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

We present an account of the linear instability of Darcy-Boussinesq convect ion in a uniform, unstably stratified porous layer at arbitrary inclination s a from the horizontal. A full numerical solution of the linearized distur bance equations is given and the detailed graphical results used to motivat e various asymptotic analyses. A careful study shows that at large Rayleigh numbers two-dimensional instability can only arise when alpha less than or equal to 31.30 degrees. However it is also demonstrated that the maximum i nclination below which this instability may be possible is the slightly gre ater value of 31.49 degrees which corresponds to a critical Rayleigh number of 104.30.