Minimization of thermal resistance in an air cooled porous matrix made up of solid spheres with heat generation

In this paper an analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of local thermal equilibrium. The analytical solution of the optimum sphere diameter was found to be independent of the heat generation rate of the solid spheres, but was dependent on the applied pressure drop and fluid properties. The analytical model compared very well to a numerical model found in a computational fluid dynamics code when air and liquid water properties were used for the fluid phase and wood and silica/sand properties were used for the solid phase.