The linear instability of a thermal boundary layer with suction in an anisotropic porous medium

We consider the combined effects of suction and transverse anisotropy on the instability of the uniform thickness boundary layer which is formed on an inclined heated surface in a porous medium. When the medium is isotropic, the stability characteristics are shown to be very similar to that of the inclined Darcy-Benard problem. In particular, longitudinal rolls are always preferred, and transverse rolls are always stable when the inclination of the surface is greater than approximately 31.9°. Transverse anisotropy has no effect on the identity of the preferred mode of convection whenever the anisotropy parameter, ξ, is less than unity. When ξ > 1, there always exists a range of surface inclinations where transverse rolls are preferred. A detailed set of numerical results are given showing how the critical Rayleigh number and wavenumber vary with both inclination and ξ. © 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.