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The industrial significance of stability analysis for dual solutions and heat transfer sets the stage for this research. Focusing on Maxwell ternary nanofluid flow, the study aims to enhance thermal conductivity and stability by delving into viscous dissipation and velocity slip effects on a stretching/shrinking sheet. Employing a mathematical model, refined with nondimensional transformations and MATLAB's BVP4C solver, the research identifies dual solutions and examines the influence of key parameters on fluid dynamics and heat transfer. Results showcase a progressive improvement in convective heat transfer and skin friction from mono nanofluid (NF) to binary hybrid nanofluid (HNF), culminating with ternary hybrid nanofluid (THNF). These improvements are significantly associated with the suction/injection parameter (S), whereas the slip (σ) and elastic (K) parameters enhance thermal transfer but negatively affect skin friction efficiency at elevated levels. The robustness of the upper branch solutions underscores the reliability of these findings. Remarkably, at λ = − 1. 25 with a nanoparticle volume fraction of 0.04, ternary nanofluids achieve a 2.9% thermal efficiency leap over HNF, which itself surpasses NF by 0.46%. These findings hold potential for significant advancements in sectors such as electronics, manufacturing, energy, biomedical, environmental engineering, aerospace, and automotive, aiming at elevating thermal efficiency. [ABSTRACT FROM AUTHOR]

Recently, researchers are facing great challenges to form the homogeneous solutions of various liquids at biomedical and industrial levels. Such homogeneous solutions can be controlled through stratification phenomenon directly which is ignored by the researchers in the existing literature specifically quadratic stratification and melting heat mechanism which is valid only for higher temperature processes. Thus, to form the homogeneous and stable liquid solutions for various industrial processes, we investigate the melting heat phenomenon in quadratic stratified Jeffery Nano fluid flow deformed due to linearly stretching sheet along with stagnation point. Inclined constant magnetic field is implemented on the fluid through an arbitrary angel. Characteristics of heat and transportations are disclosed through viscous dissipation, Brownian motion and thermphoresis. Temperature and concentration of the surrounding fluids are assumed higher than the stretching surface. The resultant governing equations are reduced to ordinary differential equations through proper transformations. Convergent analytical series solutions are computed via homotopic approach. Impact of various emerging parameters on temperature, velocity and concentration fields are illustrated and discussed comprehensively. Sherwood and Nusselt numbers and drag force are scrutinized mathematically, physically and graphically. It is analyzed from the study that (i) dominant melting reduces the temperature field (ii) higher thermal and solutal stratification decay the temperature and concentration fields respectively (iii) higher thermophoresis enhances the temperature field. Further, it is concluded that stable and homogeneous solutions may be made by increasing melting and reducing stratification phenomena. This study will help us to provide actual amount of heat for heating processes in industries and biomedicine which is the basic requirement for excellent quality of products. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate the entropy generation and thermal characteristics of couple stress blood nanofluid on the peristaltic flow of gold nanoparticles being conveyed through an asymmetric channel through a porous medium. The distinctive characteristics of the nanoparticles such as their inspiring thermal conductivity make them a vital aspect of contemporary heat exchangers and nanotechnology. To create contrast-enhanced tracers intended for dynamic X-ray imaging of blood flows, gold nanoparticles have been incorporated into human red blood cells. The possibility for dynamic imaging with X-rays of blood flows provided by red blood cells in combination with gold nanoparticles has the potential to be advantageous for clinical applications. The main investigation focuses on the current situation of peristaltic motion with gyrotactic microorganisms in which the effects of Brownian motin, thermophoresis, thermal radiations, convective boundary conditions, wall slip, magnetic field, viscous dissipation and Joule heating are present. Lubrication approximations are implicit for interpreting the controlled partial differential equations. Numerical results were obtained using an effective Runge–Kutta method was developed using MATLAB software. This technique is commonly used to solve these problems since it is affordable, effective, and accurate to fourth order. Graphical interpretations are also used to calculate the effects of different physical parameters on temperature, concentration, velocity, dynamics of gyrotactic microorganisms, entropy generation, and Bejan number. Additionally, heat and mass characteristics of blood pumping were studied. According to certain results, entropy generation rises with the couple stress parameter. Furthermore, tables and bar charts are included to illustrate how certain data categories compare to earlier model-related research The findings indicated that gold nanoparticles are effective for drug transport as well as delivery systems due to their ability to control velocity using the thermophoresis and Brownian motion parameters. Gold nanoparticles additionally improve temperature dispersion, allowing it to damage cancer cells. In addition, the validity of findings is assured by reaching an agreement with earlier investigations. Flow, heat, and mass distributions are represented by streamlines, concentrations, and microorganisms. A graphical representation of the average Nusslet number and Sherwood number is also included. It is anticipated to provide a novel concept for improving the performance of controlling energy loss and improving the fluid's thermal performance are both critical in varied engineering applications. [ABSTRACT FROM AUTHOR]

This work analyzes the impact of viscous dissipation on an unstable stretching surface in a porous medium with heat generation and thermal radiation-an important factor for numerous engineering applications like cooling baths and plastic sheets. Using MATLAB's Runge-Kutta fourth-order approach, the controlling partial differential equations are converted into highly nonlinear ordinary differential equations that can be solved numerically. The findings show that a decrease in the skin friction coefficient, temperature profiles, velocity, and Nusselt number occurs when the unsteadiness parameter is increased. In contrast to the Prandtl number, which rises with temperature profile and reduced Nusselt number, the Eckert number rises with a dimensionless temperature profile and reduced Nusselt number. Reduced Nusselt number and temperature profile affect the heat generation parameter; a decrease in skin friction coefficient and velocity profile correlate with the porosity parameter. Furthermore, the radiation parameter rises as the temperature distribution and Nusselt number decrease. [ABSTRACT FROM AUTHOR]

This study examines the molecules motion influences and thermal attributes in power-law non-Newtonian dissipative fluids' magnetohydrodynamic behavior, Joule heating, electromigration, and Cattaneo-Christov effects. Effects of Hall on both flow velocity and temperature, as well as the heat transport are considered. The investigation looks at heat transference that occurs when there is a slippage consequence, how the temperature influences the viscosity of the fluid, and how the potential parameters influence the exponential non-Newtonian flow of fluid via an extensible sheet. Runge-Kutta-Fehlberg's approach, which is based on the shooting procedure, was used to develop computational solutions for nonlinear ordinary differential equations. When exposed to a deformation that is generated by expansion, pressure, or agitation, a dilatant fluid is characterized by a phenomenon in which its viscosity rises and may harden. This phenomenon is referred to as the dilatation phenomenon. High shearing rates provide the impression that it is stable. When expanded, subjected to pressure, or agitated, dilatant fluids become more viscous and transform into solids. Both the non-equilibrium that occurs within the fluid and the reduction of the irreversibility processes that occur within it are caused by the acquired charges that are a result of Hall effect of fluid molecules. [ABSTRACT FROM AUTHOR]

