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In the present study, the thermal behavior of a longitudinal fin considering three types of heat transfer mechanisms (conduction, convection, and radiation) is investigated. For this research, thermal conductivity, heat source, and heat transfer coefficient are assumed nonindependent. A semianalytical scheme called the Galerkin Method is utilized for solving the dimensionless governing equation. The impacts of important physical variables like Peclet number, gradient of thermal conductivity, thermo‐geometric parameter, and radiation–conduction parameter on temperature profiles are analyzed comprehensively. The obtained results indicate that raising the thermo‐geometric parameter from 0 to 2 leads to a 32% reduction in the temperature profile. Also from the results, it can be found that a 28% increment in the temperature is observed by changing the gradient of thermal conductivity from 0 to 2. [ABSTRACT FROM AUTHOR]

The numerical analysis is conducted to evaluate the heat generating as well as Soret–Dufour influences on magnetohydrodynamic unsteady chemically reacting fluid. It is owing to an exponentially stimulating perpendicular porous plate entrenched in the absorbent medium by considering ramped surface temperatures and concentrations in the endurance of thermal radiating. The fundamental governing set of equations of the fluid dynamics in the flow is converted into dimensionless form by inserting suitable dimensionless parameters and variables, and the resulting equations are numerically solved by the efficient Crank–Nicolson implicit finite difference method. The influence of several important substantial parameters into the model on the velocity, temperature, and concentration of the fluid, in addition to the skin‐frictions coefficient, Nusselt's number along with Sherwood's number for both thermal conditions has been studied and explored intensely by making use of graphs and tables. It is discovered that, with mounting values of Dufour, heat generating as well as thermal radiating parameters, the fluid temperatures, and velocity enhanced. Likewise, it is noticed that increasing the Soret parameter causes escalated fluid velocity and concentration, whereas the reverse result is noted with the chemical reaction parameter. [ABSTRACT FROM AUTHOR]

A convective‐radiative fully wet porous inclined longitudinal fin of exponential profile is the focus of the current work. The thermal behavior of the fin under unsteady conditions has been analyzed for adiabatic and convective boundary conditions. The exponential fin and its counterpart inverted exponential fin are simultaneously investigated by considering temperature‐relevant thermal conductivity and heat generation. The modeled governing equation upon nondimensionalization reduces to a partial differential equation which is computed by employing the finite difference approach. The impact of relevant parameters like the convective parameter, radiative parameter, wet porous parameter, dimensionless time, exponential index, dimensionless ambient temperature, generation number, thermal conductivity parameter, and angle of inclination on thermal characteristics of exponential and inverted exponential fin structures with adiabatic and convective boundary restrictions have been examined. One of the main outcomes was that the inverted exponential fin with an adiabatic tip gives rise to the highest thermal curve, and the tapered exponential fin with a convective tip resulted in the lowest thermal curve. [ABSTRACT FROM AUTHOR]

The current scrutinization concentrated on the consequences of viscous dissipation and chemical reaction on unsteady MHD two‐dimensional free convective fluid flow past a semi‐infinite inclined permeable plate with radiation absorption and heat generation. The governing equations are determined analytically by employing the perturbation technique. The impact of various physical estimators on velocity, temperature, concentration, skin friction, and Nusselt number along with Sherwood number were exemplified quantitatively through graphs. It was concluded that velocity declined with the incremental values of Eckert number, but contradictory impact occurred in the case of skin friction. In addition temperature, Nusselt number, as well as velocity, declined with the progressive values of radiation absorption. However, skin friction was accelerated with the augmented values of radiation absorption. Velocity accelerated, with the progressive values of angle of inclination. Concentration declined with the various augmentation values of chemical reaction as well as Schmidt number. [ABSTRACT FROM AUTHOR]

