Lbm Simulation Of Hydromagnetic Double-Diffusive Convection With Variable Temperature And Concentration Gradients

The lattice Boltzmann method is a new numerical scheme based on microscopic model for fluids flow. According to LBM, fluid particles are much larger than the molecules on the microscopic level. However, on the macroscopic level, fluid particles are' infinitely small. Compared with the traditional Computational Fluid Dynamics (CFD) methods, LBM has many unique advantages, such as simple codes, easy implementation of boundary conditions, and fully parallelism. These features make LBM apply successfully to many fields, such as microscale flow and Transfer, the porous media, magnetohydrodynamics, the crystal growth etc.In this paper, the two-dimensional, hydromagnetic double-diffusive convection of a binary gas mixture is simulated by a temperature-concentration lattice Bhatnagar-Gross-Krook (TCLBGK) model in a rectangular enclosure with the top and bottom walls being insulated, while linearly variable temperature or concentration gradient or both are imposed along the left and right walls from the bottom to the top and a uniform magnetic field is applied in x-direction. We take the Prandtl number Pr=1, the Lewis Le =2, the thermal Raleigh numberRaT=105, the Hartmann number Ha=0,25,50, the dimensionless heat generation or absorption (?)=0, the aspect ration A=2 for the enclosure and the ratio of buoyancy forces N=0.8,1.3. For more details about temperature and concentration gradients on the impact of double-diffusive convection, there are three possible circumstances to consider about the left and right walls of the cavity. One is that linearly variable temperature and constant concentration are imposed along the left and right walls, another is that constant temperature and linearly variable concentration are imposed along the two walls, the other is linearly variable temperature and linearly variable concentration.In the first case, the calculation was firstly carried out at various values of the Hartmann number Ha for Le=2.0, N=0.8 and 1.3. The streamlines at N=0.8 and 1.3 are obviously stratified throughout the Ha range, and each recirculation cell splits into two smaller circulating cells of opposite directions situated close to each of the insulated upper and lower walls. The temperature gradient is larger than the constant concentration that in the upper part of the rectangular cavity, a large central clockwise thermal recirculation closes to the insulated upper wall. It is shown that thermal convection is stronger when temperature gradient is larger. For the second case, compared with the first case, however, there are some differences between them. For N=0.8, the flow is still primarily dominated by thermal buoyancy effects, but a large central clockwise thermal recirculation closes to the insulated lower wall, for N=1.3, the flow is also mainly dominated by compositional buoyancy effects, whereas, a big counterclockwise compositional recirculation exists in the insulated upper wall. It is found that variable concentration gradient has influence on the mass transfer. In the last case, For N=0.8, the zone of heat transfer ocuppies the cavity almost exclusively. For N=1.3, the diffusion of solute ocuppies the cavity almost exclusively. This situation shows that the strength of convection of the mass transfer and heat transfer depends on the strength of their buoyancy, respectively, when the concentration and temperature gradients are the same.