Approximate Analysis for Darcy-Flow Convection in Porous Media With Zero Fluid Conduction

The heat rejection device is a key component in virtually all electronic systems. New core materials for compact and efficient heat exchangers or heat rejection devices are contemporary porous media including metal and graphite foam. In such materials the solid phase has a relatively high conductivity, especially when the fluid phase has a low conductivity. This condition is realized in air-cooling thermal management systems. Simple models are needed for scientists and engineers who work with these materials. Approximate engineering analysis for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The analysis sets the conduction in the fluid’s governing equation to zero, and for simplicity assumes Darcian flow. The Darcian flow assumption is valid far enough from the solid boundaries, ant it prevails for most of the cross section. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated base increases. The results are in good qualitative agreement with more complex analytical and numerical results in the literature. The proposed model may prove to be time-savings for design purposes.