The study looks at the characteristics of an unsteady magnetohydrodynamic (MHD) free convective hybrid nanofluid flow with heat transfer to an oscillating vertical plate. The impacts of thermal radiation and internal heat generation, as well as ramped wall temperature conditions at the boundary, are included in the study. The base fluid water is combined with alumina and copper nanoparticles to model fluid flow. A flow issue like this can occur in a variety of industrial and technical processes, such as aerodynamic heating, polymer manufacturing, and so on. The built dimensional controlling equations are transformed into the nondimensional form of equations using feasible similarity variables. The Laplace transform technique is used to solve the nondimensional equations analytically. Pictorial representations are used to investigate the sway of physical characteristics on velocity and temperature distributions. For all of the implanted parameters, the values of the local skin‐friction coefficient and local rate of heat transfer are determined at the boundary and displayed in tables. The velocity profile increases as the thermal Grashof number and time increase, but the magnetic parameter has the opposite effect on the ramping surface temperature and the isothermal plate. Similarly, the temperature profile of nanofluids has been discovered to have a direct relationship with characteristics such as thermal radiation, time, and internal heat generation. [ABSTRACT FROM AUTHOR]

Fluid viscosity manages several engineering processes and keeps its leading role in lubrication models, biological models, polymer processes, melt solutions, colloidal suspensions, and mayonnaise. The cross viscosity model is the most appropriate model, which interprets the key features of non‐Newtonian fluids in the region of shear‐thinning/thickening when very high and very low shear rates are applied. This article focuses on the mathematical model of three‐dimensional Cross nanofluid and interprets its aspect of infinite shear rate of viscosity over the expanding sheet. Velocity is studied through placing inclined magnetic dipole effect, transportation phenomenon is brought by considering the radiation effects, heat generation and chemical process is engaged for concentration of nanoparticles. The geometry of this mathematical model is expanding the stretching sheet with velocity slip, and convective heat conditions are associated. Similarity variables are being utilized for conversion dimensional mathematical model into nondimensional one. For the pursuit of numerical solution of the system of nondimensional mathematical model, the numerical technique Bvp4c is utilized. Furthermore, Matlab graphs and statistical analysis for all physical parameters and physical quantities are shown in the result and debate section. Due to inclination of angle Lorentz force producing in increasing manner, hence flow is opposed, and velocity of fluid is dropped for (β*=0.5 $\beta * \,=0.5$) and (β*=0.0 $\beta * \,=0.0$) and for increasing value of n index, the velocity of fluid flow is decreasing. [ABSTRACT FROM AUTHOR]

The performance of nanofluid in the heat transport phenomena showed satisfactory results, which have been considered by scientists and researchers. The dispersion of two nanoparticles to form a mixture which named as hybrid nanofluid. It has been proved experimentally that hybrid nanofluid has good thermal performance compared to unitary nanofluid. The present study inspected the convective flow of a Williamson hybrid nanofluid through a cone and wedge in a porous medium of different shapes of nanoparticles (cylindrical‐, spherical‐, blades‐, platelets‐, bricks‐) under the influence of a magnetic field. The partial differential equations were converted to an ordinary differential equation and the resulting equations were solved using the bvp4c MATLAB code. The effect of some important physical parameters on both the velocity and temperature profile was graphically plotted and the effect of the shape and size of nanoparticles was discussed, the numerical values of the friction coefficient and Nusselt number were obtained. As observed, the friction factor of Ag–TiO2–H2O hybrid nanofluid was more than that of TiO2–H2O nanofluid. A significant enhancement in bulk temperature is seen for the Ag–TiO2 hybrid and nanofluid formed by blade‐shaped nanoparticles followed by cylindrical, platelet, brick, and spherical nanoparticles. In addition, for a 5% volume fraction of using blade nanoparticles shape givean increase in skin friction factor about 4.8% compared tobrick hybrid nanoparticles. A comparative study of different forms for Ag‐TiO2was presented graphically. [ABSTRACT FROM AUTHOR]

