THERMAL CONVECTIVE INSTABILITY IN TRANSLUCENT POROUS MEDIA WITH RADIATIVE HEAT TRANSFER

Abstract

Abstract The onset of thermal convection in a translucent porous layer is considered. Attention is focused on the effect of radiative heat transfer on the critical Rayleigh-Darcy number and the convection cell shape. If we consider the contribution of radiative heat transfer, the basic temperature profile is non-linear and the thermal convective instability is influenced by the ratio of conduction to radiation heat flux, the temperatures at the boundary surfaces, and radiative parameters such as wall emissivity, scattering albedo and extinction coefficient as well as the usual Rayleigh-Darcy number. Effects of these parameters on the onset of convective instability are investigated with the help of linear stability theory employing the Darcy's law and the radiative transport equation simplified by the P1 approximation. The increased effective thermal conductivity due lo the radiation inhibits the onset of convection and causes increased critical Rayleigh-Darcy number and decreased convection cell size. Th...