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Double Diffusive Natural Convection in Non-Darcy Porous Media with Non-Uniform Porosity
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Abstract
We studied in this paper the phenomena of double-diffusive convection in a cylindrical enclosure filled with a porous medium saturated with a Newtonian fluid. The porosity of the porous media is variable from the walls to the bulk and follows an exponential law. The enclosure is heated from below and two mass concentrations C0, C1 are applied respectively to the surfaces (bottom, top) of the cylinder. The vertical walls are rigid, impermeable and adiabatic. An extended law of Brinkman-Forchheimer (EBFD) describes the fluid flow occurring in the porous layers by using the Boussinesq approximation. The mass concentration follows the basic Fick law, and the model chosen to describe the heat transfer is based on the approximation of one temperature. The heat and mass flow are controlled by the dimensionless numbers such as Rayleigh, Lewis, Darcy, Prandtl number that appear by dimensionless of the system of equations. The finites differences method is used to solve numerically the problem. The study focused on the effect of the dimensionless numbers on the concentrations and on the rate of heat transfers profiles in the overall Nusselt number, while considering the porosity uniform or non-uniform. The numerical code developed can be used for various industrial processes involving the phenomenon of natural convection
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