In the present study, the influence of numerical analysis involves the transfer of heat for moving fin under convection and radiation with fluid properties depending on internal heat generation is considered. The temperature field for the fin is derived based on the defined geometry. This is transformed into a linear model as per the boundary conditions. The dimensionless analysis is performed, and the equations obtained are solved by Runge–Kutta Fehlberg fourth‐order method coupled with the shooting method. The effects of the relative parameters are studied and depicted graphically. Finally, the computational observation indicates that there is an enhancement of temperature variation under the influence of thermal conductivity gradient, heat generation, and opposite behavior results. In understanding the thermal characteristics of various effects, it was seen that thermo geometric film, radiation conduction, and Peclet number were very useful for many industrial applications. To validate the numerical scheme, a comparative study has been done with an earlier result on a few nondimensional parameters and was found in good agreement. [ABSTRACT FROM AUTHOR]

This study explores the entropy generation analysis on unsteady nonlinear radiative ethylene glycol‐based Casson nanofluid flow near stagnation point towards a stretching sheet through a porous medium. Analysis has been accomplished in the presence of an inclined magnetic field, heat generation, homogeneous–heterogeneous reactions, and viscous dissipation with velocity slip and convective boundary conditions. The nondimensional governing equations are solved by the shooting technique with the help of the RK45 method. We have experimented with copper and silver nanoparticles and a comparative analysis has been highlighted for both copper and silver nanofluids. Numerical outcomes are executed by the MATLAB built‐in bvp4c function. The consequences of the experiment for various pertinent flow parameters are portrayed by graphs and tables for both the Ag‐ and Cu‐Casson nanofluids. Results reveal that the enhancement of nanoparticles volume fraction accelerates temperature but it slows down concentration and velocity distributions. Higher values of the Eckert number boost velocity and temperature but reduce skin friction coefficient and Nusselt number. Enhancement of the Brinkman number boosts up entropy generation but it slows down Bejan's number. The results of the model can be applied in the movement of biological fluids, separation of biomolecules, glass manufacturing, paper production, food processing, crude oil purification, polymer drag reduction, and cooling atomic reactors. [ABSTRACT FROM AUTHOR]

The impacts of MHD and heat generation/absorption on lid‐driven convective fluid flow occasioned by a lid‐driven square enclosure housing an elliptic cylinder have been investigated numerically. The elliptic cylinder and the horizontal enclosure boundaries were insulated and the left vertical lid‐driven wall was experienced at a fixed hot temperature, and the right wall was exposed to a fixed cold temperature. COMSOL Multiphysics 5.6 software was used to resolve the nondimensional equations governing flow physics. A set of parameters, such as Hartmann number (0≤Ha≤50 $0\le {Ha}\le 50$), Reynolds number (102≤Re≤103 $1{0}^{2}\le {Re}\le 1{0}^{3}$), Grashof number (102≤Gr≤105 $1{0}^{2}\le {Gr}\le 1{0}^{5}$), heat generation‐absorption parameter (−3≤J≤3 $-3\le J\le 3$), and elliptical cylinder aspect ratio (AR) (1.0≤AR≤3.0 $1.0\le {AR}\le 3.0$) have been investigated. The current study discovered that for low Reynolds number, the adiabatic cylinder AR of 2.0 provided the optimum heat transfer enhancement for the model investigated, also the impact of cylinder size diminishes beyond Gr = 104. But for high Reynolds (Re = 1000), the size of the cylinder with AR = 3.0 offered the highest heat transfer augmentation. The clockwise flow circulation reduces because of an increase in AR, which hinders the flow circulation. In addition, heat absorption supports heat transfer augmentation while heat generation can suppress heat transfer improvement. [ABSTRACT FROM AUTHOR]

