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Natural Convection in a Porous Medium Cavity with an Applied Vertical Magnetic Field using Lattice Boltzmann Method
Abstract:We report the results of an lattice Boltzmann simulation of magnetohydrodynamic damping of sidewall convection in a rectangular enclosure filled with a porous medium. In particular we investigate the suppression of convection when a steady magnetic field is applied in the vertical direction. The left and right vertical walls of the cavity are kept at constant but different temperatures while both the top and bottom horizontal walls are insulated. The effects of the controlling parameters involved in the heat transfer and hydrodynamic characteristics are studied in detail. The heat and mass transfer mechanisms and the flow characteristics inside the enclosure depended strongly on the strength of the magnetic field and Darcy number. The average Nusselt number decreases with rising values of the Hartmann number while this increases with increasing values of the Darcy number.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331857Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1424
 G.M. Oreper and J.Szekely, "The effect of an externally imposed magnetic field on buoyancy driven flow in a rectangular cavity". J. Crystal Growth, vol. 64, 1983, pp. 505-515.
 K. Vajravelu and A. Hadjinicolaou," Nonlinear hydromagnetic convection at a continuous moving surface," Nonlinear Analysis, Theory, Methods and Applications vol. 31, 1998 , pp. 867-882.
 M.A. Al-Nimr and M.A. Hader, "MHD free convection flow in openended vertical porous channels," Chemical Eng. Sci. vol. 54, 1999, pp. 1883-1889.
 A.J. Chamkha, "Hydromagnetic combined convection flow in a vertical lid-driven avity with internal heat generation of absorption," Numer. Heat Transfer Part A vol. 41, 2002, pp. 529-546.
 M.N. Borjini, H.B. Aissia, K. Halouani, and B. Zeghmati, "Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid," Int. J. Heat Mass Transfer vol. 49,2006, pp. 3984-3996.
 S. Alchaar, P. Vasseur and E. Bilgen, "Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field," J. Heat Transfer, vol. 117, 1995, pp. 668-673.
 D.A. Nield, "Impracticality of MHD convection in a porous medium," Transport Porous Med. vol. 73, 2008, pp-379.
 A. Barletta, S. Lazzari, E. Magayri and I. Pop," Mixed convection with heating effectin a vertical porous annulus with a radially varying magnetic field," Int. J. Heat Mass Transfer vol. 51 (25-26) ,2008, pp. 5777-5784.
 N. Rudraiah, R.M. Barron, M. Venkatachalappa, and C.K. Subbaraya, "Effect of a magnetic field on free convection in a rectangular enclosure," Int. J. Engng. Sci. vol. 33, 1995, pp. 1075-1084.
 L. Robillard, A. Bahloul, and P. Vasseur, "Hydromagnetic natural convection of a binary fluid in a vertical porous enclosure," Chem. Eng. Comm. vol. 193, 2006, pp. 1431-1444.
 B.J. Pangrle, E.G. Walsh, S.C. Moore, and D. Dibiasio-o, "Magnetic resonance imaging of laminar in porous tube and shell systems flow," Chemical Eng. Sci. vol. 47 ,1992, pp. 517-526.
 J.D. McWhirter, M.E. Crawford, and D.E. Klein, "Magneto hydrodynamic flows porous media ii: Experimental results," Fusion Science and Tech. vol. 34,1998, pp. 187-197.
 P. Kuzhir, G. Bossis, V. Bashtovoi, and O.Volkova, "Flow of magnetorheological fluidthrough porous media," European Journal of Mechanics B/Fluids. vol. 22, 2003, pp. 331-343.
 K.M. Khanafer and A.J. Chamkha, "Hydromagnetic natural convection from an inclined porous square enclosure with heat generation," Numer. Heat Transfer Part A. vol. 33, 1998, pp. 891-910.
 G. R. McNamara, and G. Zanetii, , "Use of the Boltzmann Equation to Simulate Lattice-Gas Automata," Phys. Rev. Lett., vol.61, 1988, pp.2332-2335.
