Onset of Darcy-Benard convection in an inclined layer heated from below

We present an account of the linear instability of Darcy-Boussinesq convection in a uniform, unstably stratified porous layer at arbitrary inclinations α from the horizontal. A full numerical solution of the linearized disturbance equations is given and the detailed graphical results used to motivate various asymptotic analyses. A careful study shows that at large Rayleigh numbers two-dimensional instability can only arise when α≤31.30°. However it is also demonstrated that the maximum inclination below which this instability may be possible is the slightly greater value of 31.49° which corresponds to a critical Rayleigh number of 104.30.