Non-Darcy natural convection in a square cavity filled with a porous medium

The steady natural convection in a square cavity filled with a porous medium with the non-Darcy model (Darcy-Forchheimer model) is numerically studied in the present paper. The left vertical wall of the cavity is heated to a constant temperature Th, while the right wall is cooled to a constant temperature Tc. Both the horizontal walls are adiabatic. The finite volume numerical method is used to solve the non-dimensional governing equations. The results are presented to show the effect of the inertial parameter on the average Nusselt number and the fluid circulation in the porous cavity for different values of Rayleigh number. It is found that increasing the inertial effects parameter leads to a slowdown in the natural convection currents in the cavity and reduces the average Nusselt number for constant values of Rayleigh number.