MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.     

The axisymmetric flow of an MHD Powell–Eyring fluid with viscous dissipation and Newtonian heating condition: Keller-box method

A special investigation on the heat transfer by applying viscous dissipation and considering the Newtonian heating condition in magnetohydrodynamic Powell–Eyring fluid has been attempted. It is regarded as the flow in an axisymmetrical direction over a radially stretching surface. The converted governing system of equations is solved to obtain a closed-form solution using the Keller-box technique. The skin-friction coefficient's influence fully developed local Nusselt number is then presented graphically, and temperature profiles are sorted out for the pertinent parameters. The fluid overshoot towards the plate surface with rising magnetic field strength, hence, both the fluid velocity and the hydrodynamic border line layer thickness will fall, though, the skin-friction coefficient will increase. Various relevant results of the energy indulgence have been discussed from heating and in view of viscous dissipation phenomena. The decision with minimal cases from previous studies in the literature received confirmation of the findings.     

Entropy generation analysis of free convection radiative MHD Eyring–Powell fluid flow between porous parallel plates with Soret and Dufour effects

In this present study, we have investigated the entropy generation analysis and Dufour and Soret impacts on unsteady incompressible free convective radiative MHD Eyring–Powell fluid flow between parallel plates with periodic injection and suction. The governing PDEs are converted into nondimensional coupled nonlinear ordinary differential equations by using similarity variables then numerically solved by Runge–Kutta fourth-order scheme with shooting technique. The results are discussed in detail for different flow, mass, and heat transfer profiles corresponding to various active parameters and presented in tables and graphs. Also, it is noticed that the temperature profiles are enhanced with the fluid parameter, whereas the concentration profiles are decreased with the Prandtl number. The validations of present results with the existing outcomes for the viscous case of skin friction are included and have found to be in good agreement. The present numerical study is useful for the enhancement of heat transfer in various industrial and chemical processes.     

MHD radiative Casson—Nanofluid stream above a nonlinear extending surface including chemical reaction through Darcy-Forchiemer medium

The current study aims to study the magnetohydrodynamics (MHD) Casson kind nanofluid stream through a permeable medium above a nonlinear extending surface considered along with Darcy-Forchimer relation and chemical reaction. Thermophoresis and Brownian diffusion effects are considered. The MHD effect is used to highlight the physical and thermal properties of the nanofluid. The Keller Box scheme is used to solve the guiding equations numerically. Graphs are plotted for various nondimensional parameters. To justify the method, the used local parameters are calculated and compared with the existing literature. The results specify that a decreasing tendency is observed in the velocity profile for Forchiemer, magnetic, and stretching rate parameters, whereas the opposite tendency is noted for the Casson parameter. On observing temperature profiles, declination is noticed for Casson, thermal slip parameters and raising nature is detected for increasing values of Brownian diffusion, and thermophoresis, radiation parameters. From the results, it is observed that the momentum boundary layer diminishes for a higher inertial influence and the opposing force offered by the porous media to the fluid flow.     

Non‐Darcian Unsteady Flow of a Micropolar Fluid over a Porous Stretching Sheet with Thermal Radiation and Chemical Reaction

An analysis is presented to investigate the effects of a chemical reaction on an unsteady flow of a micropolar fluid over a stretching sheet embedded in a non‐Darcian porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation. The resulting nonlinear coupled differential equations are solved numerically by using a fourth‐order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, angular velocity (microrotation), temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21090     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Darcy–Forchheimer MHD radiative flow through a porous space incorporating viscous dissipation,heat source,and chemical reaction effect across an exponentially stretched surface

The impacts of viscous dissipation, Brownian motion, and the thermophoresis caused by temperature gradient on the steady two-dimensional incompressible chemically reactive and radiative flow of traditional fluid through an exponentially stretched sheet embedded in a Darcy porous media are explored by approaching boundary layer analysis. A magnetic field effect is also addressed along the transverse direction of the horizontal stretched sheet. With the implementation of some suitable nondimensional quantities, the regulating nonlinear partial differential equations, which represent the flow geometry, are transformed into coupled nonlinear ordinary differential equations. To acquire the numerical findings from this set of equations, a three-stage Lobatto IIIa, in-built MATLAB scheme named, Bvp4c is used. The effects of the dimensionless physical factors on the flow, heat, and concentration profile, as well as on the coefficient of drag force and the rate of thermal and mass transit at the surface, are graphically and numerically depicted. The thermal profile, as well as the magnitude of the coefficient of the drag force and the Sherwood number, is found to be escalated with the Darcy–Forchheimer factor, but the depreciation in the value of temperature gradient at the wall is noticed for the same.