Nonsimilarity solutions for non-Darcy mixed convection from horizontal surfaces in a porous medium

Non-Darcy mixed convection in a porous medium from horizontal surfaces with variable surface heat flux of the power-law distribution is analyzed. The entire mixed convection regime is divided into two regions. The first region covers the forced convection dominated regime where the dimensionless parameter ζf=Ra*x/Pe2x is found to characterize the effect of buoyancy forces on the forced convection with K′U∞/ν characterizing the effect of inertia resistance. The second region covers the natural convection dominated regime where the dimensionless parameter ζn=Pex/Ra*1/2x is found to characterize the effect of the forced flow on the natural convection, with (K′U∞/ν)Ra*1/2x/Pex characterizing the effect of inertia resistance. To obtain the solution that covers the entire mixed convection regime the solution of the first regime is carried out for ζf=0, the pure forced convection limit, to ζf=1 and the solution of the second is carried out for ζn=0, the pure natural convection limit, to ζn=1. The two solutions meet and match at ζf=ζn=1, and R*h=G*h.