This study aims to investigate the Joule effect, thermal radiation, and Coriolis effects in unsteady magnetohydrodynamics (MHD) micropolar flow over a 3-D unstable sheet. A magnetic field is typically applied to the surface; additionally, it is assumed that the fluid is conducting electricity. Other micro-rotations are also considered. The physical issue is resolved with the help of the fundamental equations, and the issue's complexity is reduced with the use of similarity variables. In the present approach, the homotopy analysis method (HAM) is employed. The heat, skin's friction factor, temperature, micro movements, and velocity associated with the emerging parameters and transfer rates are considered. The boundary layer thickness is increased as the parameter of vorticity increases. When the magnitude of the magnetic field increases, the skin friction coefficient decreases. The state variables are approximated up to six decimal places numerically. The numerical values of − f ″ (0) and − θ ′ (0) are computed to higher decimal places and compared with the available literature to validate the results. The outcomes obtained are compared with the available literature; the results here are corroborated, and the performance of the HAM is demonstrated. [ABSTRACT FROM AUTHOR]

Nanofluids show greater heat transfer rate and characteristics of mechanical friction diminution using nano-sized hard elements to fluid. Moreover, regarding the working of heat transfer fluid, nanofluid is widely used in areas of refrigeration, shipping, automobile, chemical industry, energy, electronics, air conditioning, computer, and many other areas to cope heat transference issues. The aforesaid utilizations motivated us to encounter entropy generation aspects for Sutterby nanofluid flow configured by permeable surface. Moreover, well-known Buongiorno's model capturing same attributes of Brownian and thermophoretic-diffusions is presented for modeling and investigation. Additionally, (MHD) as well as thermal radiation effects are the part of current work. Here, we have also considered the viscous dissipation aspects. Similarity variable are used to decrease set of nonlinear PDEs into set of ODEs then resolved numerically by using bvp4c algorithm, besides the pertinent parameters are addressed graphically. The physical aspect of fluid flow, temperature, concentration for variation of involved parameters is explained with the help of graphs. Velocity of Sutterby nano fluid has opposite behaviors versus Sutterby fluid parameter and magnetic parameters. Augmented values of Brownian moment, thermophoresis and heat source parameters intensify the temperature of nanofluid. Concentration of Sutterby nanofluid deteriorates for greater Schmidt number. [ABSTRACT FROM AUTHOR]

The remarkable thermophysical characteristics of hybrid nanofluids have considerable potential for the enhancement of heat transport. In recent years, there has been a significant surge in research on hybrid nanofluids, with findings indicating that these fluids are favorable for transferring heat in engineering contexts. Therefore, a theoretical investigation is conducted by adopting the Tiwari and Das model, for viscous dissipative flow and thermal transport characteristics of hybrid nanoparticles in an exponentially permeable porous shrinking surface. The convective thermal transport features are studied with the influence of Ohmic heating and thermal generation/absorption effects. To solve the governing flow problem of hybrid nanofluid, a standard conversion and numerical approach are used. The numerical findings indicated the existence of dual solutions within a certain range of shrinking and mixed convective parameters. The results reveal that high suction strength higher the skin friction coefficient and heat transfer rate. It also reveals that in opposing flow regions, the addition of nanoparticles resulted in a lower heat transport rate and a higher skin friction coefficient. Furthermore, as thermal radiation increases, the rate of heat transfer increases, but the upward Eckert number exhibits the opposite behavior. In addition, the velocity profile displays opposite behavior for upper and lower behavior when the mixed convection parameter increases. Besides, the thermal distribution grew when the radiation, Eckert number, and Biot number were raised. [ABSTRACT FROM AUTHOR]

In this article, the mixed convection transport of the Carreau fluid in the presence of a magnetic field and a heated circular cylinder within a trapezoidal cavity is examined. Finite element analysis is used via COMSOL Multiphysics software to simulate the two-dimensional flow. The heat equation is formulated by incorporating the effects of viscous dissipation and Joule heating. The upper and lower surfaces of the cavity are adiabatic, while the left and right sides are assumed to be cold. The temperature distribution and flow field within the cavity are visualized through the plotting of isotherms, streamlines, and total entropy generation. The graphical representations are performed to examine the impacts of physical parameters on temperature, flow field, and total entropy generation, including the Reynolds number , Weissenberg number $ ({1.0 \le We \le 6.0}) $ (1.0 ≤ We ≤ 6.0) , Power law index $ ({0.1 \le n \le 5.0}) $ (0.1 ≤ n ≤ 5.0) , Hartman number $ ({1.0 \le M \le 50}) $ (1.0 ≤ M ≤ 50) , and Richardson number $ ({0.2 \le Ri \le 5.0}) $ (0.2 ≤ Ri ≤ 5.0) and $ ({0.2 \le Rc \le 0.8}) $ (0.2 ≤ Rc ≤ 0.8). It is found that the Joule heating and Richardson number are the main reasons to increase the thermal performance within the cavity. The r $ ({100 \le Re \le 500}) $ (100 ≤ Re ≤ 500) ising values of power law index and Weissenberg numbers caused to reduce the velocity field, irreversible effects and circulation within cavity. While the entropy is augmented by elevating the Eckert and Hartmann numbers. Furthermore, heat transfer improved with the increased magnetic field and Eckert number. [ABSTRACT FROM AUTHOR]

This work conducts a numerical examination into the influence of a magnetic field and viscosity dissipation on the movement of a micropolar fluid over the surface of a vertical, hollow circular cylinder via conjugate mixed convection. In this investigation, we obtained a numerical solution for a non-linear differential equations-based modeling system by employing MATLAB and the bvp4c solver, which operates on a two-equation model. We show graphically how micropolar materials, conjugate heat transfer, viscous energy dissipation, buoyancy factors and magnetic field affect the temperature at the interface, local skin friction and heat transfer. By contrasting the acquired results with those found in the published research, which exhibit a high degree of concordance, the validity of the methodology is proven. The findings indicate that the escalation of the Eckert number correlates with an increase in both interfacial temperature and skin friction, accompanied by a reduction in local heat transfer. Furthermore, elevated magnetic and buoyancy values amplify both skin friction and thermal transfer, contributing to a decrease in dimensionless interfacial temperature distributions. [ABSTRACT FROM AUTHOR]

