Interfacial Interactions in Heat Transfer and Fluid Flow Through Porous Media.

The effects of boundary friction and inertia on convective heat transfer and fluid flow at the interface regions between a porous medium and another medium have been studied both analytically and numerically. Three fundamental configurations are investigated in depth in the present study. Throughout this study several important characteristics of the flow and the temperature fields at the interface regions of the porous medium are reported and the dependence of these characteristics on the governing parameters is also documented. First the significance of the boundary effect on natural convection from a heated vertical plate embedded in a fluid-saturated porous medium has been investigated. Consideration was given to flows which exhibit boundary layer characteristics for the constant wall temperature case and for the constant wall heat flux case. The method of matched asymptotic expansions was used to obtain the analytical solutions for both the velocity and temperature fields. The full numerical solutions for all cases were also presented. For the case where the thickness of the viscous boundary layer is larger than that of the thermal boundary layer, the Nusselt number was found to depend only on the Rayleigh number and to be independent of the permeability of the porous medium. Secondly the problem of forced convection in a porous channel subjected to constant wall heat flux is analyzed. Exact solutions are obtained for the velocity and temperature fields. It is shown that for a high permeability porous medium the thickness of the momentum boundary layer depends on both the Darcy number and the inertia parameter, while that for a low permeability porous medium depends only on the Darcy number. It is found that there is a significant increase in the rate of heat transfer as the inertia parameter increases especially for high permeability porous media. Finally the problem of forced convection over a flat plate covered with a porous substrate is investigated. Numerical solutions based on the finite difference method are obtained for the velocity and temperature fields. The generalized flow model which accounts for the effects of the boundary and inertia was used to describe the flow in the porous region. Consideration was given to convective flows which exhibit boundary layer characteristics for the constant wall temperature case. Two distinct boundary layers were shown to exist for the velocity field while only one boundary layer is observed for the temperature. Overall it is proved that the presence of a porous layer near an impermeable boundary may significantly change the convection characteristics and deserves careful consideration.