THE INSTABILITY OF POROUS CONVECTIVE HORIZONTAL BOUNDARY LAYER DUE TO A VERTICAL FLOW WITH A MECHANICAL ANISOTROPY

Abstract

We consider the Wooding problem, namely the onset of convection in a semi-infinite saturated porous medium with uniform downward suction into a horizontal and uniformly hot bounding surface. In particular we shall begin to examine the stability properties of convection for the case of a mechanically anisotropic porous medium. A linearized stability analysis is performed and the partial differential system of governing equations is transformed into ordinary differential eigenvalue problem for the critical Darcy-Rayleigh number as a function of wave number and the anisotropy ratio, ξ. The eigenvalue problem is solved numerically through the use of the MATLAB routine, BVP4C. Neutral curves are presented and the critical parameters are found as a function of ξ. It is found that both the critical Darcy-Rayleigh and wave numbers decrease with increasing values of ξ. An asymptotic analysis is also presented for ξ ≫ 1.