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Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field and heat source. (English) Zbl 1421.76211
Summary: 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)].

##### MSC:
 76R50 Diffusion 76M28 Particle methods and lattice-gas methods
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##### References:
 [1] Chamkha, A.J.; Al-Naser, H., Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients, Int. J. heat mass transfer, 45, 2465C2483, (2002) · Zbl 1101.76055 [2] Ostrach, S., Nature convection with combined driving forces, Phys. chem. hydrodyn., 1, 233-247, (1980) [3] Acharya, S.; Goldstein, R.J., Natural convection in an externally heated square box containing internal energy sources, J. heat transfer, 107, 855-866, (1985) [4] Rahman, M.; Sharif, M.A.R., Numerical study of laminar natural convection in inclined rectangular enclosure of various aspect ratios, Numer. heat transfer A, 44, 355-373, (2003) [5] Ujihara, A.; Tagwa, T.; Ozoe, H., Average heat thransfer rates measured in two different temperature ranges for magnetic convection of horizontal water layer heated from below, Int. J. heat mass transfer, 49, 3555-3560, (2006) [6] Chamkha, A.J.; Al-Naser, H., Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat and mass fluxes and opposing temperature and concentration gradients, Inter. J. thermal sci., 41, 936C948, (2002) [7] Alchaar, S.; Vasseur, P.; Bilgen, E., Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field, ASME J. heat transfer, 117, 668C673, (1995) [8] Beghein, C.; Haghighat, F.; Allard, F., Numerical study of double-diffusive natural convection in a square cavity, Int. J. heat mass transfer, 35, 833C846, (1992) [9] Churbanov, A.G.; Vabishchevich, P.N.; Chudanov, V.V.; Strizhov, V.F., A numerical study on natural convection of a heat-generating fluid in rectangular enclosures, Int. J. heat mass transfer, 37, 2969C2984, (1994) · Zbl 0900.76599 [10] Hyun, J.M.; Lee, J.W., Double-diffusive convection in a rectangle with cooperating horizontal gradients of temperature and concentration gradients, Int. J. heat mass transfer, 33, 1605C1617, (1990) [11] Morega, A.M.; Nishimura, T., Double diffusive convection by Chebyshev collocation method, Technol. rep. Yamaguchi univ., 5, 259-276, (1996) [12] Nithiarasu, P.; Seetharamu, K.N.; Sundararajan, T., Double-diffusive natural convection in an enclosure filled with fluid-saturated porous medium: A generalized non-Darcy approach, Numer. heat transfer A, 30, 413-426, (1996) [13] Nishimura, T.; Wakamatsu, M.; Morega, A.M., Oscillatory double-diffusive convection in a rectangular enclosure with combined horizontal temperature and concentration gradients, Int. J. heat mass transfer, 41, 1601-1611, (1998) · Zbl 0962.76616 [14] Guo, Z.-L.; Zheng, C.-G.; Shi, B.-C., Non-equilibruim extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chinese phys., 11, 366-374, (2002)
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