Absolute instability in a horizontal porous layer with symmetric wall heat fluxes

A linear analysis of mixed convection flow in a fluid saturated porous layer is carried out with respect to the onset of thermal instability. In particular, the threshold conditions for the onset of absolute stability are investigated. The horizontal boundary walls of the porous layer are impermeable and subjected to symmetric heating/cooling. The basic stationary state whose stability is investigated prescribes a throughflow in the horizontal direction, inclined an angle φ to the x direction, and a temperature gradient which has both horizontal and vertical components. The dependence of the disturbances on the horizontal y-direction is parametrized by employing the inclination angle φ. The perturbed problem is thus treated without any loss of generality in a two-dimensional fashion by employing the streamfunction-temperature formulation. The solutions of the problem obtained by perturbing and linearizing the governing equations are sought in form of normal Fourier modes. The resulting eigenvalue problem is solved numerically as a boundary value problem. In order to study the onset of absolute instability, the steepest descent approximation is employed. The comparison between the threshold values for the onset of convective and absolute instability is performed by varying the basic flow strength and the inclination angle φ. The inclination angle has a relevant impact on the threshold for the onset of absolute instability: as the basic stationary flow displays a non-negligible component in the propagation direction of the wavepacket, the threshold value of the Darcy–Rayleigh number for the onset of absolute instability increases rapidly.