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

Abstract

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 ζ f =Ra* x /Pe2 x 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 ζ n =Pe x /Ra*1/2 x is found to characterize the effect of the forced flow on the natural convection, with (K′U∞/ν)Ra*1/2 x /Pe x 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 ζ f =0, the pure forced convection limit, to ζ f =1 and the solution of the second is carried out for ζ n =0, the pure natural convection limit, to ζ n =1. The two solutions meet and match at ζ f =ζ n =1, and R* h =G* h .