 J. Onishi, Y. Chen, and H. Ohashi, "Lattice Boltzmann simulation of natural convection in a square cavity," JSME Int. J. Ser. B, vol. 44, 2001, pp.53-62.
 D. Zhang , R. Zhang, S. Chen, and W. Soll, "Pore scale study of flow in porous media: Scale dependency," REV, and statistical REV, Geophysical Research Letters, vol. 27, 2000, pp.1195-1198.
 D.A. Nield, and A. Bejan, Convection in Porous Media, 3rd ed, Springer, New York, 2006.
 O.Dardis, and J. McCloskey, "Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media," Phys. Rev. E, vol. 57, 1998, pp.4834-4837.
 M.A.A. Spaid, and F.R. Phelan, "Lattice Boltzmann methods for modeling micro scale flow in fibrous porous media," Phys. Fluids, vol. 9, 1997, pp. 2468-2474.
 S. J. Kim, and K.Vafai, "Analysis of natural convection about a vertical plate embedded in a porous medium," Int. J. Heat Mass Transfer, vol. 32, 1989, pp. 665-677.
 Z. Guo, and T.S. Zhao, "Lattice Boltzmann model for incompressible flows through porous media," Phys. Rev. E, vol. 66, 2002,pp.036304-1- 036304-9.
 D. Montgomery and G. D. Doolen, "Magneto hydrodynamic cellular automata," Phys. Lett. A, vol. 120, 1987 , pp.229.
 H.Chen And W.H. Matthaeus, "An analytical theory and formulation of a local magnetohydrodynamic lattice gas model," Phys. Fluids, vol. 31, 1988, pp. 1439-1455.
 D. Martinez, S. Chen and W.H. Matthaeus, "Lattice Boltzmann magneto hydrodynamics," Phys. Plasmas, vol. 6, 1994.
 A. MacNab, G. Vahala, L. P. Vahala Pavlo and M. Soe, Lattice Boltzmann model for dissipative incompressible MHD, 28rd, EPS conference on controlled fusion and plasma physics, Madeira, Portugal, 2001.
 C. Xing-Wang and S. Bao- Chang, "A new lattice Boltzmann model for incompressible magneto hydrodynamics incompressible," Chinese Physics, vol. 14 No. 7, 2005.
 P.J.Dellar, "Lattice kinetic schemes for magnetohydrodynamics," J. Comp. Phys, vol. 179, 2002,pp. 95-126.
 X. He, S. Chen and G.D. Doolen, "A novel thermal model for the lattice Boltzmann method in incompressible limit," J. Comp. Phys, vol. 146, 1998, pp. 282-300.
 X. He and L.S. Luo, "A priori derivation of the lattice Boltzmann equation," Phys. Rev. E, 2000.
 K.R. Cramer and S.I. Pai, "Magnatofluid Dynamics for Engineers and Physicists," McGraw-Hill, New York, 1973.
 T. Seta, E. Takegoshi, K. Kitano and K. Okui, "Thermal Lattice Boltzmann Model for Incompressible Flows through Porous Media," J.Thermal Science and Technology, vol. 1, No.2, 2006, pp.90.
 S. Ergun, "Flow through Packed Columns," Chemical Engineering Progress, vol. 48 , 1952 ,pp.89-94.
 Z.Guo, C. Zheng, and B. Shi, "Discrete lattice effects on the forcing term in the lattice Boltzmann method," Phys Rev E, vol. 65, 2002, pp.046308-1-046308-6.
 A.A. Mohammad, "Applied lattice Boltzmann method for transport phenomena, momentum, heat and mass transfer," Canadian J. Chemical Engineering, 2007.
 P. Nithiarasu, K.N. Seetharamuand, T. Sundararajan, "Natural convective heat transfer in a fluid saturated variable porosity medium," Int. J. Heat Mass Transfer, vol. 40,1997, pp. 3955-3967.