Mixed-convection flow adjacent to a horizontal surface in a porous medium with variable permeability and surface heat flux

A nonsimilarity solution for mixed convection from impermeable horizontal surfaces in a saturated porous medium incorporating variation of permeability and thermal conductivity due to packing of particles is obtained for the case of variable heat flux in the form q(w)(x) = bx(n). To cover the entire mixed-convection regime, two different transformations are used. In the first transformation the nonsimilarity parameter zeta(f) = Ra-x/Pe(x)(2) is found to measure the buoyancy effect in the forced-flow-dominated mixed-convection regime, and in the second transformation the nonsimilarity parameter zeta(n) = Ra-x/Pe(x)(1/2) is found to measure the forced-flow effect in the buoyancy-dominated mixed-convection regime. The two solutions provide results that cover the entire mixed-convection regime from pure forced- to pure free-convection limit. Numerical results for different values of surface heat flux variation, permeability K, and thermal diffusivity cc are presented.