In present paper the mathematical study of Slip conditions on electrically conducting nanofluid over a vertically stretching sheet is presented with effects of viscous dissipation, thermal radiation and Soret and Dufor. The state of flow has been explained mathematically with help of partial differential equations. Model equations are made convenient for calculation by suitable transformations. With the help of Kellerbox technique unknown functions are approximated in flow situation. The influence of medium porosity, magnetic field strength, thermal radiation, Soret and Dufour effects, Buoyancy forces, viscous dissipation wall slip parameter, and heat source are investigated in detail. Effects of emerging parameters on velocity, concentration, temperature and profiles are investigated. In relation to the parameters involved, we can observe the rates of momentum, heat, and mass transfer near the stretching surface. It can be concluded from the study that velocity slip parameter accelerates with fluid motion, temperature of nanoparticles is enhanced due to rise in Eckert number and Biot number, while the Soret effect enhances the nanoparticles concentration close to the stretching sheet. Also, under common assumptions, the analytical approximations for the solution of the current model that were produced by using the Keller box approach were shown to be in very excellent agreement with certain early publications. [ABSTRACT FROM AUTHOR]

In the current article, MHD flow problem of Darcy-Forchheimer nano-liquid comprising motile microorganisms with viscous dissipation impact past a nonlinear elongated sheet is addressed. The inclusion of gyrotactic microorganisms in nano-liquid assists to boost up the thermal efficiency in numerous micro-biological systems. Iterative solution of the single-phase flow problem is attained by utilizing the procedure of SOR (Successive over Relaxation). The influences of leading parameters on flow velocity, temperature, density and concentration of motile microbes are considered and depicted through tables and graphs by employing software of MATLAB. Furthermore, comparison table is developed to check the accuracy of numerical results of the flow problem under consideration. An increment in the Forchheimer parameter causes reduction in the velocity distribution. It is portrayed that the Lewis number and Brownian motion parameter tend to enhance the rate of mass transport. [ABSTRACT FROM AUTHOR]

The proficiency of hybrid nanoparticles in increasing heat transfer has impressed many researchers to further analyze the working of those fluids. In the current study, the impact of entropy generation on EMHD hybrid nanofluid (copper-alumina) flow over a rotating disk in the presence of the porous medium, Darcy‐Forchheimer, heat generation, viscous dissipation, and thermal radiation. By applying the self-similarity variables, the partial differential equations are converted into ordinary differential equations. After that, the dimensionless equations are numerically solved by using the Runge-Kutta technique, and also the comparison is done between the numerical technique (R-K method) and the homotopy perturbation method (HPM) where HPM yields a more effective and dependable conclusion. To highlight their physical significance, unique characteristic graphs are shown for the profiles of velocity, temperature, and entropy generation, along with a suitable explanation. The hybrid nanofluid velocity decreases with larger values of the magnetic parameter, but the velocity profile increases with the higher electric field. It is observed that both skin friction and nusselt number are increasing function of magnetic parameter and electric field parameter. [ABSTRACT FROM AUTHOR]

The vast significance and applications in various industrial works such as heat and cooling process, chemical reactors, food storage systems and several medical works motivated the author to conduct this type of study. The aim of this paper is to inspect the two-dimensional incompressible magnetohydrodynamic flow of Williamson fluid through a stretching sheet. The Cattaneo-Christov temperature and concentration flow is considered with the effects of double stratification and viscous dissipation. The leading nonlinear partial differential equations of flow are transformed into ordinary differential equations by means of renowned similarity transformations and the solutions of flow problem are obtained by means of bvp4c method on MATLAB software. The Williamson fluid parameter depending on time relaxation and declines the fluid motion. The motion of fluid slowed down due to Hartman number. The mass and heat flow is noted to be decline due to thermal and solutal relaxation parameters. The rises in stratification coefficient reduce the mass and heat transferal rate. [ABSTRACT FROM AUTHOR]

The present paper investigates the flow field and heat transfer in a microchannel with incorporating surface hydrophobicity and considering its thickness. The microchannel is under partial magnetic field (MF), which is applied to the top thermal-insulated wall in Hartmann numbers 0 to 30. The results show that at Ha = 0, viscous dissipation (VD) and heat transfer decrease with increasing slip coefficient. Also, raising the Hartmann number (Ha) increases the friction coefficient. The Nusselt number (Nu) reaches its highest value at Ha = 20 for all cases, but then, as the Ha increases, the average Nu reduces. [ABSTRACT FROM AUTHOR]

The main purpose current exploration is to examine the influence of viscous dissipation and nonlinear radiation in three-dimensional (3D) Williamson fluid flow on an exponentially stretching through porous medium with the effect of activation energy along with chemical reaction. By employing suitable transformation, the nonlinear partial equations (PDEs) are transmuted to nonlinear ordinary differential equations (ODEs) which are subsequently solved numerically by using Range-Kutta method with shooting technique by utilization Matlab script. Characteristics of resulting physical parameters appearing in modeling like the Weissenberg number, Prandtl number, nonlinear radiation parameter, porosity parameter, Eckert number and chemical reaction parameter are comprehensively analyzed in graphical forms with an interest in providing the physical meaning to each parameter. The outcomes anticipate that, the thermal profile is improved by the increase in the values of nonlinear radiation parameter due to inner heat. The thermal profile enhances by strengthening of Eckert number but it has opposite trend through Prandtl number. The impact of obtained parameters on skin friction coefficient, mass and heat transfer rates is illustrated by tables. The validity of the present findings is presented by comparing them with the previous investigations. [ABSTRACT FROM AUTHOR]

[Display omitted] • The influence of hybrid nanoparticles (Ag-Al 2 O 3 /H 2 O) flow patterns are examined. • Combined effects of porous medium, Riga surface, thermal radiation, Joule heating, MHD and chemical reaction is examined. • LMB algorithm is used to examine the hybrid nanofluid's performance, regression, error histograms, and fit plots. • Shooting technique using BVP5C is applied to solve the governing equations. The aim of present study is to examine the augmentation of thermal energy transfer in hybrid nanofluid flow caused by a rotating Riga disk in the presence of thermal radiation and chemical reaction. The silver and aluminium oxide nanoparticles are used to examine the thermal effect of water base fluid. The Darcy-Forchheimer model is considered to endorse the inertial and porous media effects and makes the model more realistic from the physical scenario. Levenberg-Marquardt backpropagation algorithm is considered to analyze the hybrid nanofluid's properties. Using scaling group transformations, the governing partial differential equations are transformed into a system of ordinary differential equations. Resulting ordinary differential equations are solved numerically by applying a suitable shooting technique by MATLAB. The results obtained for the governing differential equations have been incorporated into a dataset on which the neural network has been trained. The effects of physical parameters have been analyzed for velocity, temperature, and concentration profiles. The determination, designing, convergence, verification, and stability of the Levenberg-Marquardt backpropagation neural network algorithm are validated on the assessment of achieved accuracy through performance, fit, regression, and error histogram plots for the discussed hybrid nanofluid. It is observed that fluid velocity reduces for enhanced Darcy-Forchheimer number, magnetic parameters and boosted for enhanced modified Hartmann number. Temperature profile increases by increasing the Brownian motion and thermophoresis parameters. [ABSTRACT FROM AUTHOR]

