Effect of Joule heating on MHD non‐Newtonian fluid flow past an exponentially stretching curved surface

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time‐independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth‐order Runge–Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number.     

Heat generation/absorption on MHD flow of a micropolar fluid over a heated stretching surface in the presence of the boundary parameter

A model study is reported to examine the effect of magnetic hydrodynamics polar fluid over a semistretched infinite vertical porous surface in the presence of heat source, temperature, magnetic field, and thermal radiation. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via Runge–Kutta fourth order along with the shooting technique. The effects of various physical parameters on coefficient of skin friction, microrotation coefficient, and Nusselt number are studied whereas the outcomes are explained through a set of graphs. The results obtained are explained in tabular form and graphs. Prandtl and Hartman's numbers enhance the velocity profile while the opposite behavior is noticed for $\phi ,\delta$. Higher values of Pr enlarge the angular velocity near the surface. Improved temperature distribution is noticed for higher values of Ha and ϕ, However, a declined behaviour is observed for $\text{Pr},\delta$, and $fo$.     

Magnetohydrodynamic micropolar slip flow due to an exponentially stretching sheet with chemical reaction and nonuniform heat generation

The main focus of the current study is to examine the impact of melting heat transfer and chemical reaction on magnetohydrodynamic micropolar fluid flow over a sheet that is exponentially stretching and immersed in a porous medium. A nonuniform heat source is placed within this flow system. Other impacts like slip phenomena and thermal radiation are also taken into consideration. The governing partial differential equations are converted to a system of ordinary differential equations (ODEs) via similarity transformation and we also get the corresponding necessary boundary conditions. These nonlinear ODEs are resolved with the help of shooting technique and an Runge-Kutta fourth order (RK-4) iterative strategy. Also, we solve this problem using the Bvp4c approach for validating the results of the RK-4 method. Both outcomes are consistent with previously published data. With the help of tables and graphs, we examine the influence of multiple physical parameters on velocity, thermal, microrotation, concentration, Nusselt number, Sherwood number, coefficient of skin friction, and wall couple stress. We see that the temperature distribution and velocity profiles decrease when the melting parameter increases. The temperature profile boosts when the heat source parameter is increased.     

Free convective MHD micropolar fluid flow with thermal radiation and radiation absorption: A numerical study

An analysis is carried out for the free convective flow of an electrically conducting micropolar fluid through permeable stretching sheet in the presence of porous medium. Inclusion of thermal radiation to the energy equation enhances the thermal properties of polar fluid. In addition to that the radiation absorption parameter occurs due to the interaction of solutal concentration difference also considered in the heat transfer equation. Suitable similar transformation is used to convert the governing partial differential equations to ordinary differential equations. Furthermore, though analytical solutions of these complex nonlinear coupled equations are more complicated therefore, numerical solution such as Runge‐Kutta fourth order method associated with shooting technique is adopted. Behavior of characterizing parameters for the flow phenomena are presented via graphs and computed values of physical quantities of interest are obtained and shown in tabular form. Present result validates with that of earlier results in particular case which confirms the existence of present solution methodology. However, the main findings of contributing parameters are laid down as; angular velocity profile contributes a dual character from the point of contact at the middle of the channel. Fluid temperature is affected by the inclusion of absorption coefficient.     

Thermal dispersed homogeneous-heterogeneous reaction within MHD flow of a Jeffrey fluid in the presence of Newtonian cooling and nonlinear thermal radiation

The current study deals with the effects of Newtonian cooling, magnetic field, and nonlinear radiation on the flow of a Jeffrey fluid along with thermal dispersion and homogeneous-heterogeneous reaction towards a stagnation point. The developed governing equations are transformed into nondimensional equations employing suitable similarity transformations along with their related boundary conditions. To solve and analyze these equations, the BVP4C solver of MATLAB has been used. The various properties of the fluid flow such as velocity, temperature, and concentration are represented in their respective graphs. The values obtained for skin friction and Nusselt number are expressed in the form of a table. The important outcomes of the present study are that the velocity declines as we increase the melting parameter, magnetic parameter, and Prandtl number. The temperature profile increases with radiation parameter, heat source, and magnetic number. An inclination is seen in the concentration of the fluid with a rise in Schmidt number whereas declination is seen with a rise in the homogeneous reaction parameter. Also, a comparison Table 1 has been made with the previous work under limited conditions. The table shows that the current work justifies the previous work system under those conditions. The present model can be utilized for many industrial purposes. Large-scale industries like plastic and food processing industries can utilize these results to enhance their productivity.     

