onset of benard–marangoni convection in a composite layer with anisotropic porous material

The effects of thermal anisotropy and mechanical anisotropy on the onset of bernard-marangoni convection in composite layers with anisotropic porous material is studied. the upper fluid surface, free to atmosphere is considered to be deformable. the eigen value problem is solved using a regular perturbation technique with wave number a as perturbation parameter. it is observed that both stabilizing and destabilizing factors can be enhanced thermal anisotropic parameter and mechanical anisotropic parameter so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible.