On entropy generation due to transient MHD radiative free convection with induced magnetic field in a porous medium channel

Abstract

The communication pertains to transient magnetohydrodynamics radiative free convection flow with induced magnetic field in a porous medium channel of width L. The setup is subjected to a uniform magnetic field H o * normal to the channel walls and H x * stands for the induced magnetic field. A Cartesian coordinate system is chosen where x*‐axis is taken along the left channel wall and y*‐axis is normal to it. At the time t* = 0, both the walls and the fluid bear a fixed temperature T m *. At the time t* > 0, that is, the onset of the convection, the temperatures of the walls at y* = 0 and at y* = L are just changed to T o * and T L *, respectively, where T m * < T o * and T L * < T m *. The radiative flux qr in the energy equation is assumed to follow the Rosseland approximation. The Keller‐box method has been invoked to solve the governing system encompassing the momentum, energy, and magnetic field equations. The numerical solution strategy yields velocity and temperature distributions, skin friction, and Nusselt number. The velocity and temperature fields are used to compute entropy. Distributions for entropy and Bejan number are shown graphically through two‐dimensional (2D) and 3D plots and discussed. The central objective of this study is to analyze inherent thermodynamic irreversibility. The study has direct applications in plasma aerodynamics and nuclear engineering control where the magnetic field is used as a tool to control flow and heat characteristics. The present study is novel in terms of the objective of the study and the implicit finite difference solution strategy called the Keller‐box method. From the 2D and 3D plots, it is found that the entropy and Bejan number experience qualitative and quantitative variations for varying Brinkman number, radiation parameter, Darcy number, magnetic Prandtl number, Grashoff number, and time. The skin friction and Nusselt number at the channel walls witness qualitative variations for varying parameters.

Differential transform method for couple stress fluid flow in a channel with a porous base

“…Vyas et al 50 analyzed entropy for micropolar fluid flow past a plate. Vyas and Yadav 51 reported entropy in a convective regime over a vertical stretching cylinder. Vyas and Yadav 52 investigated induced magnetic field effects on entropy in a transient MHD radiative free convection in a porous medium vertical channel.…”