The effects of variable fluid properties and magnetic field on the flow of non‐Newtonian fluid film on an unsteady stretching sheet through a porous medium

Abstract

The effects of variable viscosity, variable thermal diffusivity and magnetic field on the flow and heat transfer in a laminar liquid film of non-Newtonian fluid on a horizontal stretching sheet through a porous medium are analyzed. Using a similarity transformation, the governing time-dependent boundary-layer equations for momentum and thermal energy are reduced to a set of coupled nonlinear ordinary differential equations. The resulting seven-parameter problem is solved numerically by using Chebyshev pseudospectral method for some representative value of the parameters. The numerical results show that variable viscosity, variable thermal diffusivity, the upper limit of apparent viscosity according to biviscosity model, the unsteadiness parameter, the magnetic parameter, and the permeability parameter have significant influences on the velocity and temperature profiles, shear stress, and Nusselt number. It is observed that the presence as well as the increase in the unsteadiness parameter S, variable viscosity parameter β1, the upper limit of apparent viscosity β, and the magnetic parameter M lead to decrease in the fluid film thickness η∞. Also, as film thickness approaches zero as S comes close to the critical value; then, there is no available solution for the problem. The velocity profiles supported this result, since close to this critical value the velocity of the fluid vanishes. Copyright © 2008 John Wiley & Sons, Ltd.