Determination of the unknown coefficients in stress and flux conditions at fluid-porous interface

An innovative methodology is presented for the purpose of analyzing fluid flow and heat transfer in a porous/fluid composite system, where the porous medium is assumed to have a periodic structure, i.e., solid and fluid phases repeat themselves in a regular pattern. With the present method, analytical solutions for the velocity and temperature distributions are obtained when the distributions in the adjacent fluid layer are allowed to vary in the directions both parallel and perpendicular to the interface between the porous medium and the adjacent fluid layer. The analytical solutions are validated by comparing them with the corresponding numerical solutions for the case of the ideal composite channel, and with existing experimental data. The present analytical solutions have a distinctive advantage in that they do not involve any unknown coefficients resulting from the previous interfacial conditions. Moreover, by comparing interfacial conditions derived from the present study with the stress- and flux-jump conditions developed by previous investigators, the unknown coefficients included in the stress- and flux-jump conditions are analytically determined and are shown to depend on the porosity, the Darcy number and the pore diameter.