Onset of double-diffusive convection in a rectangular porous cavity subject to mixed boundary conditions

The onset of double-diffusive convection in a horizontal porous cavity is studied numerically using linear stability analysis. In the formulation of the problem, use is made of the Darcy model with the Boussinesq approximation. Mixed boundary conditions for heat and solute are specified on the horizontal walls of the enclosure while the two vertical ones are impermeable and adiabatic. The Galerkin and the finite element methods are used to solve the perturbation equations. The onset of convection is found to be dependent of the aspect ratio of the cavity, A, normalized porosity, ε, Lewis number, Le, solutal to thermal buoyancy ratio, N, and the thermal and solutal boundary conditions. For a confined enclosure, it is shown that there exists a supercritical Rayleigh number, RsupTC, for the onset of the supercritical convection and an overstable Rayleigh number, RoverTC, at which overstability may arise. Furthermore, the overstable regime is shown to exist up to a critical Rayleigh number, RoscTC, at which the transition from the oscillatory to direct mode convection occurs. However, for an infinite layer (A→∞) the results indicate the absence of an overstable regime. Numerical results for finite amplitude convection, obtained by solving numerically the full governing equations, demonstrate that subcritical convection is possible.