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

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.

Keywords

lattice Boltzmann method / thermomagnetic convection / magnetic quadrupole field / magnetic force

References

[1] GhasemiB, AminossadatiS M, RaisiA. Magnetic field effect on natural convection in a nanofluid-filled square enclosure [J]. International Journal of Thermal Sciences, 2011, 50: 1748-1756

[2] Al-ZamilyA 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

[3] SankarM, VenkatachalappaM, ShivakumaraI S. Effect of magnetic field on natural convection in a vertical cylindrical annulus [J]. International Journal of Engineering Science, 2006, 44: 1556-1570

[4] SankarM, VenkatachalappaM, DoY. 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

[5] KuoJ S, LeongJ 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

[6] PirmohammadiM, GhassemiM. 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

[7] SathiyamoorthyM, ChamkhaA. 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

[8] YuP X, QiuJ X, QinQ, TianZ 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

[9] ElshehabeyH M, HadyF M, AhmedS E, MohamedR 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

[10] AshouriM, EbrahimiB, ShafiiM B, SaidiM H, SaidiM 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

[11] LiQ-j, ZhengZ-s, WangS, LiuJ-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

[12] SuQ, ChenA-r, ZhaoT-jun. Carbonation of sea sand concrete [J]. Journal of Central South University: Science and Technology, 2012, 42(1): 304-309

[13] MohamadA A, KuzminA. 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

[14] LiZ, YangM, ZhangY-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

[15] SheikholeslamiM, Gorji-BandpyM, GanjiD 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

[16] SheikholeslamiM, Gorji-BandpyM, GanjiD D. Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid [J]. Powder Technology, 2014, 254: 82-93

[17] SheikholeslamiM, Gorji-BandpyM, VajraveluK. 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

[18] KefayatiGHR. 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

[19] KefayatiG, HR. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution [J]. Powder Technology, 2013, 243: 171-183

[20] NematiH, FarhadiM, SedighiK, AshorynejadH R, FattahiE. 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

[21] NematiH, FarhadiM, SedighiK, FattahiE, DarziA A R. Lattice Boltzmann simulation of nanofluid in lid-driven cavity [J]. International Communications in Heat and Mass Transfer, 2010, 37: 1528-1534

[22] KefayatiG H R, Gorji-BandpyM, SajjadiH, GanjiD 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

[23] XuanY-m, LiQ, YeMeng. Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach [J]. International Journal of Thermal Sciences, 2007, 46: 105-111

[24] HusseinA K, AshorynejadH R, ShikholeslamiM, SivasankaranS. 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

[25] MahmoudiA, MejriI, AbbassiM A, OmriA. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with linear temperature distribution [J]. Powder Technology, 2014, 256: 257-271

[26] SheikholeslamiM, Gorji-BandpyM. 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

[27] KefayatiGHR. Natural convection of ferrofluid in a linearly heated cavity utilizing LBM [J]. Journal of Molecular Liquids, 2014, 191: 1-9

[28] YangL-j, RenJ-x, SongY-z, GuoZ-yuan. Free convection of a gas induced by a magnetic quadrupole field [J]. Journal of Magnetism and Magnetic Materials, 2003, 261: 377-384

[29] YangL-j, RenJ-x, SongY-z, MinJ-c, GuoZ-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

[30] HuelszG, RechtmanR. 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

[31] ContrinoD, LallemandP, AsinariP, LuoL-shi. Lattice Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers [J]. Journal of Computational Physics, 2014, 275: 257-272

[32] MehriziA A, SedighiK, FarhadiM, SheikholeslamiM. 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

[33] TagawaT, ShigemitsuR, OzoeH. 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

[34] DavisG D V. Natural convection of air in a square cavity, a benchmark numerical solution [J]. International Journal Numerical Methods Fluids, 1962, 3: 249-264