Stability analysis of an anisotropic uniformly heated/cooled porous layer

The flow resulting from the combination of forced and natural convection within a horizontal porous layer filled with Newtonian fluid is analyzed. The layer boundaries are subjected to uniform and symmetrical heating/cooling. The porous layer is anisotropic such as the permeability is function of the coordinates, and a fully developed flow occurs in the layer, where the temperature is a function of both spanwise and streamwise directions. The latter steady basic state undergoes the onset of thermal instability for adequate values of the Darcy-Rayleigh number, with the neutral stability condition being heavily influenced by the Péclet number, which is linked to the mass flow rate of the basic state. A streamfunction approach is applied and the normal modes method is employed to investigate the linear stability of the basic state. The system of ordinary differential equations obtained is tackled numerically and the critical values of the governing parameters are studied as functions of the Péclet number and of the permeabilities fraction.