Darcy-Brinkman free convection from a heated horizontal surface

The free convection boundary layer flow of a Darcy-Brinkman fluid that is i nduced by a constant-temperature horizontal semi-infinite surface embedded in a fluid-saturated porous medium is investigated in this work. It is show n that both the Darcy and Rayleigh numbers may be scaled out of the boundar y layer equations, leaving a parabolic system of equations with no paramete rs to vary. The equations are studied using both numerical and asymptotic m ethods. Near the leading edge the boundary layer has a double-layer structu re: a near-wall layer, where the temperature adjusts from the wall temperat ure to the ambient and where Brinkman effects dominate, and an outer layer of uniform thickness that is a momentum-adjustment layer. Further downstrea m, these layers merge, but the boundary layer eventually regains a two-laye r structure; irt this case, a growing outer layer exists, which is identica l to the Darcy-flow case for the Lading order term, and an inner layer of c onstant thickness resides near the surface, where the Brinkman term is impo rtant.