Thermal Interaction at the Interface Between a Porous Medium and an Impermeable Wall

The present work investigates a heat transfer phenomenon at the interface between a porous medium and an impermeable wall subject to a constant heat flux at the bottom. Currently, two possible thermal boundary conditions (which are called the First Approach and the Second Approach) at the interface are used interchangeably for the thermal analysis of convection in a channel filled with a porous medium. The focus of this paper is to determine which of these thermal boundary conditions is more appropriate in accurately predicting the heat transfer characteristics in a porous channel. To this end, we numerically examine the heat transfer at the interface between a microchannel heat sink (an ideally organized porous medium) and a finite-thickness substrate. From the examination, it is clarified that the heat flux distribution at the interface is not uniform for an impermeable wall with finite thickness. This means that a non-uniform distribution of the heat flux (First Approach) is physically reasonable. When the First Approach is applied to the thermal boundary condition, an additional boundary condition based on the local thermal equilibrium assumption at the interface is used. This additional boundary condition is applicable except in the case of a very thin impermeable wall. Hence, for practical situations, the First Approach with a local thermal equilibrium assumption at the interface is suggested as an appropriate thermal boundary condition. In order to confirm our suggestion, convective flows both in a microchannel heat sink and in a sintered porous channel subject to a constant heat flux condition are analyzed by using the two Approaches separately as a thermal boundary condition at the interface. The analytically obtained thermal resistance of the microchannel heat sink and the numerically obtained overall Nusselt number for the sintered porous channel are shown to be in close agreement with available experimental results when our suggestion for the thermal boundary condition at the interface is applied.