Journal of Central South University

, Volume 24, Issue 5, pp 1174–1182 | Cite as

Lattice Boltzmann method for thermomagnetic convection of paramagnetic fluid in square cavity under a magnetic quadrupole field

  • Nan Xie (谢楠)
  • Chang-wei Jiang (姜昌伟)
  • Yi-hai He (何贻海)
  • Ming Yao (姚鸣)
Article
  • 65 Downloads

Abstract

Numerical study was performed for a better understanding on thermomagnetic convection under magnetic quadrupole field utilizing the lattice Boltzmann method. Present problem was examined under non-gravitational and gravitational conditions for a wide range of magnetic force number from 0 to 1000. Vertical walls of the square cavity were heated differentially while the horizontal walls were assumed to be adiabatic. Distributions of the flow and temperature field were clearly illustrated. Under non-gravitational condition, the flow presents a two-cellular structure with horizontal symmetry, and the average Nusselt number increases with the augment of magnetic force number. Under gravitational condition, two-cellular structure only occurs when the magnetic field is relatively strong, and the average Nusselt number decreases at first and then rises with the enhancing magnetic field. Results show that the magnetic field intensity and the Rayleigh number both have significant influence on convective heat transfer, and the gravity plays a positive role in heat transfer under weak magnetic field while a negative one for magnetic force numbers larger than 1×105.

Key words

lattice Boltzmann method thermomagnetic convection magnetic quadrupole field magnetic force 