The present article describes the magnetohydrodynamic flow of a moving Jeffrey fluid along a convectively heated porous stretching surface with second‐order velocity slip and radiation absorption effects. Furthermore, chemical reactions and viscous dissipation impacts are also taken into account. The governing equations are converted into dimensionless ordinary differential equations (ODEs) using appropriate similarity transformations. The highly nonlinear ODEs are solved numerically by employing a shooting technique based on the Runge–Kutta Cash–Karp formula. The figures are used to study the variations in temperature, velocity, and concentration profiles for several physical factors. The numerical values of the local skin friction, Sherwood number, and Nusselt number are explained and shown in tables. The analysis reveals that the velocity profile is enhanced for amplifying values of velocity ratio parameter and first‐order velocity slip parameter. However, the temperature profile of Jeffrey nanofluid is highlighted w.r.t. Eckert number and radiation absorption parameter. This study may find significant applications in polymer production, food processing, instrumentation, combustion modeling, catalytic chemical reactors, and so on. [ABSTRACT FROM AUTHOR]

A numerical investigation on MHD fluid flow in parabolic mode has been performed to point out its significant properties. Thermal radiation, porous medium, heat generation, chemical reaction, and thermal diffusion along with variable temperature and concentration are taken into consideration in the analysis. The novelty of the work is the inclusion of heat generation and thermal diffusion along with exponentially varying temperature and concentration. The constituent governing equations are solved by using finite difference schemes in explicit form. The fluctuations in velocity, concentration, and temperature are observed and discussed with the help of graphs as well as numerical data. Their gradients are also calculated and analyzed the flow properties by using numerical tables. The existence of heat generation, as well as viscous dissipation, creates an increment in the temperature. The gradient of heat transfer rises with the impact of Prandtl number and decay in it is examined under the existence of a source of heat and viscous dissipation. [ABSTRACT FROM AUTHOR]

The key goals of this manuscript are (i) to investigate the heat transfer and unsteady flow properties of a viscous hybrid nanofluid on a stretching sheet having nonzero slot velocity, and (ii) to examine the impacts of magnetic field parameter, stretching parameter, nanoparticle volume fraction, and heat generation parameter on the Nusselt number and skin friction coefficient numerically. The Tiwari‐Das nanofluid model is used. The mathematical (PDEs) equations controlling border layer flow and heat transfer are resolved by applying a numerical finite‐difference technique in the Crank Nicolson style. For the validation process, the analytical solution is established using the Laplace transform technique and is compared with the numerical solution for a particular case and found to be in superb agreement. [ABSTRACT FROM AUTHOR]

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement. [ABSTRACT FROM AUTHOR]

The importance of including an electromagnetic actuator as a moving boundary on the dissipative flows of weakly conducting fluids had led to many published facts. But, nothing is known on the generalized differential quadrature analysis of magnetohydrodynamics over a Riga plate with emphasis on the case of viscous dissipation and space‐dependent heat source. After deriving the simplified boundary layer equation that models the transport phenomenon, appropriate variables were used to non‐dimensionalize and parameterize the partial differential equations. Thereafter, the resulting set of ordinary differential equations was solved numerically by applying a powerful differential quadrature algorithm. Based on the outcome of the simulation, it can be concluded that the viscous frictional effect can be minimized at the Riga plate either by weakening the suction process or by heightening the magnetic parameter. Moreover, the Lorentz forces have a hastening effect on the fluid motion, in the case when those magnetic causes are directed in the same sense of the developed flow. [ABSTRACT FROM AUTHOR]

