Thermoconvective instability in a horizontal porous cavity saturated with cold water

The onset of convection in a horizontal porous cavity with regard to the density maximum of water at 3.98°C is studied using a linear stability analysis. In the formulation of the problem use is made of the Brinkman-extended Darcy model which is relevant to sparsely packed porous media. A parabolic density-temperature relationship is used to model the effect of density inversion. The perturbation equations are solved with the aid of the Galerkin and finite element methods. The onset of motion is found to be dependent of the aspect ratio A of the cavity, the Darcy number Da, the inversion parameter γ and the hydrodynamic boundary conditions applied on the horizontal walls of the porous layer. The results for a viscous fluid (Da→∞) and the Darcy porous medium (Da→0) emerge from the present analysis as limiting cases. Numerical results for finite amplitude convection, obtained by solving the full governing equations, indicate that subcritical convection is possible when the upper stable layer extends over more than the half depth. Also, the existence of multiple solutions for a given range of governing parameters is demonstrated.