Linearly unstable forced and free flow in an anisotropic porous channel

The combined forced and free convection flow in a horizontal porous channel saturated by a fluid is studied. The boundary walls are considered as uniformly heated-cooled with symmetric heat fluxes. The horizontal porous layer is modelled as anisotropic with different permeabilities in the horizontal and vertical directions. A fully-developed stationary flow in the porous channel exists, endowed with a temperature gradient inclined to the vertical. This basic stationary flow turns out to become linearly unstable when the Rayleigh number is sufficiently high, with a neutral stability condition strongly dependent on the Péclet number associated with the basic flow rate. A minimum Péclet number exists below which no linear instability arises. A streamfunction formulation is introduced to test the behaviour of the small-amplitude perturbations. The stability eigenvalue problem is solved numerically for different Péclet numbers and anisotropy ratios in order to evaluate the neutral stability threshold and the critical values for the onset of the linear instability. • The mixed convection flow in a horizontal porous channel saturated by a fluid is studied. • The walls are considered as uniformly heated/cooled with symmetric heat fluxes. • The anisotropic porous layer has different horizontal/vertical permeabilities. • The conditions for the stationary flow to become linearly unstable are found. • A minimum Péclet number exists below which no linear instability arises.