Natural Convection Induced by a Centrifugal Force Field in a Horizontal Annular Porous Layer Saturated with a Binary Fluid

The Darcy Model with the Boussinesq approximation is used to study natural convection in a horizontal annular porous layer filled with a binary fluid, under the influence of a centrifugal force field. Neumann boundary conditions for temperature and concentration are applied on the inner and outer boundary of the enclosure. The governing parameters for the problem are the Rayleigh number, Ra, the Lewis number, Le, the buoyancy ratio, j{\varphi } , the radius ratio of the cavity, R, the normalized porosity, e{\varepsilon } , and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in a thin annular layer (R → 1), analytical solutions for the stream function, temperature and concentration fields are obtained using a concentric flow approximation and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection is predicted explicitly by the present model. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat and mass transfer are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations.