An improved porous medium model for microchannel heat sinks

In this paper, a new porous medium model for microchannel heat sinks is presented. The substrate is taken into account in the temperature equation. Thus, an approximate boundary condition at the position of the bottom of microchannel is avoided. For hydrodynamically and thermal fully developed flow in the microchannel, an analytical solution is derived. The normalized temperatures from the present analytical solution are compared with those from three-dimensional numerical simulation and the previous porous medium model. The present model and the numerical simulation correctly reproduce the temperature distribution while the previous porous medium model cannot describe the temperature distribution in the substrate and in the region near the channel bottom. The convective thermal resistance calculated from the present model shows good agreement with that from numerical simulation without any additional modification since the substrate has been taken into account. With the increase of the channel height, the discrepancy between the numerical simulation and the porous medium model increases. Much attention should be given to the cases with high aspect ratio.