The nondarcy regime for vertical boundary layer natural convection in a porous medium

This paper reports similarity solutions for vertical boundary layer natural convection near a solid wall adjacent to a fluid-saturated porous medium, in the case where the pore Reynolds number is high enough for the Darcy flow model to break down. Based on scaling arguments, it is shown that the departure from the Darcy flow model is dictated by the dimensionless number G = (v/K)(bgβΔT)− 1 2 , with G → 0 representing the high pore Reynolds number limit, and with G → ∞ representing the Darcy flow limit. Similarity solutions are reported for flow and heat transfer in the following cases: (1) the nonDarcy limit G = 0 near an isothermal wall and near a constant-heat-flux wall, and (2) the intermediate regime G = 0(1) for natural convection near an isothermal wall. It is shown that the heat transfer results differ fundamentally from those known from traditional Darcy flow studies.