A numerical study was carried out on dual solutions of rotating stretching/shrinking surfaces to explore the influence of convective boundary conditions, viscous dissipation, thermal radiation, and heat sources/sinks on 3-D hybrid nanofluid flow. Hybrid nanofluids have great potential for a variety of applications due to their unique properties and versatility. It is improved the effectiveness of heat transfer rates. The main objective of this study is to investigate the influence that certain parameters on the temperature and velocities profiles against the parameters, including the volume fraction of copper, suction effect, viscous dissipation, thermal radiation, Biot number and rotating parameter. Further, the impact of the suction effect and shrinking sheet on reduced heat transfer and skin friction is also considered against the volume fraction of copper. The nonlinear partial differential equations are transformed into a collection of ordinary differential equations by including linear similarity variables. The generated combination of higher order nonlinear ODEs is solved via a boundary value algorithm called bvp4c, which executes on the MATLAB computing tool. The findings confirmed the existence of two branches (dual solution) with varied quantities of copper volume fraction according to the shrinking surface and suction effect. Additionally, as the Biot number, Eckert number, thermal radiation, and copper volume fraction all increase in strength, the rate at which heat flows in both solutions also increases. However, the heat transfer rate declined as increased the suction effect. Besides, when a positive and negative increment is applied to the rotational parameter, both solutions suffer an increase in both velocities. In summary, unique solutions are obtained S < S ci for suction effect and λ < λ ci for the shrinking region. The outcomes came to the conclusion that hybrid nanofluid has a faster rate of transferring heat than standard nanofluid offers. [ABSTRACT FROM AUTHOR]

An incompressible unsteady free convective viscous MHD rotating flow past a moving plate embedded in a porous medium is considered with the influence of viscous dissipation, heat source effects. It is assumed that the flow rotates with angular velocity which is normal to the plate and also that a transverse magnetic field is applied along the normal to the plate. Appropriate dimensionless quantities are applied to change the governing equations into dimensionless form. Then the equations are solved numerically using the Galerkin finite element method. Some important characteristics of the fluid are studied. The results are in good agreement with the available literature. [ABSTRACT FROM AUTHOR]

In this study, the mixed convective stagnation-point flow of a Al 2 O 3 - C u / H 2 O hybrid nanofluid towards a stretched disc with a convective boundary and zero mass flux condition is described with mass suction and viscous dissipation effects. The process is accomplished by using thermophoretic and Brownian motion physical phenomena. After performing a similarity transformation on the PDEs in order to convert them into an ODE system, the bvp4c solver is then employed in order to carry out a numerical solution. In the study that was described above, the flow, heat, and mass transfer characteristics were investigated with the assistance of the Buongiorno model and the Devi and Devi model. The following characteristics were brought up as points of contention: ϕ 1 , ϕ 2 , λ , S , N t , N b , L e , E c , B i and B. There is a very good consonance among the existing and antecedent results in undeniable cases, as well as a connection error of approximately 0%. The velocity and temperature profiles upsurge with the increment of the nanoparticle volume fraction and mixed convection parameter, while the velocity increases with the addition of the suction parameters. As a result of this study, we are able to estimate the flow and thermal behavior of Al 2 O 3 - C u / H 2 O when the physical parameters are embedded. [ABSTRACT FROM AUTHOR]

Radiation in dissipative flow of hybrid nanofluid TiO 2 + Pb/water bounded between two coaxial cylinders is addressed. The hybrid nanomaterial is synthesized by adding nanoparticles lead and titanium dioxide TiO 2 and Pb in water as conventional fluid. Geometrically the outer cylinder exhibits rotation and the inner cylinder fixed. Constant strength magnetic field is taken radially. Thermal radiation and viscous dissipation describe heat transfer analysis. Mathematical equations (continuity, momentum, and energy) are obtained via mathematical modeling. Bvp4c method is used for solutions development. Influences of flow and heat related parameters on skin friction, velocity, temperature and Nusselt number have been shown. Velocity of fluids (hybrid nanofluid and nanofluid) is controlled by higher magnetic parameter while temperature and skin friction intensifies with it. Higher nanoparticle volume fractions (for both nanoparticles) reduce velocity while skin friction and Nusselt number are intensified. Moreover, higher radiation parameter causes temperature drop. In comparative analysis, the effects of hybrid nanofluid TiO 2 + Pb/water are dominant when compared with nanofluid TiO 2 + water . [ABSTRACT FROM AUTHOR]

Household warming, distillation, cooling systems, manufacturing heat, power plants, and irrigation water pumps are all applications for a parabolic trough surface accumulator (PTSC). This research examines the consequences of mixing nanosolid materials on PTSC installed on a solar aircraft wing, as well as the production of entropy. The Newtonian nanofluid model was used to investigate the consequences of thermal radiative fluxing, changing thermal conductivity, and upstream magnetism force limitations. Thermal radiative, and variable thermal conducting, the heat transfer discharge from solar aircraft wings is enhanced. Ordinary differential equations (ODEs) are numerically treated using a method known as the Keller-box method. Thermal radiative and thermal conducting effect adjustments that are positive develop the heat transference coefficient of solar aircraft wings. It is thought that graphene oxide (GO) based kerosene oil (K) can help with PTSC performance monitoring. We will also experiment with different nanoparticle concentrations to see how they affect the system's active characteristics. The thermodynamic performance of GO-K nanofluid has been described better than that of base nanofluid. GO-K has a heat transition rate of 15.03% higher than conventional fluid without GO. Theoretical simulations with documentation can be more useful in improving solar thermal energy schemes. [ABSTRACT FROM AUTHOR]

The aim of deploying hybrid nano fluids is to optimize the thermal transport characteristics of the model under study. Hybrid nano fluids incorporate composite nanopar-ticles that enhance thermal conductivity. Here, Silver(Ag) and Graphene oxide(Go) areused as nanoparticles with kerosene oil as the base fluid. The impacts of Ohmic heating, viscous dissipation, and thermal radiation are considered in order to model the problem of steady flow over a stretching/shrinking geometry. The model equations are tackled by a built-in scheme, bvp4c, in MATLAB.Moreover, there are dual solutions for a givenrange of pertinent parameters. The impact of the melting heat transfer parameter on the coefficient of skinfriction and Nusselt number for both hybrid nano fluid and nanoparticlesis considered. A comparison is established between our results and the pre-existing results, which are in good agreement. It is noted that the values of the coefficient of friction drag for the upper branch are reduced for a particular range of shrinking parameter values, while the opposite trend is observed for the lower branch. The magnetic force reduces the flow field and energy distribution for the stable branch while increasing them for the lower branch. [ABSTRACT FROM AUTHOR]

