Darcy-Brinkman free convection from a heated horizontal surface

The free convection boundary layer flow of a Darcy-Brinkman fluid that is induced by a constant-temperature horizontal semi-infinite surface embedded in a fluid-saturated porous medium is investigated in this work. It is shown that both the Darcy and Rayleigh numbers may be scaled out of the boundary layer equations, leaving a parabolic system of equations with no parameters to vary. The equations are studied using both numerical and asymptotic methods. Near the leading edge the boundary layer has a double-layer structure: a near-wall layer, where the temperature adjusts from the wall temperature to the ambient and where Brinkman effects dominate, and an outer layer of uniform thickness that is a momentumadjustment layer. Further downstream, these layers merge, but the boundary layer eventually regains a two-layer structure; in this case, a growing outer layer exists, which is identical to the Darcy-flow case for the leading order term, and an inner layer of constant thickness resides near the surface, where the Brinkman term is important.