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

Contemporary porous media that are used in cooling designs include metal and graphite foam. These materials are excellent heat transfer cores due to their large surface area density and the relatively high conductivity of the solid phase. Engineering models for convection heat transfer in such media are needed for thermal system design. When the cooling fluid has a low conductivity, e.g., air, its conduction can be set to zero. Engineering analysis for the fully-developed convection heat transfer inside a confined cylindrical isotropic porous media subjected to constant heat flux is presented. The analysis considers the Darcy flow model and high Pe´clet number. 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 wall increases. The effects of the Biot number and the Darcy number are investigated. The results are in qualitative agreement with more complex analytical and numerical results in the literature. The solution is of utility for initial heat transfer designs, and for more complex numerical modeling of the heat transfer phenomenon in porous media.