Newtonian heating effect on laminar flow of Casson fluids: Thermal analysis

In the present study, free convective, laminar flow of Casson fluid is investigated numerically over a nonlinear stretched sheet to observe the characteristics of heat transfer in the presence of Newtonian heating. Nonlinear differential equations are derived from the present flow by utilizing the appropriate transformations. Thereafter, for the linear stretching case, an exact solution is applied for the momentum equation, and for the nonlinear stretching case, a convergent numerical technique, SRM, is applied. Computations of SRM and exact solutions are displayed through graphs. For various physical parameters, variation in velocity profile is observed by means of numerical computations and presented graphically. For checking the accuracy and convergence of the proposed method, outcomes are validated with the available outcomes in the literature and compared. The outcomes demonstrate that the velocity profile is reduced for the nonlinear stretching parameter effect, and, with increasing $\mathit{Pr}$, the temperature is decreased and there is a reduction in the thickness of the thermal boundary layer.     

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Nonlinear radiation and cross-diffusion effects on the micropolar nanoliquid flow past a stretching sheet with an exponential heat source

Metallurgy, polymer and processing engineering, and petrochemical enterprises frequently encounter polar nanoliquid flows due to stretchable surfaces with radiative heat energy. Therefore, the radiative flow of a polar nanoliquid over a stretchable sheet is analyzed considering cross-diffusion and magnetic heat flux effects. The heat transport phenomenon is explored, including the characteristics of nonlinear radiation and exponential space-based heat generation. The highly nonlinear governing equations are converted to ordinary differential equations using apt transformations. These are, in turn, solved employing the finite difference method. The behavior of contributing parameters is presented using graphical visualizations. The interactive impacts of the pertinent constraints on the rate of heat transfer and skin friction are analyzed using three-dimensional surface plots. The enhancement of the temperature profile is observed by incrementing the radiation and exponential heat generation parameters. The magnetic field can be used to regulate the fluid flow as it decreases the flow field. Also, the heat generation factor has a predominant decreasing effect on the Nusselt number.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Dual solution of heat transfer in hydromagnetic micropolar fluid flow over a stretching sheet in a porous media: A numerical approach

In this study, the researcher looks at the heat transmission of an incompressible magnetohydrodynamics micropolar fluid across a moving stretched surface in a Darcian permeable medium. The proper boundary conditions are used to facilitate the numerical solution (bvp4c) of the transformed governing equations. Graphical discussions have been made of the influence of the physical parameters on the velocity, angular velocity (microrotation), and temperature, and the distributions are accentuated on the plots via MATLAB. The study is validated by the previous work and it is found appropriate for investigation, where the absolute difference between the previous work and the present investigation by adopting the finite difference scheme is smaller than which implies that the scheme is stable and convergent. The microrotation has a great impact on the micropolar fluid with the influences of buoyancy forces, source, and suction over the stretching surface in a Darcian regime. With a rise in the heat source parameter, both velocity and microrotational profiles lessen, but the opposite is true for temperature. Eringen number () rises with the flow velocity, whereas temperature and microrotational profiles show the reverse relationship. The current study focused on particular applications in non-Newtonian fluid mechanics, polymer flows in filtration systems and metallurgical procedures that included cooling unbroken strips or filaments via a static fluid.     

Heat and mass transfer of magnetohydrodynamic Casson fluid flow over a wedge with thermal radiation and chemical reaction

A numerical computation to analyze the heat and mass transfer mechanism of a magnetohydrodynamic radiative Casson fluid flow over a wedge in the presence of Joule heating, viscous dissipation, and chemical reaction is carried out in this study. The flow-governing partial differential equations are transformed as ordinary differential equations by relevant similarity transformations and subsequently resolved by Runge–Kutta numerical approach with a shooting technique. The characteristics of momentum, thermal, and concentration border layers due to various influencing parameters are graphically outlined and numerically computed by MATLAB software. We present comparative solutions to construe the relative outcomes of Casson fluid versus Newtonian fluid. Computational outcomes of friction factor and Nusselt and Sherwood numbers are tabulated with suitable interpretations. An increase in skin friction values is noted due to an increment in the thermal Grashof number, whereas a decrease is observed due to the chemical reaction parameter. The Casson fluid displays a superior heat transfer mechanism than the Newtonian fluid. Obtained outcomes are in good agreement with the prevailing literature in the limiting case.     

Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition

This article investigates the effect of double dispersion on the natural convective flow of a micropolar fluid along an inclined plate in the presence of the convective thermal condition. In addition, the nonlinear convection is considered to analyze the heat and mass transfer phenomena of thermal systems, which are performed at moderate‐ and high‐level temperatures. A combination of local nonsimilarity and successive linearization techniques is used to evaluate the associated complicated nondimensional governing equations. This study discusses the impact of relevant factors on the fluid characteristics through graphs. The influence of nonlinear convection parameters on the heat and mass transfer rates seems to be more in Darcy porous media compared with that in non‐Darcy porous media.     

Comprehensive analysis of radiation impact on the transfer of heat and mass micropolar MHD free convective fluid flow across a stretching permeability sheet with suction/injection

As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built-in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.     

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.     

Effects of slip conditions on stretching flow with ohmic dissipation and thermal radiation

The present work addresses the magnetohydrodynamic (MHD) flow and heat transfer over a permeable stretching sheet. Analysis has been carried out in the presence of thermal radiation and ohmic dissipation. The velocity and thermal slip effects are given main attention. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non‐linear partial differential equations are reduced to a set of non‐linear ordinary differential equations which are solved analytically by the homotopy analysis method (HAM). The effects of emerging physical parameters on the velocity and temperature profiles are interpreted. Numerical data for skin friction coefficient and Nusselt number have been tabulated for various values of the parameters. The results have been compared with the known exact solution from the literature in a limiting sense. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20367     

Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity

The aim of this paper is to present the unsteady boundary layer flow and heat transfer of a fluid towards a porous stretching sheet. Fluid viscosity and thermal diffusivity are assumed to vary as linear functions of temperature. Using similarity solutions partial differential equations corresponding to the momentum and energy equations are converted into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the help of shooting method. It is noted that due to increase in unsteadiness parameter, fluid velocity decreases up to the crossing over point and after this point opposite behaviour is noted. The temperature decreases significantly in this case. Fluid velocity decreases with increasing temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity) up to the crossing over point but increases after that point and the temperature decreases in this case. Due to increase in thermal diffusivity parameter, temperature is found to increase.     

Insight into the dynamics of micropolar fluid about a vertical cone when nonlinear thermal radiation is significant: The case of triple mixed convection

This novel research investigates the nonlinear triple diffusive combined convective micropolar liquid flow past a vertical cone in the presence of nonlinear thermal radiation, cross-diffusion, and a convective boundary condition. We aim to analyze this present problem using nonsimilar transformations. This report presents the significance of nonlinear mixed convection, energy flux due to the concentration gradient, and mass flux due to the temperature gradient and nonlinear thermal radiation in the dynamics of the fluid subject with micropolar fluid is presented. The differential equations defining the boundary-layer parameters are then transformed into dimensionless view, taking into account the nonsimilar transformation. Furthermore, the method of quasilinearization and implicit finite difference approximation is used to work out the nondimensional governing equations for the solution. The velocity pattern diminishes, while dimensionless temperature and concentration distributions enhance with growing values of microrotation parameter. Furthermore, species concentrations of the fluid increase with increasing Soret effect values, while opposite results appear for mass transfer rates. Also, drag coefficient enhances for assisting buoyancy flow whilst diminishes for opposing buoyancy flow with increasing values of the microrotation parameter. The microrotation pattern reduces with growing values of the nonsimilarity characteristics. Furthermore, the Prandtl number is displayed on a comparison graph, and the results are very similar.     

Numerical investigation of ferromagnetic liquid film flow over an unsteady stretching surface in the presence of radiation and aligned magnetic field

An investigation of the two-dimensional unsteady flow of a thin layer of ferromagnetic liquid past a stretching sheet is performed. The flow is exposed to an external magnetic field in the axial direction along with the thermal radiation effect. Relevant Maxwell's equations are considered together with the conservation laws of fluid dynamics to model the problem. The mathematical model is constructed using a system of partial differential equations with relevant boundary conditions, which are transformed into two-point boundary value problem (BVP) using similarity transformations. The resultant BVP is numerically solved by a shooting technique that involves Runge–Kutta–Fehlberg (RKF45) method to integrate the initial value problem and the Newton–Raphson method to refine the guessed initial values. The influence of the dimensionless parameters on the flow and heat exchange characteristics is graphically analyzed. It is found that the thickness of the film increases for higher values of the thermal radiation parameter. The thermal profile shows increasing behavior with the radiation parameter and reverse effect with the Prandtl number.     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.