Numerical Study of Natural Convection in a Porous Cavity with Sinusoidal Thermal Boundary Condition

The steady natural convection in a rectangular cavity filled with a heat-generating porous medium was numerically investigated using a thermal non-equilibrium model for the heat transfer between the fluid and solid phases. All of the walls of the enclosure are adiabatic, except for the left wall, which is partially heated and cooled by a spatial sinusoidal temperature profile. The results show that the temperature fields near the left wall and the local Nusselt number of the left wall vary periodically because of the sinusoidal boundary condition. There exists an optimal fluctuant parameter of N (N=3) to maximize the heat transfer rate of the fluid phase in the square enclosure. The periodicity parameter N has a significant influence on the value of the average Nusselt number of the fluid phase when the Darcy and Rayleigh numbers increase.