Abstract: The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical
and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.

Key words: nonlinear dynamical system, dissipative system, projection operator, long-term behaviour, porous medium, conduction-convection-radiation, enclosure, Darcy-Brinkman-Forchheimer drag