Buoyant convection in a parallelogrammic enclosure filled with a porous medium – General analysis and numerical simulations

A numerical study is made of buoyant convection in a parallelogrammic enclosure, which is filled with a porous medium. The enclosure is equipped with insulated non-vertical sidewalls and isothermal horizontal endwalls. The temperature at the top horizontal endwall is higher than the temperature at the bottom horizontal endwall. This provides a generally stable fluid stratification in the interior. Emphasis is given to the explicit role of local baroclinicity, which is induced in the immediate neighborhood of the non-vertical portions of the sidewalls. Comprehensive numerical solutions to the governing equations are acquired. The Boussinesq-fluid assumption is used, and the Brinkman-extended Darcy flow model is adopted in the momentum equation. In order to represent local thermal non-equilibrium, the two-equation model is utilized in the energy equation. A systematic scale analysis is performed, which produces descriptions of general flow and heat transport characteristics. These results are shown to be consistent with the detailed numerical solutions. Enhancement of heat transfer through the cavity is more pronounced as the inclination angle of the non-vertical sidewall increases.