Numerical study of natural convection in a tilted rectangular porous material

Abstract Two-dimensional natural convective flow in a tilted rectangular porous material saturated with fluid is analyzed by solving numerically the mass, momentum and energy balance equations, using Darcy's law and the Boussinesq approximation. Isothermal boundary conditions are considered, where two opposite walls are kept at constant but different temperatures and the other two are thermally insulated. The external parameters considered are the tilt angle, the aspect ratio and the Darcy-Rayleigh number. Three main convective modes are found: conduction, single and multiple cell convection and their features described in detail. Local and global Nusselt numbers are presented as functions of the external parameters. Multiplicity of solutions is explored for aspect ratio unity. The existence of more than one solution is found when the bottom wall is at a higher temperature and in a horizontal or close to horizontal position.