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

Abstract

In this study we have investigated MHD stokes free convection of an incompressible, electrically conducting fluid between two horizontal parallel infinite plates subjected to a constant heat flux and pressure gradient. A uniform magnetic field is applied normal to the plates. The flow is steady and considered heat generating due to frictional heating of fluid particles. This implies that flow variables are independent of time. 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. An analysis of velocity profiles and temperature distribution that have been obtained has been done. In addition, an investigation on how Prandtl number, Eckert Number and Hartman Number affect velocity profiles and temperature distribution has been carried out. Differential equations that have been generated from this study are non-linear. The equations have been solved by finite difference method. The results that have been obtained are discussed in detail and presented graphically. It has been noted that an increase in Hartmann number causes a decrease in velocity profiles. However an increase in Hartmann number leads into an increase in temperature distribution.It is also revealed that an increase in values of Eckert results into an increase in temperature distribution between the plates. Further an increase in Prandtl Number leads to a fall in temperature distribution.