The numerical contribution of the natural heat flow of dusty hybrid nanofluid due to a square cavity filled with a porous medium with the effects of internal heat generation and the magnetic field is presented in this paper. The system of the problem equations is divided into hybrid nanofluid (Al2O3–Cu) phase equations and dusty phase equations, which are converted to a dimensionless form to be suitable for solving them numerically using the finite difference method. The results manifest in the streamlines, isotherms contours for both hybrid nanofluid phase and dust phase as well in local and average Nusselt numbers profiles. The numerical computations are performed and presented via graphs and tables due to the influence of governing physical parameters like (10≤Ra≤1400), (0≤Ha≤10), (0≤Dρ≤10), (0 ≤ Σ ≤ π/2), (0.1≤αd≤10), (0.0≤Φ≤0.1), (0.1≤αt≤0.9), and (0.01≤Ec≤0.07). The results indicate that increasing of fluid–particle interaction parameter for velocity leads to increment of the streamlines and isotherms of both the dust and hybrid nanofluid phases. A notable enhancement is found in the streamlines of the hybrid nanofluid phase and dust phase for high values of the Rayleigh number. The average Nusslet number ameliorates due to suspended dust particles in the hybrid nanofluid while deteriorates with increasing nanoparticle volume fraction. Furthermore, rising values of Hartmann number lead to reducing streamlines of the hybrid nanofluid and dust phases but an increase occurs with an increment of the inclined angle of the magnetic field. A notable agreement is obtained between the data of the present study and other previously published work. [ABSTRACT FROM AUTHOR]

Microporous channels are extensively elaborated technologies in a variety of engineering, and scientific applications, for example, microelectromechanical systems that are useful in developing the heat exchangers in miniaturized products such as heat sinks of the microchannel, micromixtures, and fuel cells of miniaturized products. Hybrid nanofluids have a better thermal performance as compared to the nanofluid. Based on this, the present study aims to concentrate on the magnetohydrodynamics Powell–Eyring hybrid nanofluid flow in a vertical porous channel with the aspects of porous medium, magnetism, convective condition, dissipation energy, heat generation, and radiation. A nondimensional technique is applied to alter the governing equations into a nonlinear system of ordinary differential ones that contain the convective boundary condition. The RKF 4–5th order method coupled with the shooting method has been utilized to find the numerical solution. From the perspective of numerical results, it is clear that the entropy generation boosts up for Grashof number, Biot number, and radiation parameter and it is the minimum for magnetism, Darcy number, and Eyring–Powell parameters. The comparison of results has been performed and it provides an excellent agreement. [ABSTRACT FROM AUTHOR]

In this paper, the analytical investigation of non‐Newtonian fluid flow through a turbine disc with a heat generation effect is considered. The flow mechanics through the turbine disc is modeled using a coupled system of higher‐order partial equations, which are transformed into ordinary order utilizing proper similarity transforms. Governing models are analyzed using the variation iteration and homotopy perturbation analytical methods. As observed from the results, the study shows enhancement of heat generation for non‐Newtonian fluid flow through turbine disc, reveals abating thermal distribution. More so, the graphical expression shows that heat generation improves up till mid‐disc. Thereafter, an increasing trend toward the fluid injection surface is observed. Validation of analytical solutions with numerical analysis boosts confidence in this study, which may be used to provide further insights into the engineering science of non‐Newtonian flow of hydraulic/lube oil in practical applications, such as hydraulic couplings. [ABSTRACT FROM AUTHOR]

The effect of multifluid flow on internal heat generation or absorption in a vertical channel in the presence of concentration is investigated in this paper. The fluids are incompressible in both regions, that is, Region‐I and Region‐II, and it is assumed the transport properties of fluid flow are constant. With the help of the analytical method, all the basic equations transformed into governing coupled nonlinear ordinary differential equations are solved, and the solutions obtained for fluid velocity, temperature, and concentration. These results are illustrated by plotting graphs and for various physical parameters. Here, we can control the results by means of the heat absorption coefficient, width ratio, and viscosity ratio. [ABSTRACT FROM AUTHOR]

The heat transfer assessments in a Sisko nanofluid flow over a stretching surface in a Darcy–Forchheimer porous medium with heat generation and thermal radiation are studied. The numerical analysis technique is used to assess the governing nonlinear equations of the model. The influence of Forchheimer number, porosity, heat generation, radiation, and material parameters is examined. The outlines of Nusselt number and skin friction coefficient corresponding to pertinent parameters are revealed. The comparison of Nusselt number outlines of working fluid and New- tonian fluid is depicted. From the analysis, it has been examined that with the increase in Forchheimer number and material parameter values, heat transfer function decreases, whereas heat transfer characteristics of Sisko nanofluid increase with heat generation and material parameters. Moreover, working fluid velocity outlines depreciate when there is an increase in porosity parameter for both shear‐thinning and shear‐ thickening. The comparison of this study with previous research has been conducted. [ABSTRACT FROM AUTHOR]

