Mixed convection heat transfer in porous media in the non-darcy regime

In this study mixed convection heat transfer in a homogeneous porous duct of square cross section in a horizontal orientation is examined. Results from a generalized Forchheimer model are compared with that from the Darcy model. The heat transfer rate and the flow behavior depend on the following parameters: Grashof number, Gr = Q'gβKa/kv², an axial flow pressure drop parameter, ζ = (aK/vμ)dp'/dz', an inertial parameter ξ = mK/a, appearing in the Forccheimer model and the Prandtl number, Pr = C_pμ/k. In the Darcy limit, ξ → 0, the role of the axial flow parameter, λ is reduced to a mere scale factor and the flow behavior is determined by a single parameter, λ = Gr · Pr. Both the Darcy and the Forchheimer models exhibit dual solutions and a hysteresis behavior over a certain range of Gr. Such parametric dependence can be used as an additional tool along with carefully designed experiments to determine the importance of inertial and Prandtl number effects on convective heat transfer in porous media.