Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field and heat source

In this paper, we develop a temperature-concentration lattice Bhatnagar-Gross-Krook (TCLBGK) model, with a robust boundary scheme for simulating the two-dimensional, hydromagnetic, double-diffusive convective flow of a binary gas mixture in a rectangular enclosure, in which the upper and lower walls are insulated, while the left and right walls are at a constant temperature and concentration and a uniform magnetic field is applied in the xx-direction. In the model, the velocity, temperature and concentration fields are solved by three independent LBGK equations which are combined into a coupled equation for the whole system. In our simulations, we take the Prandtl number Pr=1Pr=1, the Lewis number Le=2Le=2, the thermal Rayleigh number RaT=105,106RaT=105,106, the Hartmann number Ha=0,10,25,50Ha=0,10,25,50, the dimensionless heat generation or absorption ϕ=0.0,−1.0ϕ=0.0,−1.0, the buoyancy ratio N=0.8,1.3N=0.8,1.3, and the aspect ratio A=2A=2 for the enclosure. The numerical results are found to be in good agreement with those of previous studies [A.J. Chamkha, H. Al-Naser, Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients, Int. J. Heat Mass Transfer 45 (2002) 2465C2483].