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

*(English)*Zbl 1421.76211Summary: 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 \(Ra_T=10^{5},10^{6}\), the Hartmann number \(Ha=0,10,25,50\), the dimensionless heat generation or absorption \(\phi =0.0, -1.0\), 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 and H. Al-Naser [Int. J. Heat Mass Transfer 45, No. 12, 2465–2483 (2002; Zbl 1101.76055)].

##### Keywords:

lattice BGK simulations; double-diffusive flow; heat and mass transfer; magnetic field; numerical results
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\textit{C. Ma}, Nonlinear Anal., Real World Appl. 10, No. 5, 2666--2678 (2009; Zbl 1421.76211)

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##### References:

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