Effects of non-Darcian and temperature dependent heat source on two-phase flow in a vertical porous space with thermal radiation

In this article, influences of viscous dissipation and thermal radiation on MHD flow of two immiscible fluids in a vertical channel filled with porous materials have been studied theoretically. The equations governing the problem are transformed to a system of ODE and are solved by homotopy analysis method (HAM). The effects of physical parameters on flow and heat transfer characteristics have been discussed with the help of graphs. It is found that viscous dissipation parameter, heat source parameter, thermal parameter lead to enhance velocity as well as temperature field. Also, increasing Brinkmann number and heat source parameter lead to suppress Coefficient of skin friction at the left wall but the opposite is true at the other wall. However, these parameters give reverse trend on Nusselt number distribution. Further, increasing thermal conductivity ratio and fluids height ratio leads to increase heat transfer coefficient significantly at the left wall. In addition, we have compared present HAM solution with analytical solution of the problem (ie, absence of radiation parameter and Brinkmann number).