Abstract Numerical results of laminar fully developed natural convection in an inclined composite channel are presented. The mathematical model relies on the Method of Volume Averaging and thus a single domain approach is applied. The Forchheimer correction and thermal dispersion effects are considered while local thermal equilibrium between the porous matrix and the fluid is assumed. Velocity and temperature profiles are displayed and their rather weak dependence upon porosity and fluid properties assessed. Forces acting on the fluid are identified and discussed. Thermal performances of the composite channel in laminar conditions are evaluated. One of the main results of the present investigation is that when non-Darcian effects and thermal dispersion are negligible, the Nusselt number of the composite system in natural convection regime is independent of the channel inclination.