Two- and three-dimensional multiple steady states in a porous cavity heated and salted from below

Two- and three-dimensional numerical studies of double-diffusive natural convection in homogeneous and isotropic porous media, saturated with a binary fluid are analyzed. Top and bottom faces of the enclosures are subject respectively to different but uniform temperatures and concentrations, while its vertical boundaries are considered adiabatic and impermeable to mass transfer. The flow through the medium is governed by the Darcy model. The existence of multiple steady-state solutions is proved for both 20 and 3D models and all the solutions obtained are presented and described. Conjugate effects of the thermal Rayleigh number and the buoyancy ratio on heat transfer, mass transfer and existence range of each flow structure are discussed. Important differences in terms of heat and mass transfer are observed between different solutions. Depending on the governing parameters and the type of solution, the flow structure could be 2D or 3D. It is also found that all the 2D solutions are obtained with the 3D model but the latter has more degrees of freedom allowing a reorganization of the flow not possible in the case of 2D model. For Ra = 200 and opposing thermal and species buoyancy forces, there exists a critical value of N (N = -0.6) below which the concentration stabilizes the flow by settling a bulk stratification. In such a case, the corresponding heat and mass transfer processes are ruled by pure diffusion solely (Nu = Sh = 1). (C) 2011 Elsevier Masson SAS. All rights reserved.