This article focuses on the three‐dimensional Cross fluid flow of a radiative nanofluid over an expanding sheet with aligned magnetic field, chemical reaction, and heat generation phenomenon. The stretching sheet has convective heat and slip boundary conditions. The similarity variables are properly used for the conversion of a dimensional mathematical model into a nondimensional one. The transformed ordinary differential equations are handled for the numerical outcomes of the suggested fluidic model by incorporating the shooting scheme. Furthermore, the numeric investigations are also compared by bvp4c MATLAB built‐in package. In a limited case, both the techniques are checked with already published articles, thereby revealing good agreement. Furthermore, the effects of few parameters like Prandtl number, Weissenberg number, heat generation, stretching rate parameter, magnetic parameter, thermal radiation, Brownian and thermophoresis parameters, and Lewis number on concentration, temperature, and velocity profiles have been presented using figures and numerical tables. The strong intensity of the magnetic field across the fluid and increment in the inclination angle (ϑ) result in a lower velocity profile. Temperature is more prominent for the higher slip mechanism. Furthermore, there in an increase in thermophoretic force, which pushes the nanoparticles, and this mixing of nanoparticles helps to increase the concentration profile. A higher Cross fluid index responds to a larger velocity. [ABSTRACT FROM AUTHOR]

In this paper, unsteady upper‐convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature‐dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature‐dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence. [ABSTRACT FROM AUTHOR]

The scope of the introduced study focuses on the analysis of heat as well as flow transportation in an oblique Casson nanofluid in the presence of an aligned magnetic field. The fluid is supposed to impinge obliquely on a sheet that stretches in both directions of the x-axis with heat generation. The moulded partial differential equations computed numerically with the shooting procedure by adopting the Runge Kutta Fehlberg method. The change in the behaviour of the emerging fluid parameters are described graphically and their results are shows in tables. The outcomes disclosed that the fluid velocity declined for Casson fluid parameter and the aligned angle of the magnetic field. In addition, with the increase in the Casson fluid parameter and aligned angle of magnetic field, the fluid temperature and concentration rise. The outcomes of this study may be beneficial to control the rate of heat and mass transportation as well as controlling fluid velocity in industry to obtain a final product of the desired quality. [ABSTRACT FROM AUTHOR]

This project mainly concentrates on the numerical investigation of the Hall and Ion impact on couple stress nanofluid flow through an inclined microchannel considering the hydraulic slip and convective boundary conditions in the presence of radiative heat flux. The analysis has been made via assuming that the fluid is incompressible, electrically conducting, and viscous. The parameters of couple stress, convection, and heat generation have been employed. Different water-based nanofluids containing Cu,Ag, Cuo, MoS2, Al2O3, and TiO2 are taken into account. To reduce the nonlinear system of ordinary differential equations, suitable nondimensional variables are applied to the governing equations. Then, this system is solved numerically utilizing the Runge-Kutta-Fehlberg fourth-fifth-order method along with the shooting technique. Maple software was employed to get numerical solutions. The results found that the fluid velocity is retarded for larger estimations of the Hall and Ion parameter. The drag force and the Nusselt number are diminished for higher estimations of the nanoparticle volume fraction and Brinkman number, respectively. Furthermore, it is noted that the nanoparticles have a maximum heat transfer rate as compared with the oxides of nanoparticles. The obtained results are compared with existing ones in a limiting case, and provide good agreement. [ABSTRACT FROM AUTHOR]

