonstrates a superior geometric design in enhancing mixing characteristics compared to the other configurations.

The primary purpose of this research is to examine how the presence of thermal features variation affects the velocity and heat transfer rate of nanofluids composed of sodium alginate and molybdenum disulfide [Na-Alg/MoS2]mand sodium alginate and molybdenum disulfide and graphene oxide [Na-Alg/MoS2+ GO]h, respectively, flowing between two rotating, permeable plates. Both centripetal and Coriolis forces, which act on a spinning fluid, are taken into account. The impacts of magnetized force, thermal radiative flux, heat source (sinking), and varied pressure in the Darcy–Forccheimer material are considered. Using the physical vapor deposition method, single and hybridity nanofluid thin films of thickness 150 ± 5 nm may be created. The controlling mathematical equations of the suggested model are solved using the Keller-box technique in MATLAB software. The surface friction coefficient of a hybrid nanofluid is less, and the heat transfer rate is greater than that of a regular nanofluid. The rate of heat transmission is slowed by the rotational parameter. The thermal efficiency of mono nanofluids is as low as 6.16% and as high as 21.88% when compared to those of hybrid nanofluids. In particular, the findings of density functional theory (DFT) calculations reveal that the energy bandgap ΔEgOpt\Delta {E}_{{\rm{g}}}^{{\rm{Opt}}}drops from 1.641 eV for conventional nanofluid to 0.185 eV for hybridity nanofluid. Based on the findings, the addition of graphene oxide nanoparticles to the base nanofluid converts it from a semi-conductor to a hybridity nanofluid as a superconductor.

This theoretical work suggests a novel nonlinear thermal radiation and an applied magnetic feature-based three-dimensional Casson nanomaterial flow. This flow is assumed in the rotating frame design. Gyrotactic microorganisms (GMs) are utilized in the Casson nanofluid to investigate bioconvection applications. The altered Buongiorno thermal nano-model is used to understand the thermophoretic and Brownian mechanisms. Convective boundary conditions must be overcome to solve the flow problem. With suitable variables, the dimensionless pattern of equations is obtained. The solutions to the nonlinear formulations are then obtained using semi-analytical simulations using a homotopy analysis mechanism. It was found that the velocity outline is enhanced with the enhancing estimations of the buoyancy ratio, rotation factor, and Casson parameter while it is reduced with mixed convection, porosity, slippery parameters, and Rayleigh number. The temperature profile is increased with radiation, the temperature ratio, the thermophoretic parameter, the Brownian parameter, and the Biot number. The Brownian parameter reasons an improvement in the concentration outline contrary to the thermophoretic parameter. The concentration of GMs is decreased with the Peclet number inversely to the Lewis number effect, which causes an increase in the microorganisms’ concentration.

In this study, an incompressible, steady, and magnetohydrodynamic flow of Buongiorno nanofluid through a stretchable surface has been analyzed by adopting a theoretical and numerical approach. This paper involves the impacts of buoyancy forces, thermal conductivity, chemically diffusion, and Arrhenius activation energy. Moreover, the influence of the suspension of gyrotactic microorganisms in the nanofluids is also a part of this study. It is assumed that the behavior of viscosity varies as a function of time and the suspension of microorganisms remain consistent throughout the study. A system of PDEs is reduced to a solvable system of ODEs by applying a suitable similarity transformation. For the sake of numerical solutions, the shooting method has been employed. Wolfram Mathematica has been used to deal with the BVP. In addition, the behaviors of different emerging parameters comprising velocity outline, temperature outline, concentration distribution, the density outline of gyrotactic microorganisms have also been demonstrated by graphical illustrations. From the extracted results, it has been observed that the rising values of viscosity of fluid produce a decline in the velocity parameter. Also, an increment has been noticed in the temperature profile for the growing behavior of the mixed convective factor.

The foremost energy source originating from the sun, which is solar energy is widely utilized in solar technologies such as photovoltaic cells installed in energy plates, street lights, and water pumping. Meanwhile, the combination between solar radiations and nanotechnology is utilized in solar aircraft (SA). Therefore, this article investigated the performance of SA wings, together with the parabolic trough surface collector (PTSC) placed inside the wings of SA. The SA performance is reported due to the heat transfer analysis in the working fluid flows in PTSC, where tangent hyperbolic hybrid nanofluid (THHNF) is chosen as a working fluid. The THHNF is this article contains the blend of two nanoparticles (NP), including Copper (Cu) and Silica (SiO2), in the viscous fluid of EG-Ethylene glycol. The heat transfer in the working fluid flows in the wings is discussed by considering the influencing factors such as porous media, thermal radiations, and variable thermal conductivity. In addition, entropy generation is also conducted for THHNF. The set of momentum and energy equations has been handled using a well-established numerical scheme, namely the finite difference method. The distributions of velocity, temperature fields, shear stress, coefficient of surface drag, and Nusselt number are displayed in figures and tables: These numerical results are subjected to the effect of controlling parameters. The main finding from this article is: The aircraft wings experience an enhancement in the heat transmission due to an amplification of thermal radiative flow and variant thermal conductivity. In comparison with conventional nanofluid, hybrid nanofluid shows better performance in heat transmission. The thermal efficacy of SiO2/Cu-EG over Cu-EG recorded a minimal level of 0.2%, and reached maximum percentage at 3.9%.