Instability of stationary two-dimensional mixed convection across a vertical porous layer

The two-dimensional and stationary mixed convection in a vertical porous layer is studied. This mixed convection flow is caused by the pressure and temperature difference between the parallel boundaries of the porous layer. In the limiting case where the boundary pressure difference is zero, the two-dimensional flow actually becomes the one-dimensional conduction regime of natural convection. On the other hand, when the boundary temperature difference tends to zero, the two-dimensional flow becomes a simple uniform horizontal through flow. The linear stability of the basic two-dimensional mixed convection is analysed. The growth rate and the angular frequency of the perturbations are evaluated numerically. The neutral stability curves are obtained by plotting the Rayleigh number versus the wave number, for different values of the Péclet number associated with the boundary pressure difference. The effect of the dynamic boundary conditions on the onset of the convective instability is discussed.