Numerical Approach of Thermal non Equilibrium Natural Convection in a Square Porous Cavity with Partially Thermally Active Side Walls

Document Type : Special Issue Manuscripts


1 University of Mentouri Brothers, Constantine 25000, Algeria

2 University of Mentouri Brothers

3 IRTES-M3M Laboratory, UTBM, Belfort 90000, France



A numerical study was conducted to investigate thermal non equilibrium natural convection heat transfer in a square porous cavity with partial active vertical walls. The left vertical side wall is partially heated while the right side wall is partially cooled. The remaining portions of the vertical side walls as well as the top and bottom of the cavity are adiabatic. Depending on the location of hot part and cold part, respectively on the left and right side walls, different cases may be obtained. In this study we are limited to two cases: Upper-Lower and Lower-Upper active walls. The Brinkman Forchheimer extended Darcy model is used in the present study. Moreover, the two equations model is used to take into account separately local temperatures of the fluid and the solid. The resulting governing equations are solved by finite volume method and the standard SIMPLER algorithm. Numerical experiments have been carried out for a wide range of parameters, namely: Rayleigh number, Darcy number, inter-phase heat transfer coefficient and modified conductivity ratio. The obtained results reveal that the location of the hot and cold parts on the vertical side walls has a significant influence on the flow structure and the rate of heat transfer within the enclosure.