The two-equation energy equations are solved analytically for the temperature of the solid phase inside a two-dimensional rectangular porous media subjected to constant heat flux on one side. The fluid conduction is neglected in the governing equations and the Darcy flow model is used. Several simplifying assumptions are made regarding the boundary layers. The solid temperature decays in what looks like an exponential fashion as the distance from the heated base increases. Applications of such solution may be found in porous media with high solid phase conductivity cooled by low-conductivity fluids, e.g., open-cell metallic and graphite foams cooled by air.

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