Boundary layer and stability analysis of natural convection in a porous cavity

Natural convection in a rectangular porous medium is studied analytically and numerically. The two vertical walls of the cavity are maintained at different temperature while the two horizontal ones are adiabatic. Governing parameters of the problem under study are the Rayleigh number, Ra, and the aspect ratio of the cavity, A. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. For a large Rayleigh number, an approximative model of the boundary layer regime is obtained based on the numerical results. Simplified model for the stratification parameter, γ, have been obtained for high heating, γ=1.22A−0.47Ra0.46. The thermal stratification coefficient, τ, was shown to depend essentially on the aspect ratio of the enclosure, A, and becomes almost independent of the Rayleigh number, Ra, in the boundary layer regime, τ≈3/2A. The linear stability theory of the parallel flow is employed to obtain the critical Rayleigh number (Hopf's bifurcation) for a tall cavity (A≫1). It is found that the flow is stable independent of the stratification coefficient, τ.