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 f=Ra*x/Pe2x is found to characterize the effect of buoyancy forces on the forced convection with KU/ characterizing the effect of inertia resistance. The second region covers the natural convection dominated regime where the dimensionless parameter n=Pex/Ra*1/2x is found to characterize the effect of the forced flow on the natural convection, with (KU/)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 f=0, the pure forced convection limit, to f=1 and the solution of the second is carried out for n=0, the pure natural convection limit, to n=1. The two solutions meet and match at f=n=1, and R*h=G*h. Also a non-Darcy model was used to analyze mixed convection in a porous medium from horizontal surfaces with variable wall temperature of the power-law form. The entire mixed convection regime is divided into two regions. The first region covers the forced convection dominated regime where the dimensionless parameter f=Rax/Pex3/2 is found to measure the buoyancy effects on mixed convection with DaxPex/ as the wall effects. The second region covers the natural convection dominated region where n=Pex/Rax2/3 is found to measure the force effects on mixed convection with DaxRax2/3/ as the wall effects. Numerical results for different inertia, wall, variable surface heat flux and variable wall temperature exponents are presented.