Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium

Abstract

In the present study a general criterion for local thermal equilibrium is presented in terms of parameters of engineering importance which include the Darcy number, the Prandtl number, and the Reynolds number, For this, an order of magnitude analysis is performed for the case when the effect of convection heat transfer is dominant in a porous structure. The criterion proposed in this study is more general than the previous criterion suggested by Carbonell and Whitaker, because the latter is applicable only when conduction is the dominant heat transfer mode in a porous medium while the former can be applied even when convection heat transfer prevails, In order to check the validity of the proposed criterion for local thermal equilibrium, the forced convection phenomena in a porous medium with a micro-channeled structure subject to an impinging jet are studied using a similarity transformation. The effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium are systematically studied by comparing the temperature of the solid phase with that of the fluid phase as each of these parameters is varied. The proposed criterion is also validated with the existing experimental and numerical results for convection heat transfer in various porous materials that include some of the parameters used in the criterion such as a microchannel heat sink with a parallel flow, a packed bed, a cellular ceramic, and a sintered metal. It is shown that the criterion presented in this work well-predicts the validity of the assumption of local thermal equilibrium in a porous medium. (C) 2002 Elsevier Science Ltd. All rights reserved.