In the present article, the heat transfer rate and the fluid flow of a micropolar fluid along with temperature‐dependent transport properties are scrutinized in the presence of heat generation. The variability in transport properties leads to a rise in the heat transfer and decreases the skin friction. Furthermore, Fourier's heat flux model is implemented in the analysis of heat transfer, employing a suitable transformation to convert the flow model into nonlinear ordinary differential equations. Numerical solutions are obtained by using the shooting method/bvp4c technique. Physical quantities of interest, such as local skin friction and Nusselt number, are discussed and computed. Skin friction decreases with the micropolar parameter but the Nusselt number shows the opposite behavior for the micropolar parameter. [ABSTRACT FROM AUTHOR]

In the present paper, we have discussed the thermosolutal Marangoni force acting on the electrically conducting Casson fluid flow over a permeable horizontal stretching surface. It is presumed that the condition at the interfaces is influenced by the surface tension, which is proportional to the temperature and concentration profiles. At the interface, both concentration and temperature are heated in such a way that they are quadratic functions in x. Furthermore, we have introduced the magnetic field in the transverse direction of the fluid flow along with heat generation/absorption, thermal radiation, viscous dissipation, and first‐order chemical effect with heat and mass flux into the present system. Similarity transformations have been used to convert the system of the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The reduced ODEs are then solved using the MATLAB program bvp4c, which is based on the fourth‐order Runge‐Kutta and shooting method. The impact of various pertinent flow parameters on the flow field, temperature, and species concentration has been studied through graphs. To know the characteristics of shear stress, heat and mass rate near the boundary, numerical values of them are also calculated and given in the tabular form. The results show that the momentum boundary layer's thickness is getting thicker with an increase in solutal surface tension ratio, while its opposite trends have been observed in the thermal boundary layer region, this is due to the Marangoni effect. This Marangoni effect is very much important in the field of melting metals, crystal growth, welding, and electron beam. Highlights: Highlights of the present manuscript are: We have discussed the influence of the Marangoni convection on the non‐Newtonian Casson fluid flow over a permeable stretching sheet.Marangoni convection is based on the surface tension variation due to variations of the surfactant concentration and temperature.Influences of the non‐Newtonian nature of the fluid have been studied in the form of the Casson parameter.The governing equations of the model are also incorporated with the heat and mass flux along with the viscous dissipation term to analyze their effects on the system.Due to the significant contribution of the parameters like radiation, heat absorption/generation, and chemical reaction of the first‐order in the flow field, those terms are also being considered in the present system. [ABSTRACT FROM AUTHOR]

The effect of thermophoresis on a magnetic field generation in a non‐Daracian porous medium flow with the variation of the viscosity fluid in the presence of Soret and Dufour, thermal reaction and diffusion effects over a stretching surface is investigated in the present analysis. The governing equations of continuity, momentum, energy, and concentration are transformed into nonlinear ordinary differential equations, using similarity transformations and then solved numerically. The influence of various physical parameters on velocity, temperature, and concentration profiles are illustrated graphically, and the physical aspects are discussed in detail. Finally, the effects of related physical parameters on the skin friction, the rate of heat and mass transfer are also studied. [ABSTRACT FROM AUTHOR]

An analysis has been implemented to study the influences of nonconstant viscosity and magnetohydrodynamics on pseudoplastic nanofluid through a porous medium. Ohmic dissipation, chemical reaction, and heat generation are taken into consideration. The current problem is debated under the molds of tiny or zero Re and δ approximation. Two models of nonconstant viscosity are deliberated. Model (I)—all parameters are nondimensional and have been measured as constants inside the flow. Model (II)—all these stated nondimensional parameters have been considered to differ with the temperature. Comparison among the solutions achieved by utilizing numerical results and multi‐step differential transform method (Ms‐DTM) is displayed in excellent agreement. Attention is dedicated to β, η‐, and Nb parameters. The governing equations for each case have been explained by an easy and highly perfect series established seminumerical Ms‐DTM utilizing Mathematica 11, which uses mathematical software package. Nanofluids are active for drug carrying and drug delivery systems because of the Nb control with the velocity of fluid. [ABSTRACT FROM AUTHOR]