Boundary Layer Analysis of Unsteady Forced Convection of a Newtonian Fluid with Variable Thermo-physical Properties in the Presence of Induced Magnetic Field

Abstract

This paper attempts to effectively model the effects of variable viscosity and thermal conductivity on the unsteady hydromagnetic boundary layer flow past a semi-infinite plate when the oncoming free-stream is perturbed by an arbitrary function of time and applied magnetic field is far from and parallel to the plate. The two dimensional boundary layer equations are separated into those representing steady and unsteady parts of the flow. For, steady flow equation and unsteady flow equation, viscosity and thermal conductivity are considered as inverse linear functions of temperature. The basic steady flow governing partial differential equations are transformed into ordinary differential equations by means of similarity transformation which are solved numerically using shooting method and the resulting approximate solution have been used in the subsequent study of the unsteady flow. The unsteady flow equations are subject to the Laplace Transformation technique. In this case, solution for large time is obtained assuming velocity, temperature and Magnetic field as asymptotic expansion. The relevant flow and heat transfer characteristics that is the skin-friction coefficient, the plate temperature and the tangential magnetic field at the plate are derived and discussed numerically.