Forced convection of a non-Newtonian fluid in a channel partially filled with porous layers is studied. In order to study the problem in its most realistic conditions, the Brinkman−Forchheimer model for momentum conservation and two equations, the local thermal equilibrium and nonequilibrium models for energy conservation, are used. Flow is assumed to be fully developed, but development of the thermal boundary layer is taken into account. The effect of the power-law index of the non-Newtonian fluid (n) as well as thermal conductivity of the solid matrix and the thickness of the porous layer are studied. It is shown that thinner porous layer fluids with smaller n show better heat-transfer capability in the same modified Reynolds number, whereas when the porous layer fluids are thicker, fluids with larger n have a greater Nusselt number, except when the thickness ratio is very close to 1.