Thermal Non-Equilibrium Free Convection in a Cavity Filled With a Non-Darcy Porous Medium

Abstract

In modelling a fluid saturated porous system, two kinds of theoretical approaches have been used. Based on the first and oldest model, the fluid and solid structure are assumed to be in local thermal equilibrium. This assumption is satisfactory for small-pore media such as geothermal reservoirs and fibrous insulations and small temperature differences between phases. In the second kind of approach, the fluid and solid structure are assumed to be in thermal non-equilibrium. For many applications, involving high-speed flows or large temperature differences between the fluid and solid phases, it is important to take account of the thermal non-equilibrium effects. If the temperature between phases is a very important safety parameter, for example in the study of a nuclear reactor core, the thermal non-equilibrium convection model in the porous matrix is an indispensable model. The problem of free convection flow in differentially heated cavities, with top and bottom walls insulated, and filled with Darcian or non-Darcian fluid-saturated porous media, is of fundamental interest to many technological applications in the modern industry. Bejan [9], Lai and Kulacki [15], Manole and Lage [16], Baytas and Pop [3,4] and Baytas et al. [6,7] have contributed with some important theoretical results to this topic. However, it was assumed in these studies that the convecting fluid and the porous medium are everywhere in local thermodynamic equilibrium. As aforesaid, the assumption of