Approche numerique de la convection naturelle thermosolutale dans des enceintes fermées

Abstract

The problem related to thermosolutal natural laminar and permanent convection in horizontal annulus situated between two eccentric cylinders filled with Newtonian and incompressible binary fluid oriented at an arbitrary angle  is examined numerically. The inner cylinder is heated with hot temperature T1 and high concentration S1 while the outer cylinder is maintained at a cold constant temperature T2 and low concentration S2. The fluid is air and the substance diffused in the enclosure is the vapor. The flow is driven by the thermal and solutal buoyancies. The annular space is filled by a Newtonian and incompressible fluid. The number of Prandtl is fixed at (0.71) but the thermal Rayleigh number, the Lewis number, the slope angle, the relative eccentricity and the buoyancy ratio vary. By using the approximation of Boussinesq and the vorticity-stream function formulation, the flow is modeled by the differential equations with the derivative partial: the equations of continuity, the momentum, the energy and mass are expressed in a frame of reference known as "bicylindrical", to facilitate the writing of the boundary conditions and to transform the curvilinear field into a rectangular one. A computer code was developed, the latter uses finished volumes, for the discretization of the equations and in order to show its reliability, the authors compare results resulting from the latter with other similar results existing in the literature and they examine the effects of the slope of the system, of the relative eccentricity, of the thermal Rayleigh number, of the Lewis number and of the buoyancy ratio values on the results obtained that it is qualitatively or quantitatively.