Etude de la stabilité d'un écoulement paralléle dans une cavité verticale soumise à des flux de chaleur uniformes

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. A numerical solution is developed by employing the control volume method. For the aspect ratio A greater than five, excellent agreement was obtained between analytical and numerical results.

To compute instability problem due to natural convection, the finite difference method was used to determine the critical Rayleigh numbers for a series of Prandtl numbers. Numerical results have shown the existence of two modes of oscillatory instability: thermal mode occurred for Prandtl numbers greater than unity. However, for Prandtl numbers less than unity the hydrodynamic mode appeared. The structure of both modes was determined in terms of the governing parameters, such as: the Rayleigh number, the Prandtl number and the flux ratio q. Other numerical results have led us to conclude that there is a common feature between the thermal mode and the hydrodynamic mode called codimension-2 points.