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 $x$-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 $Pr=1$, the Lewis number $Le=2$, the thermal Rayleigh number $R{a}_T={10}^5,{10}^6$, the Hartmann number $Ha=0,10,25,50$, the dimensionless heat generation or absorption $?=0.0,?1.0$, the buoyancy ratio $N=0.8,1.3$, and the aspect ratio $A=2$ 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].