Buoyancy-driven convection in a horizontal porous layer saturated by a power-law fluid: The effect of an open boundary

An infinitely wide horizontal porous layer saturated by a power-law fluid is heated from below by an imposed heat flux. The basic stationary state is characterised by a horizontal throughflow and a constant temperature gradient along the vertical direction. A linear stability analysis is performed by employing the method of normal modes. The eigenvalue problem obtained is solved by employing two different approaches: a hybrid analytical/numerical technique and a fully numerical technique. The critical values defining the threshold configurations for the onset of thermal convection are presented. These threshold values display a non monotonic dependence on the basic flow rate while they are monotonically increasing functions of the power-law index.