Magneto-Hydrodynamics Analysis of Free Convection Flow between Two Horizontal Parallel Infinite Plates Subjected to Constant Heat Flux

Abstract

A steady MHD stokes free convection flow of an incompressible, electrically conducting fluid between two parallel infinite plates subjected to constant heat flux and pressure gradient has been studied. The flow is considered heat generating due to frictional heating of fluid particles. The upper plate is impulsively started at constant velocity while the lower plate is assumed to be porous and stationary. The two plates are separated by a distance h. A constant magnetic field is applied normal to the main flow direction and is found to affect velocity profiles considerably. Further, an investigation on how Prandtl number, Eckert Number and Hartman Number affect velocity profiles and temperature distribution has been carried out. The non-linear differential equations generated in this study are solved by finite difference method. The results that have been obtained on velocity profiles and temperature distribution are discussed in detail. An increase in Hartmann is found to cause a decrease in velocity profiles and an increase in temperature distribution. In addition, an increase in Eckert number causes an increase in temperature while an increase in Prandtl leads to a fall in temperature distribution. These results are found to merge with the physical situation of the flow.