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

The problem of free convective heat transfer from an impermeable vertical p late embedded in a thermally stratified, fluid-saturated porous medium is a nalyzed for the case of power-law variation in the wall temperature. The no n-Darcian effects, such as solid-boundary viscous resistance, high-flow-rat e inertia force, near-wall nonuniform porosity distribution and thermal dis persion, have been considered in the present analysis. Due to the variation of porosity in the near wall region, the stagnant thermal conductivity var ies accordingly. The present work examines the effects of non-Darcian flow phenomena and thermal stratification on free convective transport and demon strates the variation in heat transfer prediction based on different flow m odels. The nonsimilar system of transformed equations is solved using Kelle r's Box method. It is shown that the thermal stratification reduces the hea t transfer rate from the vertical surface, while a higher value of the wall temperature exponent oz increases the heat transfer rate. Also, the non-Da rcian and thermal dispersion effects have significant influences on velocit y and temperature profiles as well as the local heat transfer rate. (C) 199 8 Elsevier Science Ltd. All rights reserved.