Solutions of the laminar boundary layer equations for a conducting power law non-Newtonian fluid in a transverse magnetic field

Abstract

This paper is concerned with the boundary layer flow of a power law non-Newtonian fluid in the presence of a magnetic field B(x) applied perpendicular to the surface and an electric field E(x) perpendicular to B(x) and the direction of the longitudinal velocity in the boundary layer. Approximate analytical solutions are given, and numerical solutions to the resulting nonlinear ordinary differential equation are presented. Important particular cases like boundary layer flow along a wedge, two-dimensional stagnation point flow, flow over a flat plate and flow in a convergent channel have been studied. The combined effects of the magnetic forces gamma and the flow index n on the velocity profiles, the shear stress on the surface tau _w, the displacement thickness delta ₁ and the momentum thickness delta ₂ are studied. It is found that the velocity of the fluid increases with increase of either gamma or n individually, with the other kept constant. Also, it is established that both analytical and numerical solutions must be used together to solve such problems.