DOUBLE-DIFFUSIVE CONVECTION INSTABILITY IN A VERTICAL POROUS ENCLOSURE

The Galerkin and the finite element methods are used to study the onse t of the double-diffusive convective regime in a rectangular porous ca vity. The two vertical walls of the cavity are subject to constant flu xes of heat and solute while the two horizontal ones are impermeable a nd adiabatic. The analysis deals with the particular situation where t he buoyancy forces induced by the thermal and solutal effects are oppo sing each other and of equal intensity. For this situation, a steady r est state solution corresponding to a purely diffusive regime is possi ble. To demonstrate whether the solution is stable or unstable, a line ar stability analysis is carried out to describe the oscillatory and t he stationary instability in terms of the Lewis number, Le, normalized porosity, epsilon, and the enclosure aspect ratio, A. Using the Galer kin finite element method, it is shown that there exists a supercritic al Rayleigh number, R-TC(sup), for the onset of the supercritical conv ection and an overstable Rayleigh number, R-TC(over), at which oversta bility may arise. Furthermore, the overstable regime is shown to exist up to a critical Rayleigh number, R-TC(osc), at which the transition from the oscillatory to direct mode convection occurs. By using an ana lytical method based on the parallel flow approximation, the convectiv e heat and mass transfer is studied. It is found that, below the super critical Rayleigh number, R-TC(sup), there exists a subcritical Raylei gh number, R-TC(sup), at which a stable convective solution bifurcates from the rest state through finite-amplitude convection. In the range of the governing parameters considered in this study, a good agreemen t is observed between the analytical predictions and the finite elemen t solution of the full governing equations. In addition, it is found t hat, for a given value of the governing parameters, the converged solu tion can be permanent or oscillatory, depending on the porous-medium p orosity value, epsilon.