MAGNETOHYDRODYNAMIC FREE CONVECTION FLOW OF FLUID OF A VERTICAL PLANE WITH VISCOSITY AND THERMAL CONDUCTIVITY DEPENDING ON TEMPERATURE

Abstract

A two-dimensional natural convection flow of a viscous incompressible and electrically conducting fluid with both the viscosity and the thermal conductivity depending on temperature past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to non-similar boundary layer equations by introducing coordinate transformations appropriate to the cases (i) near the leading edge (ii) in the region far away from the leading edge and (iii) for the entire regime from leading edge to down stream. The governing equations for the flow in the upstream regime are investigated by perturbation method for smaller values of x, the stream-wise distributed magnetic field parameter. The equations governing the flow for large x and for all x, have been investigated by employing the implicit finite difference method with Keller box scheme. The effects of the viscosity variation parameter, e and the thermal conductivity variation parameter g, on the skin friction as well as the rate of heat transfer for the fluid for low Prandtl number are shown graphically.