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


1 Department of Civil Engineering, Babol University of Technology, Babol, Iran

2 Department of Mechanical Engineering, University of Idaho, 1776 Science Center


In this study, the effects of different 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 filled 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 profile with different 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 significant effects of  and a on the streamlines and isotherms as

well as the local and average Nusselt numbers at various values ofDa , andRa . Effects of

the governing parameters on heat transfer and fluid flow in the upper and lower parts of the

enclosure are also investigated.