Multiple steady states in a porous enclosure partially heated and fully salted from below

Abstract

The Darcy model with the Boussinesq approximation is used to study natural convection in a porous medium saturated by a binary fluid. The geometry considered is a square cavity whose portion of the bottom surface is isothermally heated, the upper surface is cooled at a constant temperature and all other surface are adiabatic. The solutal buoyancy forces are assumed to be induced by the imposition of uniform concentration on the upper and lower boundaries. The governing parameters for the problem are the thermal Rayleigh number, R T , the Lewis number, Le, the buoyancy ratio, φ, the dimensionless length of the bottom plate, B T , the aspect ratio of the cavity A, the normalized porosity of the porous medium, ε, and the relative position of the heating element with respect to the vertical centerline of the cavity, δ T . Two main convective modes are studied, namely single and double-cell convection, and their features are described. Also the possible existence of tricellular flows is demonstrated. Maximum streamfunction and global Nusselt and Sherwood number are presented as functions of the external parameters. The existence of up to three steady-state solutions for a given set of the governing parameters is demonstrated.