A segregated spectral element method for thermomagnetic convection of paramagnetic fluid in rectangular enclosures with sinusoidal temperature distribution on one side wall

References

• D. Braithwaite, E. Beaugnon, and R. Tournier, “Magnetically controlled convection in paramagnetic fluid,” Nature, vol. 354, pp. 667–673, 1991.
   Web of Science ®Google Scholar
• J. W. Qi, N. I. Wakayama, and A. Yabe, “Magnetic control of thermal convection in electrically non-conducting or low conducting paramagnetic fluids,” Int. J. Heat Mass Transfer, vol. 44, no. 16, pp. 3043–3052, 2001. DOI:10.1016/S0017-9310(00)00354-9.
   Web of Science ®Google Scholar
• L. B. Wang and N. I. Wakayama, “Control of natural convection in non- and low-conducting diamagnetic fluids in a cubical enclosure using inhomogeneous magnetic fields with different directions,” Chem. Eng. Sci., vol. 57, no. 11, pp. 1867–1876, 2002. DOI:10.1016/S0009-2509(02)00090-8.
   Web of Science ®Google Scholar
• T. Tagawa, R. Shigemitsu, and H. Ozoe, “Magnetizing force modeled and numerically solved for natural convection of air in a cubic enclosure: effect of the direction of the magnetic field,” Int. J. Heat Mass Transfer, vol. 45, no. 2, pp. 267–277, 2002. DOI:10.1016/S0017-9310(01)00149-1.
   Web of Science ®Google Scholar
• T. Tagawa, A. Ujihara, and H. Ozoe, “Numerical computation for Rayleigh-Benard convection of water in a magnetic field,” Int. J. Heat Mass Transfer, vol. 46, no. 21, pp. 4097–4104, 2003. DOI:10.1016/S0017-9310(03)00223-0.
   Web of Science ®Google Scholar
• M. Akamatsu, M. Higano, Y. Takahashi, and H. Ozoe, “Numerical computation on the control of aerial flow by the magnetizing force in gravitational and nongravitational fields,” Numer. Heat Transfer A, vol. 43, no. 1, pp. 9–29, 2003. DOI:10.1080/10407780307301.
   Web of Science ®Google Scholar
• C. W. Jiang, E. Shi, Z. M. Hu, X. F. Zhu, and N. Xie, “Numerical simulation of thermomagnetic convection of air in a porous square enclosure under a magnetic quadrupole field using LTNE models,” Int. J. Heat Mass Transfer, vol. 91, pp. 98–109, 2015. DOI:10.1016/j.ijheatmasstransfer.2015.07.103.
   Web of Science ®Google Scholar
• I. E. Sarris, N. Katsavos, I. Lekakis, and N. S. Vlachos, “Modelling the influence of combustion on glass melt flow,” presented at the Proc. 6th National Conf. of Solar Technology Institute, Volos, Greece, vol. 2, pp. 201–209, 1999.
   Google Scholar
• C. Q. Jian, A. Dutta, A. Mukhopadhyay, and D. P. Tselepidakis, “Explicit coupling between combustion space and glass tank simulation for complete furnace analysis,” presented at the Proc. 1st Balkan Conf. on Glass Science and Technology, Volos, Greece, pp. 402–409, 2000.
   Google Scholar
• T. Basak, S. Roy, and A. R. Balakrishman, “Effects of thermal boundary condition on natural convection flows with a square cavity,” Int. J. Heat Mass Transfer, vol. 49, no. 23–24, pp. 4525–4535, 2006. DOI:10.1016/j.ijheatmasstransfer.2006.05.015.
   Web of Science ®Google Scholar
• I. E. Sarris, I. Lekakis, and N. S. Vlachos, “Natural convection in a 2D enclosure with sinusoidal upper wall temperature,” Numer. Heat Transfer A, vol. 42, no. 5, pp. 513–530, 2002. DOI:10.1080/10407780290059675.
   Web of Science ®Google Scholar
• Y. Varol, H. F. Oztop, and I. Pop, “Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall,” Int. Commun. Heat Mass, vol. 35, no. 1, pp. 56–64, 2008. DOI:10.1016/j.icheatmasstransfer.2007.05.015.
   Web of Science ®Google Scholar
• E. Bilgen and R. B. Yedder, “Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side,” Int. J. Heat Mass Transfer, vol. 50, no. 1–2, pp. 139–150, 2007. DOI:10.1016/j.ijheatmasstransfer.2006.06.027.
   Web of Science ®Google Scholar
• Q. H. Deng and J. J. Chang, “Natural convection in a rectangular enclosure with sinusoidal temperature distribution on both side walls,” Numer. Heat Transfer A, vol. 54, no. 5, pp. 507–524, 2008. DOI:10.1080/01457630802186080.
   Web of Science ®Google Scholar
• M. Bhuvaneswari, S. Sivasankaran, and Y. J. Kim, “Magnetoconvection in a square enclosure with sinusoidal temperature distributions on both side walls,” Numer. Heat Transfer A, vol. 59, no. 3, pp. 167–184, 2011. DOI:10.1080/10407782.2011.541219.
   Web of Science ®Google Scholar
• T. P. Bednarz, W. X. Lin, J. C. Patterson, C. W. Lei, and S. W. Armfield, “Scaling for unsteady thermo-magnetic convection boundary layer of paramagnetic fluids of Pr > 1 in micro-gravity conditions,” Int. J. Heat Fluid FL, vol. 30, no. 6, pp. 1157–1170, 2009. DOI:10.1016/j.ijheatfluidflow.2009.08.003.