The flow of an electrically conducting fluid across a vertically positioned oscillating semi-boundless plate with uniform mass diffusion and temperature is examined in this study in terms of the effects of thermal radiation and viscous dissipation. The dimensionless governing equations were solved using an effective and unconditionally stable implicit finite-difference approach known as the Crank-Nicolson method. Based on the numerical results, the impacts of various physical parameter values on concentration, temperature; velocity; Sherwood numbers, Nusselt numbers and skin-friction profiles are displayed graphically and their consequences thoroughly analyzed. We observed that when the magnetic field, radiation and phase angle parameters are increased, the velocity is reduced. This shows that plate oscillation, radiation and magnetic fields affect the flow pattern significantly. [ABSTRACT FROM AUTHOR]

The current study proposes an eficient numerical method to evaluate the effects of the variable heat ux, viscous dissipation, and slip velocity on the viscous Casson Heat Transfer (CHT), considering the unsteady stretching sheet that took into account the effect of heat generation or absorption. In this respect, Finite Element Method (FEM) was employed to solve the resulting ODEs that described the problem. The effects of the factors governing the HT such as unsteadiness parameter, slip velocity parameter, Casson parameter, local Eckert number, heat generation parameter, and Prandtl number were studied. In addition, the local skin friction coeficient and local Nusselt number on the stretching sheet were also computed. Finally, the obtained solutions confirmed that the proposed procedure could be an easy and eficient tool for finding a solution to such uid models. [ABSTRACT FROM AUTHOR]

The energy transition to enhance heat transport during the flow of ternary hybrid nanofluid comprised of Copper (Cu), Iron oxide (Fe 3 O 4), Silicon dioxide (SiO 2) nanoparticles and Polymer as base liquid over a revolving disk surface has been reported. From the several existing techniques, adding nanoparticles to standard working fluids is an effective approach that might dramatically improve the rate of heat transfer. The Hall and radiation impacts are also considered. A mathematical model is developed by assuming the flow as incompressible and purely radial in a cylindrical coordinate system and appropriate similarity variables are introduced for problem simplification and dimensionless analysis. The solution of complex generated PDEs was calculated using semi analytical method known as Homotopy Analysis Method (HAM) after translating them into corresponding ODEs. It has been observed that the consequences of thermal radiation, dissipation term, unsteadiness and rotation parameters boost the energy transmission rate and enhances the heat transfer rate of tri hybrid nanofluids. However, Cu - Fe 3 O 4 nanoparticles in the base fluid remarkably magnifies the energy transmission rate. The unitary ternary hybrid nanofluid (Cu, Fe 3 O 4 , SiO 2) has higher velocity profiles as compared to unitary nano fluid (Cu) and hybrid nano-fluid (Cu-Fe 3 O 4). [ABSTRACT FROM AUTHOR]

A mixed convective driven wavy motion of the pseudo-plastic materials is very significant in different practical fields, like the production of paints and ketchup, etc. Blood flow through wavy vessels is another very practical aspect of this study. Energy conversion processes and effective resource use are one of the burning and hot topics when studying heat flow rate through materials. Main theme of this work is to optimize the heat energy conversion by introducing irreversible viscous dissipation and thermally radiative factors. In particular cases, the heat flow rate needs to be enhanced for low energy consumption. This is why, in such cases, the wavy surface flows are preferred by plane surfaces. The proposed problem is presented with highly non-linear mathematical equations. Some assumptions and variables address the mathematical equations in easily solvable forms. The findings are shown regarding the material's velocity, concentration, temperature, resistive forces, and heat-mass flow rates. A remarkable reduction in liquid velocity and enhancement in concentration and temperature is observed with the variation in amplitude of the wavy surface. The irreversible process is maximized due to the higher involvement of temperature ratio and thermal radiation factors, respectively. The ratio of infinite and zero shear rate viscosities reduced the concentration of the liquid. For method validation, a best-matched comparison is provided with literature. [ABSTRACT FROM AUTHOR]

An analysis has been carried out to study the two-dimensional free convective boundary layer MHD nanofluid flow past an inclined plate with heat generation, chemical reaction and radiation effects under convective boundary conditions. The partial differential equations describing the flow are coupled nonlinear. They have been reduced to nonlinear ordinary differential equations by utilizing a similarity transformation, which is then solved numerically with the aid of the Runge-Kutta-based shooting technique. Graphs depict the influence of different controlling factors on the velocity, temperature, and concentration profiles. Numerical findings for skin friction, Nusselt number and Sherwood number are reviewed for distinct physical parameter values. In a limited sense, there is a good correlation between the current study's results and those of the earlier published work. [ABSTRACT FROM AUTHOR]

The research explores the use of iron oxide nanoparticles to enhance the thermal properties of fluids like water and ethylene glycol. These nanoparticles find applications in engineering and medicine, including wastewater treatment and coatings. The study investigates magnetic nanoparticle movement in a permeable enclosure, considering heat, magnetic field, and electromagnetic effects. Using the MAC method, dimensionless equations were solved, and results were presented through graphs, charts, and tables. Findings show nanoparticle volume significantly impacts heat transfer in nanofluids compared to base fluids. Increasing nanoparticle volume from 0 to 0.05 improved nanofluid heat transfer by 0.278% and base fluid by 0.303%. Heat absorption and generation improved nanofluid transfer by 15.819% and base fluid by 0.596%. Nusselt number increased with higher Eckert number and heat source/sink parameters in both nanofluids and base fluids. [ABSTRACT FROM AUTHOR]

The present work investigates quadratic convection on magnetized viscous fluid flow on a circular elastic surface susceptible to Rosseland nonlinear thermal radiation and the nonlinear Boussinesq approximation. The flow is traversing through a Darcy-Brinkman-Forchheimer porous material. The energy equation investigates the implications of heat source/sink, Joule heating, and viscous dissipation. Utilizing suitable similarity variables, the hypothesized mathematical modelling is converted into nonlinear systems. Numerical solutions of nonlinear differential equations are computed using the spectral technique, often recognized as the spectral local linearization method (SLLM). The proposed approach SLLM is based on decoupling and linearizing systems of linear equations using a basic linearization process combined with spectral collocation linearization. The computational findings for nondimensional parameters are reported for the velocity and temperature profiles. As a particular case of our investigation, we also perform a comparison with published results. [ABSTRACT FROM AUTHOR]

