Convection in a vertical cavity submitted to crossed uniform heat fluxes

In this study, free convection in a vertical cavity heated from the four walls by uniform heat fluxes is considered. Analytical solutions are derived for a fully developed base flow, for which linear stability analysis predicts the growth of oblique, threedimensional disturbances in general. A Hopf type bifurcation occurs at the critical Rayleigh number, over the entire range of Prandtl numbers and heat flux ratios considered, characterized by oscillating instabilities. Depending mostly on the value of the Prandtl number, either thermal, for Pr>1, or hydrodynamic, for Pr<1, instability modes are predicted. For small Prandtl numbers, both modes can occur at the codimension two intersection points of the critical branches.