Influence of the Induced Magnetic Field and Viscous Dissipation on Williamson Fluid Flow With Variable Viscosity Through a Non-Darcy Porous Medium

Abstract

The objective of the present investigation is to study and analyze the magnetohydrodynamic boundary layer flow of Williamson fluid with consideration of induced magnetic field (IMF), temperature-dependent viscosity, and thermal conductivity through non-Darcy porous media. The novelty of this investigation is to analyze the characteristics of the IMF in Williamson fluid flow subject to temperature-dependent fluid properties. Governing partial differential equations have been first converted into a coupled system of ordinary differential equations along with revised boundary conditions by introducing suitable similarity transformations and have been solved numerically by using the shooting method. Also, the graphs showing the effects of various parameters on profiles of velocity, temperature, and IMF have been presented. At the last, a comparative table for skin friction and a table showing the effects of various parameters on skin friction and Nusselt number have been presented. The significant outcomes of the present findings are that the IMF decreases with an increase in the Williamson parameter, while it increases with the magnetic parameter. Also, skin friction decreases with increasing variable viscosity coefficient $ϵ$ and thermal conductivity coefficient $\delta$. The outcomes of the present work are very close to those studied earlier.