Free Convection in a MHD Porous Cavity with using Lattice Boltzmann Method
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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] D.A. Nield, "Impracticality of MHD convection in a porous medium,"
Transport Porous Med. vol. 73, 2008, pp-379.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] D.A. Nield, and A. Bejan, Convection in Porous Media, 3rd ed,
Springer, New York, 2006.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] D. Montgomery and G. D. Doolen, "Magneto hydrodynamic cellular
automata," Phys. Lett. A, vol. 120, 1987 , pp.229.
[24] 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.
[25] D. Martinez, S. Chen and W.H. Matthaeus, "Lattice Boltzmann magneto
hydrodynamics," Phys. Plasmas, vol. 6, 1994.
[26] 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.
[27] C. Xing-Wang and S. Bao- Chang, "A new lattice Boltzmann model for
incompressible magneto hydrodynamics incompressible," Chinese
Physics, vol. 14 No. 7, 2005.
[28] P.J.Dellar, "Lattice kinetic schemes for magnetohydrodynamics," J.
Comp. Phys, vol. 179, 2002,pp. 95-126.
[29] 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.
[30] X. He and L.S. Luo, "A priori derivation of the lattice Boltzmann
equation," Phys. Rev. E, 2000.
[31] K.R. Cramer and S.I. Pai, "Magnatofluid Dynamics for Engineers and
Physicists," McGraw-Hill, New York, 1973.
[32] 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.
[33] S. Ergun, "Flow through Packed Columns," Chemical Engineering
Progress, vol. 48 , 1952 ,pp.89-94.
[33] 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.
[34] A.A. Mohammad, "Applied lattice Boltzmann method for transport
phenomena, momentum, heat and mass transfer," Canadian J. Chemical
Engineering, 2007.
[35] 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
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] D.A. Nield, "Impracticality of MHD convection in a porous medium,"
Transport Porous Med. vol. 73, 2008, pp-379.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] D.A. Nield, and A. Bejan, Convection in Porous Media, 3rd ed,
Springer, New York, 2006.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] D. Montgomery and G. D. Doolen, "Magneto hydrodynamic cellular
automata," Phys. Lett. A, vol. 120, 1987 , pp.229.
[24] 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.
[25] D. Martinez, S. Chen and W.H. Matthaeus, "Lattice Boltzmann magneto
hydrodynamics," Phys. Plasmas, vol. 6, 1994.
[26] 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.
[27] C. Xing-Wang and S. Bao- Chang, "A new lattice Boltzmann model for
incompressible magneto hydrodynamics incompressible," Chinese
Physics, vol. 14 No. 7, 2005.
[28] P.J.Dellar, "Lattice kinetic schemes for magnetohydrodynamics," J.
Comp. Phys, vol. 179, 2002,pp. 95-126.
[29] 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.
[30] X. He and L.S. Luo, "A priori derivation of the lattice Boltzmann
equation," Phys. Rev. E, 2000.
[31] K.R. Cramer and S.I. Pai, "Magnatofluid Dynamics for Engineers and
Physicists," McGraw-Hill, New York, 1973.
[32] 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.
[33] S. Ergun, "Flow through Packed Columns," Chemical Engineering
Progress, vol. 48 , 1952 ,pp.89-94.
[33] 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.
[34] A.A. Mohammad, "Applied lattice Boltzmann method for transport
phenomena, momentum, heat and mass transfer," Canadian J. Chemical
Engineering, 2007.
[35] 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
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:53712", author = "H.A. Ashorynejad and M. Farhadi and K.Sedighi and A.Hasanpour", title = "Free Convection in a MHD Porous Cavity with 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.", keywords = "Lattice Boltzmann method , Natural convection ,
Magnetohydrodynamic , Porous medium", volume = "5", number = "1", pages = "52-6", }
