Etude de la convection bidiffusive dans un milieu poreux anisotrope

Abstract

The phenomenon of the natural convection in porous anisotropic media has been studied by several authors because of its importance in many industrial applications. The literature shows that the studies of heat and mass transfer induced by thermosolutal convection in an anisotropic porous medium are few compared to those of natural convection in isotropic media. It is in this context that our present work is part. It is to study the two‐dimensional problem of thermosolutal natural convection within an anisotropic porous medium saturated by a binary fluid, assumed to be incompressible, confined within a horizontal rectangular enclosure. The vertical walls of the cavity are subjected to constant temperatures and concentrations (boundary conditions of Dirichlet), while the horizontal walls are kept waterproof and adiabati . The convective flow is governed by different control parameters, namely the Darcy number, the Rayleigh number, the ratio of volume forces, the Lewis number, and the aspect ratio of the cavity. The conservation equations of mass, momentum, energy and concentration were derived taking into account the Boussinesq approximation. The mathematical model used is the Darcy‐Brinkman‐Forchheimer. A numerical code based on the finite volume method was developed to solve the basic equations in anisotropic saturated porous medium. The influence of parameters such as the anisotropy in thermal conductivity and the anisotropy in permeability on the transfer of heat and mass and on the flow structures were analyzed. The results are validated by comparison with previous work reported in the literature. A satisfactory agreement was observed. The parametric study involved the aspect ratio of the cavity, the Darcy number that characterizes the permeability of the medium, the thermal Rayleigh number, which characterizes the deviation of the temperature, the ratio of volume forces and the number of Lewis which characterizes the ratio of thermal and solutal diffusions on the evolution of flow structures and heat and mass transfer. It was concluded that the thermal anisotropy affect significantly transfers in different situations. The numerical solution shows that for high volume forces, mass transfer is the vi same regardless of the conductivity ratio. The ratio of volume forces has no effect on the heat transfer. The study of the influence of anisotropy in permeability rate on transfers identified two flow regimes. A fully convective and the other moderately convective. The comparison between Darcy model and Darcy‐Brinkman‐Forchheimer model has also allowed highlighting: Identification of three transfer zones; flow and heat and mass transfer are proportional to Darcy number; heat and mass transfer increase with Rayleigh number; the appearance of two secondary convection cells inside the main flow at low values of Rayleigh number; the anisotropy in permeability causes thermal anisotropy; the occurrence of two side convection cells within Master for low values of the Rayleigh number flow, and the permeability anisotropy leads to anisotropy and thermal and vice versa.