Forced convection boundary layer flow and heat transfer along a flat plate embedded in a porous medium

DURING the past decade, fluid flow and heat transfer through porous media have experienced renewed research interest due to a broad range of applications, including geothermal systems, thermal insulation, metals processing, catalytic reactors, direct-contact heat exchangers, transpiration cooling, filtration, etc. In many practical systems, the porous medium has a high permeability (i.e. the porous media Reynolds numbers are high) and is bounded by an impermeable wall. making Darcy’s law inapplicable. This has led to the inclusion of inertia and boundary effects in recent studies of fluid flow through porous media. Inertia effects can be included in the momentum equation through the socalled Forchheimer’s extension [I], where Darcy’s law is modified by the addition of a quadratic term in velocity. The boundary effects can be modeled through the inclusion of a viscous shear stress term, which has become known as Brinkman’s extension [2]. Inertia, boundary and variable-porosity effects have been studied extensively [3-61 in forced convection boundary layer flow and heat and mass transfer along a flat plate embedded in a porous medium. Vafai and Tien [4] have solved the governing equations numerically and found that the velocity boundary layer develops in a short distance from the leading edge, while its thickness is of the order J(K/e). On the other hand. the boundary effects can significantly alter the heat transfer from the plate, especially at high Prandtl numbers. As expected, the inertia effects are more pronounced in high permeability porous media and in low viscosity fluids. In the present study, the problem of forced convection flow and heat transfer along a flat plate in a porous medium is reexamined by including both, the inertia and boundary effects, while porosity variations close to the wall are not considered. Since the developing part of the momentum boundary layer has been found to be negligibly small [4], it is not included in the present analysis. For the case of the fully-developed momentum boundary layer, closed-form expressions are derived for the velocity and temperature profiles. From these results, the wall shear stress and the Nusselt number are determined as functions of modified Reynolds and Prandtl numbers. In addition, comparisons are made with the limiting cases of no inertia and/or boundary effects. Finally, several results are presented for the case of blowing in the wall bounding the porous medium.