The energy loss during the beating cilia phenomenon in the human stomach causing acidity in the blood flow under certain conditions has been a serious topic in the modern medical field. In the current study, authors have focused the entropy generation effects and irreversibility comparison on the flow of cilia generated metachronal waves of Cu-blood nanofluid through a curved channel by considering the effects of viscous dissipation and externally applied magnetic field. Due to the complex nature of the stream regime, curvilinear coordinates system is taken into consideration to present the constitutive expressions for bi-dimensional flow. Due to metachronal waves generated due to row wise beating cilia, authors have employed the constraints like large wave number so that the uniform pressure can be assumed over the cross section and the low Reynolds number to neglect the inertial forces. Unsteady flow of the problem producing partial differential equations is made steady by transforming it from a fixed frame to the wave frame of reference which finally provides the system of coupled ordinary differential equations along with cilia oriented non-homogeneous boundary conditions. This system has been solved analytically by incorporating a perturbation technique (HPM) to get the expressions for velocity, stream functions, pressure gradient and thermal profile. In the whole analysis, key findings are: The magnetic field reduces the flow speed in left side of the channel but increases the temperature of the system in the whole region. Entropy of the system can be reduced by diminishing the magnetic field effects and viscous dissipation, also the magnetic field is affecting the flow in the sense of contracting the bolus size. It is concluded that entropy due to thermal transfer is less than that of the whole system. More studies on the topic can be developed by considering the microorganism effects in three dimensional geometries with cilia at the boundaries. [ABSTRACT FROM AUTHOR]

In this study, we investigated the heat and mass transport properties of a non-Newtonian Casson-Williamson nanofluid flow. We explore the effect of viscous dissipation and the velocity slip boundary condition on the mechanism of heat and mass transfer due to a stretching sheet which embedded in a porous medium with heat generation under the influence of both thermal radiation and a uniform magnetic field. All physicochemical characteristics of Casson-Williamson nanofluid are considered to be constant. The nanofluid concentration is investigated under chemical repercussions as a result of the movement of the nanofluid particles. This study assumes that there is no suction (solid wall). A set of nonlinear partial differential equations with boundary conditions are used to mathematically model this physical problem. The numerical solution for the differential equations with the related boundary conditions was illuminated using the Runge–Kutta approach in conjunction with the shooting technique. The numerical examination is then pictorial displayed to show the impact of various governing factors on velocity, temperature, and concentration. The non-Newtonian nanofluid has a faster velocity in the absence of a magnetic field than in the presence of it, although the temperature field has the opposite trend. Further, the skin-friction coefficient increased as the porosity parameter increased, whereas the rate of heat transfer dropped. [ABSTRACT FROM AUTHOR]

The present study investigates MHD Casson nano fluid under the influence of exponential temperature-dependent thermal conductivity and variable viscosity past a stretching surface. After the application of similarity transformations, the governing partial differential equations of the modelled problem are converted into ordinary differential equations and then a solution is achieved with the assistance of the shooting method. The solution obtained with the help of shooting technique is used to analyze the distribution of mass and heat flux over sheet. The effects of various governing parameters on the dimensionless velocity, temperature, and concentration distribution were analyzed and discussed in detail. The simulations of the presented model demonstrated that the surface drag increases as each of the Casson parameter and temperature-dependent thermal conductivity parameter is boosted while the rate of heat transfer is diminished. It is also observed that an increment in the temperature near the surface is noted against the thermal conductivity parameter, whereas the opposite trend is observed away from the surface. [ABSTRACT FROM AUTHOR]

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution's validity. [ABSTRACT FROM AUTHOR]

Here flow for radiative hybrid-nanomaterial (MgO + M o S 2) satisfying Darcy-Forchheimer relation is addressed. Ethylene glycol C 2 H 6 O 2 is utilized as a base fluid. Magnesium oxide (M g O) and Molybdenum disulfide (M o S 2) are considered as distinct nanoparticles. Thermal expression is examined through heat generation and viscous dissipation. Analysis for Cattaneo-Christov theory is carried out. Condition for melting heat is deliberated. Entropy generation is examined. Variable thermal conductivity of hybrid nanomaterial is taken. Suitable transformations are implemented to obtain nonlinear dimensionless systems. Optimal homotopy analysis method (OHAM) is implemented for computations. Temperature, velocity and entropy generation are scrutinized physically. Nusselt number and skin friction are discussed. Conclusion synthesis salient points. Present work is relevant in metallurgical engineering and polymer processing. The findings conclude that Forchheimer number correspond to decline in velocity. Entropy rate and thermal field have similar trend for heat generation variable. A decrease in velocity against melting variable is noted. Temperature increases for variable thermal conductivity and thermal relaxation parameters. Entropy optimization improved for Brinkman number. Skin friction decays for porosity parameter and Forchheimer number. Skin friction improves for melting variable and Forchheimer number. Entropy augments against higher thermal relaxation time. Higher melting variable lead to an enhancement for Nusselt number. There is an improvement for radiation through Nusselt number and temperature. [ABSTRACT FROM AUTHOR]

Convection differential equations that include momentum, energy and mass balance equations are used for the simulations of boundary layer (BL) flows. In convection analysis, it is in execution to dimensionless the BL system through similarity variable. However, a wide range of convection differential equations cannot be non-dimensionalized using similarity variable therefore the intent of this manuscript is to develop non-similar model for the forced convective magnetic flow of a viscous fluid above an exponentially expanding surface saturated by nano-fluid. The non-similarity is due to the exponential stretching of the surface and viscous dissipation. Influences of chemical reaction and heat generation are also incorporated. The non-similarity transformation is applied to the nonlinear partial differential system (PDE's) to transform them into dimensionless PDE's. Non-similar system is analytically approximated by adapting local non-similarity (LNS) and then it is numerically simulated by finite difference based bvp4c algorithm to explore the influences of significant numbers named as Prandlt number, chemical reaction, magnetic field, Brownian motion, heat generation, Eckert number, thermophoresis on concentration, velocity and temperature distribution. Auxiliary consequences presume that the heat penetration in fluid rises with enhancements in Brownian motion and Prandtl number, while it can be perceived here that for positive estimations of heat generation causes the thicker temperature field. Increasing non-similarity variable and magnetic number become reason for the reduction of temperature profile and chemical reaction is reason of reduced concentration profile. [ABSTRACT FROM AUTHOR]

In this paper, the classical Rayleigh–Bénard convection model is considered and solved numerically for extremely large viscosity variations (i.e., up to 10 30 ) across the mantle at a high Rayleigh number. The Arrhenius form of viscosity is defined as a cut-off viscosity function. The effects of viscosity variation and viscous dissipation on convection with temperature-dependent viscosity and also temperature- and pressure-dependent viscosity are shown through the figures of temperature profiles and streamline contours. The values of Nusselt number and root mean square velocity indicate that the convection becomes significantly weak as viscosity variation and viscous dissipation are increased at a fixed pressure dependence parameter. [ABSTRACT FROM AUTHOR]

