Effects of porosity on the free convection flow of non-Newtonian fluids along a vertical plate embedded in a porous medium

Abstract

In recent years, great interest has been shown in porous media. The applications of porous media in geophysics, petroleum processes, and air conditioning are well established. Many studies of porous media have been carried out, mostly dealing with constant porosity. In this study, the variable porosity effects are investigated for a vertical plate in a variable porous medium. The governing partial nonlinear differential equations were transformed into a set of coupled ordinary differential equations, which was solved using the fourth-order Runge-Kutta method. The results obtained for the different power law index n, and variable porosity of the bed, were found to be in good agreement with previous studies. Results show that when porosity increases temperature variation becomes steeper, and the Nusselt number increases almost linearly with increasing porosity.