   Web of Science ®Google Scholar
• M. Kaneda, A. Tsuji, H. Ooka, and K. Suga, “Heat transfer enhancement by external magnetic field for paramagnetic laminar pipe flow,” Int. J. Heat Mass Transfer, vol. 90, pp. 388–395, 2015. DOI:10.1016/j.ijheatmasstransfer.2015.06.078.
   Web of Science ®Google Scholar
• M. Akamatsu, K. Yasuhara, M. Kaneda, and H. Ozoe, “Heat transfer rate characteristics of the magnetothermal Rayleigh-Benard convection of paramagnetic air,” Int. J. Therm. Sci., vol. 89, pp. 13–22, 2015. DOI:10.1016/j.ijthermalsci.2014.10.007.
   Web of Science ®Google Scholar
• S. Kenjereš, L. Pyrda, E. F. Wajs, and J. S. Szmyd, “Numerical and experimental study of Rayleigh-Bénard-Kelvin convection,” Flow Turbul. Combust., vol. 92, no. 1–2, pp. 371–393, 2014. DOI:10.1007/s10494-013-9490-8.
   Web of Science ®Google Scholar
• D. G. Kang and J. M. Hyun, “Resonant enhancement of natural convection in a cubic enclosure under time-periodic magnetizing force,” J. Mech. Sci. Technol., vol. 31, no. 2, pp. 717–724, 2017. DOI:10.1007/s12206-017-0123-3.
   Web of Science ®Google Scholar
• E. Shi, X. Q. Sun, Y. C. He, and C. W. Jiang, “Effect of a magnetic quadrupole field on entropy generation in thermomagnetic convection of paramagnetic fluid with and without a gravitational field,” Entropy, vol. 19, no. 3, pp. 96–113, 2017. DOI:10.3390/e19030096.
   Web of Science ®Google Scholar
• G. R. Kefayati, “Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field,” Theor. Comput. Fluid Dyn., vol. 27, no. 6, pp. 865–883, 2013. DOI:10.1007/s00162-012-0290-x.
   Web of Science ®Google Scholar
• N. Xie, Y. H. He, M. Yao, and C. W. Jiang, “Lattice Boltzmann simulation of transient natural convection of air in square cavity under a magnetic quadrupole field,” Int. J. Numer. Meth. HFF, vol. 26, no. 8, pp. 2441–2461, 2016. DOI:10.1108/HFF-07-2015-0277.
   Web of Science ®Google Scholar
• N. Xie, C. W. Jiang, Y. H. He, and M. Yao, “Lattice Boltzmann method for thermomagnetic convection of paramagnetic fluid in square cavity under a magnetic quadrupole field,” J. Cent. South Univ., vol. 24, no. 5, pp. 1174–1182, 2017. DOI:10.1007/s11771-017-3520-y.
   Web of Science ®Google Scholar
• A. T. Patera, “A spectral element method for fluid dynamics: laminar flow in a channel expansion,” J. Comput. Phys., vol. 54, no. 3, pp. 468–488, 1984. DOI:10.1016/0021-9991(84)90128-1.
   Web of Science ®Google Scholar
• T. Gjesdal, C. E. Wasberg, and B. A. P. Reif, “Spectral element benchmark simulation of natural convection in two-dimensional cavities,” Int. J. Numer. Meth. Fluids, vol. 50, no. 11, pp. 1297–1319, 2006. DOI:10.1002/fld.1121.
   Web of Science ®Google Scholar
• C. Bosshard, A. Dehbi, M. Deville, E. Leriche, R. Puragliesi, and A. Soldati, “Large Eddy simulation of the differentially heated cubic cavity flow by the spectral element method,” Comput. Fluids, vol. 86, pp. 210–227, 2013. DOI:10.1016/j.compfluid.2013.07.007.
   Web of Science ®Google Scholar
• S. Patel, M. Min, and T. Lee, “A spectral-element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications,” Int. J. Numer. Meth. Fluids, vol. 82, no. 12, pp. 932–952, 2016. DOI:10.1002/fld.4250.
   Web of Science ®Google Scholar
• Y. Z. Wang, G. L. Qin, W. Q. He, and Z. Z. Bao, “Chebyshev spectral element method for natural convection in a porous cavity under local thermal non-equilibrium model,” Int. J. Heat Mass Transfer, vol. 121, pp. 1055–1072, 2018. DOI:10.1016/j.ijheatmasstransfer.2018.01.024.
   Web of Science ®Google Scholar
• S. V. Patankar and D. B. Spalding, “A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows,” Int. J. Heat Mass Transfer, vol. 15, no. 10, pp. 1787–1806, 1972. DOI:10.1016/0017-9310(72)90054-3.
   Web of Science ®Google Scholar
• J. E. Jaramillo, C. D. Pérez-Segarra, A. Oliva, and K. Claramunt, “Analysis of different RANS models applied to turbulent forced convection,” Int. J. Heat Mass Transfer, vol. 50, no. 19–20, pp. 3749–3766, 2007. DOI:10.1016/j.ijheatmasstransfer.2007.02.015.
   Web of Science ®Google Scholar
• B. Klein, F. Kummer, and M. Berlack, “A SIMPLE based discontinuous Galerkin solver for steady incompressible flows,” J. Comput. Phys., vol. 237, pp. 235–250, 2013. DOI:10.1016/j.jcp.2012.11.051.
   Web of Science ®Google Scholar
• J. G. Rice and R. J. Schnipke, “An equal-order velocity-pressure formulation that does not exhibit spurious pressure modes,” Comput. Meth. Appl. M, vol. 58, no. 2, pp. 135–149, 1986. DOI:10.1016/0045-7825(86)90093-9.
   Web of Science ®Google Scholar