Control volume nite element modeling of free convection inside an inclined porous enclosure with a sinusoidal hot wall

In this study, the eects of dierent governing parameters on natural convection heat transfer between an inclined hot basement roof and a cold environment are investigated numerically, using the Control Volume based Finite Element Method (CVFEM). The medium between the cold and hot surfaces is lled by soil, which can be considered as a porous media. The physical model can be approximated as an enclosure with various inclination angles. The cold wall of the enclosure is assumed to mimic a sinusoidal prole with dierent dimensionless amplitudes. The numerical investigations are conducted at the Prandtl number (Pr = 1) and various values of non-dimensional governing parameters, namely, the porosity ("), Darcy number (Da) and Rayleigh number (Ra). The geometrical variables in this study are the inclination angle ( ) and dimensionless amplitude (a) of the sinusoidal cold wall. The obtained results show the signicant eects of and a on the streamlines and isotherms, as well as the local and average Nusselt numbers at various values of Da, " and Ra. Eects of the governing parameters on heat transfer and uid ow in the upper and lower parts of the enclosure are also investigated.