Onset of convective instability within an inclined porous layer with a permeable boundary

The investigation of the thresholds that identify the onset of convective instability in a fluid saturated porous layer is performed. The layer is inclined with respect to the horizontal and the boundaries are held at different uniform temperatures. The layer is also semi-permeable: one boundary is impermeable and the other one is permeable. This configuration yields a basic state characterised by a single convective cell, with zero mass flow rate, that fades for small inclination becoming completely motionless for the horizontal case. Since the central part of this cell is considered, the basic flow is parallel and the basic temperature profile is dominated by conduction. This basic state is perturbed employing small-amplitude disturbances such that the linear stability analysis can be performed. A Squire-type transformation is applied to reduce the complexity of the problem. A numerical procedure is employed to obtain the critical values of the governing parameters.