Exact Solutions for a Thermal Nonequilibrium Model of Fluid Saturated Porous Media Based on an Effective Porosity

Abstract

An effective porosity concept has been introduced to account for the effects of tortuosity and thermal dispersion on the individual effective thermal conductivities of the solid and fluid phases in a fluid-saturated porous medium. Using this effective porosity concept, a thermal nonequilibrium model has been proposed to attack locally thermal nonequilibrium problems associated with convection within a fluid-saturated porous medium. Exact solutions are obtained, assuming a plug flow, for the two cases of thermally fully developed convective flows through a channel, namely, the case of isothermal hot and cold walls and the case of constant heat flux walls. These exact solutions for the cases of metal foam and air combination reveal that the local thermal equilibrium assumption may hold for the case of isothermal hot and cold walls, but may fail for the case of constant heat flux walls.