Natural Convection of a Two-Component Fluid in Porous Media Bounded by Tall Concentric Vertical Cylinders

This paper reports an analytical and numerical study of the behavior of a binary mixture saturating a vertical annular porous medium. Uniform heat fluxes are applied to the vertical walls while the horizontal walls are impermeable and adiabatic. Solutal gradients are assumed to be induced either by the imposition of constant gradients of concentration on the vertical walls (double diffusive convection, $a=0$⁠) or by the Soret effect (⁠$a=1$⁠). Governing parameters of the problem under study are the thermal Rayleigh $RT$⁠, buoyancy ratio $φ$⁠, Lewis number $Le$⁠, aspect ratio $A$⁠, constant $a$⁠, and curvature $η$⁠. An analytical solution, valid for tall enclosures (⁠$A⪢1$⁠), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. For large Rayleigh numbers (⁠$RT⪢1$⁠), an approximate solution valid in the limit of the boundary layer regime is obtained.