The viscoelastic fluid flow over a non linear stretching porous sheet is considered in this analysis. The case of suction and injection is also discuused. The effects of thermophoresis and brownain motion with viscous dissipation is taken into account. Under the flow assumptions, boundary layer approximation applied on the mathematical model and developed the partial differential equations. The similarity variable is applied on the partial differential equations which converted into ordinary differential equations. The dimensionless system further solved through numerical technique bvp4c method. The results of the current problem achieved after solving the problem which presented through graphs and table. Influence of numerous physical parameters on velocity function, concentration function and temperature function are manipulated through graphs. The tabular results are schemed to display skin friction and local Nusselt number. The higher values of N b which enhanced the velocity profile but declines velocity profile due to higher values of Ec. The thermal thickness enhances due larger values of γ and Pr but thermal thickness declines due to higher values of Ec and N t. The concentration profile enhances due to enhancing the values of Ec and Pr but concentration profile declines due to increasing the values of N t. Nusselt number enhaced due to higher values of Ec , S c and N t but declines of higher values of Pr. [ABSTRACT FROM AUTHOR]

Owing to the improved thermophysical properties of nano-materials, the nanofluid convey novel applications in industries, engineering as well as bio-medicals. With high efficiency performances, the nanoparticles include applications in various cooling and heating systems, energy production, aerospace engineering, thermal extrusion, bio-medical applications like treatment of diseases, brain tumour, surgical applications and many more. Moreover, the magneto-nanofluids have the characteristics in the flow of blood in the human artery. The current analysis deals with the free convective unsteady flow of viscous nanofluid subject to the magnetic force over a vertical plate in presence of porous space. The heat transfer phenomenon is accessed by utilizing the additional features like Joule heating, viscous dissipation and absorption coefficients. In addition to the volume fraction of the nanofluid, the effect of the chemical reaction is also introduced. The solution procedure for the modified time-dependent boundary value problem is performed by using the code in-build MATLAB namely Built-in-Shooting method. The change in velocity, temperature and concentration of nano-materials is examined through various graphs. The physical consequences of flow parameters like porosity parameter K p 1 ⩽ K p ⩽ 3 , thermal Grashoff number Gr 1 ⩽ G r ⩽ 3 , solutal Grashoff number Gc 1 ⩽ G c ⩽ 3 , magnetic field parameter M 1 ⩽ M ⩽ 3 , thermal radiation parameter Nr 0.1 ⩽ N r ⩽ 1 , radiation absorption parameter Q 0 ⩽ Q ⩽ 0.5 , Prandtl number Pr 2 ⩽ Pr ⩽ 21 , Eckert number Ec 0 ⩽ E c ⩽ 0.4 , heat source S - 0.2 ⩽ S ⩽ 0.2 , chemical reaction parameter Kc 1 ⩽ K c ⩽ 4 , nanoparticles volume fraction ϕ 0.0 ⩽ ϕ ⩽ 0.1 , Lewis number Le 1 ⩽ L e ⩽ 10 on velocity, temperature and concentration distributions is graphically analyzed. The results show that skin friction coefficients decline with buoyant forces. A lower numerical variation in Nusselt number is resulted with heat source parameter. Moreover, a sharp fall in nanofluid concentration is noticed with increment of chemical reactants and Lewis number. [ABSTRACT FROM AUTHOR]

The present study aims to present an elaborated evaluation of stratified magnetohydrodynamics (MHD) Jeffrey nanouid flow towards a stretching surface in the presence of gyrotactic micro-organisms. The flow was analyzed by considering viscous dissipation, Brownian motion, Joule heating, and thermophoresis as well as assuming the thermal, solutal, and motile density stratification aspects. The governing nonlinear system of Partial Differential Equations (PDEs) that controls the flow was turned into a group of nonlinear Ordinary Differential Equations (ODEs) using appropriate similarity transformation and later, they were numerically solved through Keller-box approach and algebraic software Matlab. The effects of different parameters on the fluid motion, heat, mass, density of the motile micro-organisms, local skin friction, local Nusselt number, local Sherwood number, and local density number of the motile micro-organisms were also evaluated using graphs and tables. The results indicated that the density of motile micro-organisms was a decreasing function of the bioconvection Lewis number, bioconvection Pecket number, and microorganisms' concentration difference. The Sherwood number and density rate of motile micro-organisms were higher in the case of magnetic parameter and Lewis number. [ABSTRACT FROM AUTHOR]

• MHD Maxwell fluid. • Melting surface. • Entropy Generation Analysis. • Heat transfer in Maxwell fluid flow over a melting surface alongwith entropy generation has not been discussed in literature yet. This research article is aimed to investigate the behavior of MHD two dimensional flow of Maxwell nanofluid. Non-Newtonian Maxwell nanofluid is considered in the present study to evaluate the phenomena of heat transfer of steady boundary layer flow. The flow of fluid is derived over a stretching melting surface. Observation are made for the concise and terse effect of viscous dissipation, magnetic field and Joule heating. Porous medium is taken into account to observe the flow. The entropy generation model for Maxwell nanofluid is analyzed against different parameters. The set of highly non linear PDE's are generated. A pertinent and relevant similarity transformation is applied to alter the fundamental PDE's of momentum and energy into set of ODE's. The set of non-linear ODE's are solved by using the homotopy analysis method. The flow features and the heat transfer characteristics prevailing this phenomena are investigated and argued for different engaging flow parameters. Tabulated and graphical results for the skin-friction coefficient and Nusselt number are presented for various values of the flow concerened parameters. Entropy generation get hightened increases against increasing values of porosity parameter, Reylond number, nanoparticle fraction, Brinkman number and Hartman number during the flow. [ABSTRACT FROM AUTHOR]

In this work, the flow of ternary hybrid nanomaterials filling porous spaces is investigated in the presence of magnetohydrodynamics (MHD) and nonlinear convection. Three dissimilar nanoparticles copper (C u) , alumina (Al 2 O 3) , and magnesium oxide (M g O) are employed. Various features including Ohmic heating, heat generation, and variable thermal conductivity are studied, along with nonlinear radiation and entropy analysis. Solutions are developed using the ND Solve (shooting) method in Mathematica software. Analysis of parameters of interest is conducted, with conclusions highlighting key outcomes. Results show an increase in the thermal field for Eckert number and radiation, while a decrease in liquid flow is observed with increasing the magnetic parameter. The heat transport rate exhibits an opposite trend between heat generation and radiation. Temperature ratio parameter and Prandtl number show opposite trends in the thermal field, while the temperature gradient decreases against variable thermal conductivity. The drag force follows a similar trend against nonlinear convective and porosity variables. The entropy rate increases with the Brinkman number, and both porosity and radiation have an increasing impact on entropy rate. An increase in liquid flow is noted with the nonlinear convection variable. A comparative study of heat transport rate through the Prandtl number shows good agreement. [ABSTRACT FROM AUTHOR]

