A mathematical study of porous medium equation under the effect of heat generation and hall current

Abstract

This study examines the impact of velocity slip and temperature jump on steady fully developed MHD natural convection flow in a vertical micro-porous-channel under the action of Hall current and heat generation. The mathematical model responsible for the present physical situation is presented in non-dimensional form under relevant boundary conditions. The analytical solutions have been obtained for momentum and energy equations. A parametric study of physical parameters is conducted and a representative set of numerical results for the primary velocity, secondary velocity, volume flow rate due to primary flow and volume flow rate due to secondary flow are discussed graphically. It is observed that magnetic field plays a significant role in flow formation inside the micro-channel. Numerical computation reveals that increase in Hartmann number reduces the volume flow rate due to primary flow for symmetric and asymmetric wall heating conditions while impact is just converse on the volume flow rate due to secondary flow for symmetric and asymmetric wall heating conditions.