Linear stability of free convection in a vertical cavity heated by uniform heat fluxes

A linear stability analysis is performed of the free convection flow in a vertical cavity heated by uniform heat fluxes at the four walls. As the flow under such heating conditions is quasi-parallel, it is possible to derive analytical solutions for the basic flow which are then used to determine the critical Rayleigh numbers, solving the stability equations by a shooting method for different values of the governing parameters. Comparison of the stability analysis predictions with the numerical simulations shows the validity of the parallel flow approximation for cavity aspects ratios of 4, or higher.