The significance of the study lies in illuminating the consequences of thermophoresis and Brownian motion on heat and mass transfer, offering valuable insights crucial for practical applications. The purpose of this study is to look into how Casson–Williamson and Maxwell nanofluids flow over a stretching sheet in order to understand how heat and mass move in that situation. The mathematical structure comprises a set of partial differential equations (PDEs) converted into ordinary differential equations (ODEs) through a similarity transformation. Subsequently, the well-established MATLAB BVP4C method, integral to the finite difference approach, is applied to solve these ODEs. For the assurance of the method's reliability and precision, the acquired outcomes are cross-referenced with existing literature, which is a crucial step in validation. The numerical results are depicted visually and in tables, specifically highlighting the impulse of different influencing elements on the Nusselt number, friction factor, and Sherwood number. Notably, an enhancement within the Brownian motion parameter (N b) and the thermophoresis parameter (N t) is found to correspond to higher local Nusselt numbers, indicating an enhancement in heat transfer. Conversely, elevated quantities of the Brownian motion parameter (N b) result in a reduction in local Sherwood numbers. Physically, a higher Brownian motion parameter causes significant nanofluid particle displacement, enhancing their kinetic energy and intensifying heat generation in the boundary layer. The magnetic parameter (M) influences speed profile decline caused by the Lorentz force, which hinders fluid motion. • The study performed to investigate Maxwell nanofluid flow over a stretching sheet. • BVP4c technique in MATLAB is utilized to solve the governing equations of the system. • Numerical simulations are run on Maxwell nanofluid flow over a porous medium. • Magnetic parameter influence fluid behavior by inducing MHD effects. [ABSTRACT FROM AUTHOR]

In this study, authors explore how magnetic fields and the buoyancy force resulting from temperature differences work together. The study is focusing at how an Eyring-Powell nanofluid behaves in a ciliated channel when both natural convection and magnetic effects are at play. A technique called the symplectic metachoronal wave has been used to analyze this analysis. A physical assumption of small Reynolds number is considered to simplify the equations describing the flow rate of the Eyring-Powell nanofluid, making it easier to understand. To get a closed form solution, we have incorporated Adomian decomposition method (ADM). It has been observed that the flow is sped up by 10% with increase in the Eyring-Powell fluid parameter M. The quantity of heat transfer increases with increasing values of the Hartmann, Eyring-Powell fluid parameters, and Brinkmann numbers. This study has implications for bio-inspired engineering, medical applications, and the design of microfluidic devices. [ABSTRACT FROM AUTHOR]

This research article elaborates the salient attributes of sundry variables i.e., Darcy-Forchheimer number, mixed convection parameter, porosity parameter, Weissenberg number, slip parameter, Prandtl number, activation energy parameter and chemical reaction parameter on the forced convective Darcy-forchheimer flow of non-Newtonian fluid (Carreau-Yasuda fluid) subject to stretchable and flat surface of the sheet. A general mathematical form of the entropy generation rate for Carreau-Yasuda fluid is derived in the presence of porosity irreversibility, fluid friction irreversibility, heat transfer irreversibility and Joule heating irreversibility through second law of thermodynamics. The fluid flow is saturated and magnetized through Darcy-Forchheimer porous medium and applied magnetic field. The energy equation is modeled in the presence of viscous dissipation. Series solutions are calculated by semi analytical method HAM. The behavior of pertinent flow parameters is discussed graphically. The main interest in giving to the engineering curiosity like velocity gradient and Nusselt number. The main theme of this research communication is to enhance the information of entropy optimized flow and heat and mass transport, and to inspire the investigators and analysts to scrutinize gradually innovative attributes that can take improvement on the entropy generation minimization. [ABSTRACT FROM AUTHOR]

This article unveils the combined impact of heat generation/absorption and Joule heating on MHD flow of Ag-H2O nanofluid into a porous stretching/shrinking divergent/convergent channel with viscous dissipation and solid volume fraction. The mathematical modeling is presented for the existing equations of continuity, momentum, and energy fraction. The reduced boundary value problem is solved numerically employing Runge-Kutta-Fehlberg (RKF) method via shooting scheme and then the outcomes are sketched and interpreted. The results explore that the thermal boundary layer thickness of the stretching divergent and the shrinking divergent channels enhance by increasing the value of the Eckert number, while the opposite tendency is scrutinized on the momentum boundary layer thickness by increasing the value of the porosity parameter for the stretching divergent and the shrinking convergent channels. [ABSTRACT FROM AUTHOR]

In recent years, investigations on hybrid nanofluids have rapidly increased, and results show that hybrid nanofluids are more valuable heat transfer fluids for engineering applications due to their excellent thermophysical characteristics. Therefore, the present numerical study is conducted to approximate the thermal transport characteristics of hybrid nanofluids over a vertical stretching/shrinking surface. The hybrid nanoparticles are alumina (Al 2 O 3) and silver (Ag), with water as the base fluid. The transportation phenomenon occur in Darcy-Forchheimer medium porous material with thermal radiation, Joule heating and heat source/sink effects. The governing PDEs are transformed by a appropriate similarity transformations into non-linear ODEs. In MATLAB, the built-in numerical approach bvp4c is used to proceed the approximate integration of flow work. The behaviors of some physical flow constraints are analyzed through graphs and numerical values. The results revealed that a rise in nanoparticles volume fraction boosts the friction drag coefficient and shows a declining trend toward thermal transfer. Furthermore, for the first solution, the skin friction coefficient and heat transfer rate rise as the suction strength increases. In addition, raising the magnetic parameter value enhances the flow field while reducing the fluid temperature. [ABSTRACT FROM AUTHOR]

The studied problem focuses on the flow of Casson nanofluid induced by a stretched surface in the presence of a magnetic field and exposed to variable surface heat flux, with an emphasis on enhancing thermal efficiency. This research aims to highlight the flow of Casson nanofluid at the stagnation point on a stretching sheet, taking into account the influence of heat generation and variable thermal conductivity. The fluid being examined exhibits a steady-state two-dimensional flow. The formulation of the model involves deriving partial differential equations, which are later converted into ordinary differential equations using similarity transformations. This particular research stands out by introducing an innovative mathematical model for Casson nanofluid, taking into account variable surface heat flux and covering several implications that have not been explored in current literature. We utilize the shooting method to compute numerical solutions for the formulated equations. Graphical representations are used to illustrate the numerical results for velocity, concentration, and temperature distribution. Furthermore, tabulated findings encompass the Sherwood number, skin friction coefficient, and local Nusselt number. A comparison with a previous study from the literature was conducted, demonstrating a robust agreement between our results and theirs. Several compelling findings indicate that the local Nusselt number rises as the velocity ratio parameter, suction parameter, thermal conductivity parameter, and heat flux exponent increase. Conversely, the Casson parameter, magnetic number, heat generation parameter, and thermophoresis parameter are observed to lower the local Nusselt number. • This study aims to investigate heat and mass transfer phenomena in MHD Casson nanofluid flow, influenced by varying surface heat flux.. • The main aim is to enhance thermal efficiency using a magnetic field while considering heat generation during heat transport. • A less explored area in this field concerns boundary conditions, specifically regarding suction velocity with varying thermal conductivity properties. [ABSTRACT FROM AUTHOR]