On the horizontal throughflow across a vertical porous wall

The stationary two-dimensional mixed convection flow in a vertical porous wall subject both to a temperature and to a pressure gap across its boundaries is studied. The instability of this flow is investigated by adopting a linear modal analysis. The two-dimensional transverse rolls are shown to be the preferred pattern at onset of instability. Transverse rolls turn out to be travelling modes. They are driven by the net vertical flow predicted by the basic solution. A numerical procedure based on the joint use of the Runge-Kutta method and on the shooting method is employed to solve the perturbation eigenvalue problem. This numerical solution yields both the neutral stability curves, defining the threshold of linear instability, and the critical Darcy-Rayleigh number yielding the onset condition of instability.