The present work investigates a heat transfer phenomenon at the interface between a porous medium and an impermeable wall. In an effort to appropriately describe the heat transfer phenomenon at the interface, the heat transfer at the interface between the microchannel heat sink, which is an ideally organized porous medium, and the finite-thickness substrate is examined. From the examination, it is clarified that the he heat flux distribution at the interface is not uniform for the impermeable wall with finite thickness. On the other hand, the first approach, based on the energy balance for the representative elementary volume in the porous medium, is physically reason able. When the first approach is applied to the thermal boundary condition, and additional boundary condition based on the local thermal equilibrium assumption at the interface is used. This additional boundary condition is applicable except for the very th in impermeable wall. Hence, for practical situations, the first approach in combination with the 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. 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 conditions is applied.