Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall

Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.