Onset of buoyancy driven convection in an inclined porous layer with an isobaric boundary

The linear stability analysis of a fluid saturated porous layer is carried out. The porous layer is inclined to the horizontal and is infinitely wide. One boundary of the layer is permeable while the other one is impermeable. The two boundaries are subject to different temperatures, so that convective instability may arise when such a temperature difference exceeds a threshold value. The basic state whose stability is studied consists of a single cell with no net mass flow rate. The critical values of the governing parameters are computed numerically and are presented as functions of the inclination angle. The threshold relative to the horizontal layer recovers the results already present in the literature. The inclination angle comes out to be a stabilising parameter such that the vertical layer cannot become unstable.