Non-Darcy free convection along a nonisothermal vertical surface in a thermally stratified porous medium

Abstract

The problem of free convective heat transfer from an impermeable vertical plate embedded in a thermally stratified, fluid-saturated porous medium is analyzed for the case of power-law variation in the wall temperature. The non-Darcian effects, such as solid-boundary viscous resistance, high-flow-rate inertia force, near-wall nonuniform porosity distribution and thermal dispersion, have been considered in the present analysis. Due to the variation of porosity in the near wall region, the stagnant thermal conductivity varies accordingly. The present work examines the effects of non-Darcian flow phenomena and thermal stratification on free convective transport and demonstrates the variation in heat transfer prediction based on different flow models. The nonsimilar system of transformed equations is solved using Keller’s Box method. It is shown that the thermal stratification reduces the heat transfer rate from the vertical surface, while a higher value of the wall temperature exponent m increases the heat transfer rate. Also, the non-Darcian and thermal dispersion effects have significant influences on velocity and temperature profiles as well as the local heat transfer rate.