Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: Multi-solutions and oscillations
Using the Darcy model, this paper considers analytically and numerically the problem of combined heat and mass transfer with opposing horizontal heat and solute gradients in an anisotropic porous cavity. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. It is also assumed that the principal directions of permeability tensor are oblique to the gravity vector, while those of thermal and solutal diffusivity coincide with horizontal and vertical coordinate axes. The novelty of this problem is that the vertical walls of the cavity are maintained at constant fluxes of heat and mass, and this is a situation which occurs in oceanography, geophysics, metallurgy and electro-chemistry. The authors prove the existence of multiple solutions and the occurence of oscillatory convection. An analytical solution, valid for high aspect ratio and based on parallel flow approximation, is presented. This analytical solution is confirmed by numerical solution in a reasonably good range of anisotropic parameters. The authors show that for the range of parameters studied, the interval of buoyancy ratio for the existence of permanent oscillation turns out to be a subset of the same interval in which multiple solutions exist. It is also shown that a small rotation of the permeability tensor makes a significant change in the strength of the flow as well as in temperature and concentration profiles. The local direction of the flow changes due to the variation in the extent of thermal and concentration layers, due to the opposite buoyant mechanism, and due to anisotropy.
scientific article; zbMATH DE number 1797426