Onset of thermal convection in an anisotropic and inhomogeneous porous layer underlying a fluid layer
Journal
Journal of Applied Physics
Journal Volume
69
Journal Issue
9
Pages
6289-6301
Date Issued
1991
Author(s)
Hsu, L.H.
Abstract
The onset of thermal convection in a single-component fluid layer bounded above by a rigid wall and saturating an underlying porous medium whose permeability and thermal diffusivity may be anisotropic and inhomogeneous is considered. A linear stability analysis is used to systematically implement a parametric study that covers a wide range of depth ratio ζ (ratio of fluid layer depth to saturated porous layer depth), the permeability ratio ξ (ratio of horizontal to vertical permeability), thermal diffusivity ratio ξT (ratio of horizontal to vertical thermal diffusivity), and inhomogeneities of permeability and thermal diffusivity of the porous medium in the vertical direction. For ζ≤0.1, the critical Rayleigh number Rcm was found to be essentially an explicit function of ξT/ξ and the corresponding critical wave number acm was found to be a function of (ξ×ξT)−1/4; since the porous layer dominates the two-layer system by convection, the anisotropic and inhomogeneous effects are significant. For ζ≥0.2, however, no explicit function for either Rcm or acm is obtained and the anisotropic and inhomogeneous effects are not significant because the onset of convection is largely confined to the fluid layer. Generally, the vertically increasing permeability leads to a less stable state with smaller critical wavelength; and the vertically increasing thermal diffusivity leads to a more stable state with larger critical wavelength.<lz> <lz>
Type
journal article