Simulation numerique de La convection naturelle doublement diffusive au sein d’une enceinte rectangulaire excitee periodiquement

Abstract

We studied in this work the phenomenon of the double diffusive natural, laminar and permanent convection in a rectangular enclosure filled with a binary fluid mixture supposed incompressible with a constant horizontal thermal gradient where one of the vertical walls (left) is heated with a sinusoidal spatial periodic function « TAB » and the other wall (right) is kept at a cold constant temperature « TCD » with TAB > TCD and also an horizontal constant solutal gradient in the same way. The horizontal walls are insulated and no permeable. The Prandtl and Lewis numbers are fixed respectively to 0,701 and 1 while thermal Rayleigh number vary from 50 to 5x104. The flow is incompressible and the mathematical model governing our problem was based on the Boussinesq approximation and vorticity-stream function formulation. The continuity, heat, mass and momentum equations are numerically solved with a self-developed code using the finite volume method to discretize the equations. Obtained numerical results are presented in isopaths, isotherms, isoconcentrations and local and average Nusselt and Sherwood numbers graphs on enclosure’s walls. These results show that the thermal excitation nature, the aspect ratio of enclosure and the buoyancy ratio affect strongly the structure flow and also the heat and mass transfer rate.