Onset of convection in an anisotropic porous layer of finite lateral extent

A linear stability analysis is performed to study the onset of convection in a horizontal saturated porous layer of finite aspect ratio and anisotropic in permeability. The critical Rayleigh number is established as a function of the permeability ratio, the inclination angle of the principal axes and the enclosure aspect ratio. A linear stability analysis is conducted through a numerical procedure. Also, for the weak finite amplitude convection, results are obtained by solving numerically the full governing equations.