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References

  1. [1]
    GHASEMI B, AMINOSSADATI S M, RAISI A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure [J]. International Journal of Thermal Sciences, 2011, 50: 1748–1756.CrossRefGoogle Scholar
  2. [2]
    AL-ZAMILY A M J. Effect of magnetic field on natural convection in a nanofluid-filled semi-circular enclosure with heat flux source [J]. Computers & Fluids, 2014, 103: 71–85.CrossRefGoogle Scholar
  3. [3]
    SANKAR M, VENKATACHALAPPA M, SHIVAKUMARA I S. Effect of magnetic field on natural convection in a vertical cylindrical annulus [J]. International Journal of Engineering Science, 2006, 44: 1556–1570.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    SANKAR M, VENKATACHALAPPA M, DO Y. Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure [J]. International Journal of Heat and Fluid Flow, 2011, 32: 402–412.CrossRefGoogle Scholar
  5. [5]
    KUO J S, LEONG J C. Analysis of a conducting fluid in a thin annulus with rotating insulated walls under radial magnetic effect [J]. Applied Mathematical Modelling, 2013, 37: 3021–3035.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    PIRMOHAMMADI M, GHASSEMI M. Effect of magnetic field on convection heat transfer inside a tilted square enclosure [J]. International Communications in Heat and Mass Transfer, 2009, 36: 776–780.CrossRefGoogle Scholar
  7. [7]
    SATHIYAMOORTHY M, CHAMKHA A. Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s)[J]. International Journal of Thermal Sciences, 2010, 49: 1856–1865.CrossRefGoogle Scholar
  8. [8]
    YU P X, QIU J X, QIN Q, TIAN Z F. Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field [J]. International Journal of Heat and Mass Transfer, 2013, 67: 1131–1144.CrossRefGoogle Scholar
  9. [9]
    ELSHEHABEY H M, HADY F M, AHMED S E, MOHAMED R A. Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field [J]. International Communications in Heat and Mass Transfer, 2014, 57: 228–238.CrossRefGoogle Scholar
  10. [10]
    ASHOURI M, EBRAHIMI B, SHAFII M B, SAIDI M H, SAIDI M S. Correlation for Nusselt number in pure magnetic convection ferrofluid flow in a square cavity by a numerical investigation [J]. Journal of Magnetism and Magnetic Materials, 2010, 322: 3607–3613.CrossRefGoogle Scholar
  11. [11]
    LI Qiao-jie, ZHENG Zhou-shun, WANG Shuang, LIU Jian-kang. Numerical simulation of powder flow in high velocity compaction by lattice Boltzmann method [J]. The Chinese Journal of Nonferrous Metals, 2012, 22(6): 1754–1762. (in Chinese)Google Scholar
  12. [12]
    SU Qing, CHEN Ai-rong, ZHAO Tie-jun. Carbonation of sea sand concrete [J]. Journal of Central South University: Science and Technology, 2012, 42(1): 304–309. (in Chinese)Google Scholar
  13. [13]
    MOHAMAD A A, KUZMIN A. A critical evaluation of force term in lattice Boltzmann method, natural convection problem [J]. International Journal of Heat and Mass Transfer, 2010, 53: 990–996.CrossRefMATHGoogle Scholar
  14. [14]
    LI Zheng, YANG Mo, ZHANG Yu-wen. A coupled lattice Boltzmann and finite volume method for natural convection simulation [J]. International Journal of Heat and Mass Transfer, 2014, 70: 864–874.CrossRefGoogle Scholar
  15. [15]
    SHEIKHOLESLAMI M, GORJI-BANDPY M, GANJI D D. Numerical investigation of MHD effects on Al2O3-water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM [J]. Energy, 2013, 60: 501–510.CrossRefGoogle Scholar
  16. [16]
    SHEIKHOLESLAMI M, GORJI-BANDPY M, GANJI D D. Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid [J]. Powder Technology, 2014, 254: 82–93.CrossRefGoogle Scholar
  17. [17]
    SHEIKHOLESLAMI M, GORJI-BANDPY M, VAJRAVELU K. Lattice Boltzmann simulation of magnetohydrodynamic natural convection heat transfer of Al2O3-water nanofluid in a horizontal cylindrical enclosure with an inner triangular cylinder [J]. International Journal of Heat and Mass Transfer, 2015, 80: 16–25.CrossRefGoogle Scholar
  18. [18]
    KEFAYATI GHR. Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method [J]. International Communications in Heat and Mass Transfer, 2013, 40: 67–77.CrossRefGoogle Scholar
  19. [19]
    KEFAYATI G H R. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution [J]. Powder Technology, 2013, 243: 171–183.CrossRefGoogle Scholar
  20. [20]
    NEMATI H, FARHADI M, SEDIGHI K, ASHORYNEJAD H R, FATTAHI E. Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann model [J]. Scientia Iranica, 2012, 19(2): 303–310.CrossRefGoogle Scholar
  21. [21]
    NEMATI H, FARHADI M, SEDIGHI K, FATTAHI E, DARZI A A R. Lattice Boltzmann simulation of nanofluid in lid-driven cavity [J]. International Communications in Heat and Mass Transfer, 2010, 37: 1528–1534.CrossRefGoogle Scholar
  22. [22]
    KEFAYATI G H R, GORJI-BANDPY M, SAJJADI H, GANJI D D. Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated wall [J]. Scientia Iranica B, 2012, 19(4): 1053–1065.CrossRefGoogle Scholar
  23. [23]
    XUAN Yi-min, LI Qiang, YE Meng. Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach [J]. International Journal of Thermal Sciences, 2007, 46: 105–111.CrossRefGoogle Scholar
  24. [24]
    HUSSEIN A K, ASHORYNEJAD H R, SHIKHOLESLAMI M, SIVASANKARAN S. Lattice Boltzmann simulation of natural convection heat transfer in an open enclosure filled with Cu–water nanofluid in a presence of magnetic field [J]. Nuclear Engineering and Design, 2014, 268: 10–17.CrossRefGoogle Scholar
  25. [25]
    MAHMOUDI A, MEJRI I, ABBASSI M A, OMRI A. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with linear temperature distribution [J]. Powder Technology, 2014, 256: 257–271.CrossRefGoogle Scholar
  26. [26]
    SHEIKHOLESLAMI M, GORJI-BANDPY M. Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field [J]. Powder Technology, 2014, 256: 490–498.CrossRefGoogle Scholar
  27. [27]
    KEFAYATI GHR. Natural convection of ferrofluid in a linearly heated cavity utilizing LBM [J]. Journal of Molecular Liquids, 2014, 191: 1–9.CrossRefGoogle Scholar
  28. [28]
    YANG Li-jun, REN Jian-xun, SONG Yao-zu, GUO Zeng-yuan. Free convection of a gas induced by a magnetic quadrupole field [J]. Journal of Magnetism and Magnetic Materials, 2003, 261: 377–384.CrossRefGoogle Scholar
  29. [29]
    YANG Li-jun, REN Jian-xun, SONG Yao-zu, MIN Jing-chun, GUO Zeng-yuan. Convection heat transfer enhancement of air in a rectangular duct by application of magnetic quadrupole field [J]. International Journal of Engineering Science, 2004, 42: 491–507.CrossRefMATHGoogle Scholar
  30. [30]
    HUELSZ G, RECHTMAN R. Heat transfer due to natural convection in an inclined square cavity using the lattice Boltzmann equation method [J]. International Journal of Thermal Sciences, 2013, 65: 111–119.CrossRefGoogle Scholar
  31. [31]
    CONTRINO D, LALLEMAND P, ASINARI P, LUO Li-shi. Lattice Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers [J]. Journal of Computational Physics, 2014, 275: 257–272.MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    MEHRIZI A A, SEDIGHI K, FARHADI M, SHEIKHOLESLAMI M. Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus [J]. International Communications in Heat and Mass Transfer, 2013, 48: 164–177.CrossRefGoogle Scholar
  33. [33]
    TAGAWA T, SHIGEMITSU R, OZOE H. Magnetizing force modeled and numerically solved for natural convection of air in a cubic enclosure: effect of the direction of the magnetic field [J]. International Journal of Heat and Mass Transfer, 2002, 45: 267–277.CrossRefMATHGoogle Scholar
  34. [34]
    DAVIS G D V. Natural convection of air in a square cavity, a benchmark numerical solution [J]. International Journal Numerical Methods Fluids, 1962, 3: 249–264.CrossRefGoogle Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Nan Xie (谢楠)
    • 1
  • Chang-wei Jiang (姜昌伟)
    • 1
  • Yi-hai He (何贻海)
    • 1
  • Ming Yao (姚鸣)
    • 1
  1. 1.Key Laboratory of Efficient and Clean Energy Utilization of College of Hunan Province, School of Energy and Power EngineeringChangsha University of Science and TechnologyChangshaChina

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