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Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Power-Law Nanofluids in Rectangular Enclosures

  • Lei Wang (a1), Zhenhua Chai (a1) (a2) and Baochang Shi (a1) (a2)
Abstract
Abstract

In this paper, the magnetic field effects on natural convection of power-law nanofluids in rectangular enclosures are investigated numerically with the lattice Boltzmann method. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles and the investigations are carried out for different governing parameters including Hartmann number (0.0≤Ha≤20.0), Rayleigh number (104Ra≤106), power-law index (0.5≤n≤1.0), nanopartical volume fraction (0.0≤ϕ≤0.1) and aspect ratio (0.125≤AR≤8.0). The results reveal that the flow oscillations can be suppressed effectively by imposing an external magnetic field and the augmentation of Hartmann number and power-law index generally decreases the heat transfer rate. Additionally, it is observed that the average Nusselt number is increased with the increase of Rayleigh number and nanoparticle volume fraction. Moreover, the present results also indicate that there is a critical value for aspect ratio at which the impact on heat transfer is the most pronounced.

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*Corresponding author. Email: shibc@hust.edu.cn (B. C. Shi)
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[1] Lim K. O., Lee K. S. and Song T. H., Primary and secondary instabilities in a glass-melting surface, Numer. Heat Transfer A, 36 (1999), pp. 309325.
[2] Iwanik P. O. and Chiu W. K., Temperature distribution of an optical fiber traversing through a chemical vapor deposition reactor, Numer. Heat Transfer A, 43 (2003), pp. 221237.
[3] Polezhaev V. I., Myakshina M. N. and Nikitin S. A., Heat transfer due to buoyancy-driven convective interaction in enclosures: Fundamentals and applications, Int. J. Heat Mass Transfer, 55 (2012), pp. 156165.
[4] Choi U. S., Enhancing thermal conductivity of fluids with nanoparticels, ASME FED, 231 (1995), pp. 99106.
[5] Das S. K., Choi U. S., Yu W. and Pardeep T., Nnaofluids: Science and Technology, John Wiley & Sons, 2007.
[6] Nnanna A. G., Experimental model of temperature-driven nanofluid, ASME J. Heat Transfer, 129 (2007), pp. 697704.
[7] Khanafer K., Vafai K. and Lightstone M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46 (2003), pp. 36393653.
[8] Jahanshahi M., Hosseinizadeh S. F. and Alipanah M. et al., Numerical simulation of free convection based on experimental measured conductivity in a square cavity using water/SiO2 nanofluid, Int. Commun. Heat Mass Transfer, 37 (2010), pp. 687694.
[9] Moreau M., Magnetohydrodynamics, Kluwer Acadamic Publishers, 1990.
[10] Sathiyamoorthy M. and Chamkha A., Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s), J. Therm. Sci., 49 (2010), pp. 18561865.
[11] Sheikholeslami M., Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition, Euro. Phys. J. Plus, 129 (2014), pp. 112.
[12] Sheikholeslami M. and Ellahi R., Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid, Int. J. Heat Mass Transfer, 89 (2015), pp. 799808.
[13] Kefayati G. H. R., Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution, Powder Technol., 243 (2013), pp. 171183.
[14] Mejri I., Mahmoudi A. and Abbassi M. A. et al., Magnetic field effect on entropy generation in a nanofluid-filled enclosure with sinusoidal heating on both side walls, Powder Technol., 266 (2014), pp. 340353.
[15] Sheikholeslami M. and Ganji D. D., Entropy generation of nanofluid in presence of magnetic field using lattice Boltzmann method, Phys. A, 417 (2015), pp. 273286.
[16] Sheikholeslami M., Ashorynejad H. R. and Rana P., Lattice Boltzmann simulation of nanofluid heat transfer enhancement and entropy generation, J. Mol. Liq., 214 (2016), pp. 8695.
[17] Sheikholeslami M., Vajravelu K. and Rashidi M. M., Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field, Int. J. Heat Mass Transfer, 92 (2016), pp. 339348.
[18] Sheikholeslami M., Hayat T. and Alsaedi A., MHD free convection of Al2O3-water nanofluid considering thermal radiation: A numerical study, Int. J. Heat Mass Transfer, 96 (2016), pp. 513524.
[19] Sheikholeslamia M. and Chamkha A. J., Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall, Numer. Heat Tranfer A Appl., 69 (2016), pp. 781793.
[20] Sheikholeslamia M. and Chamkhab A. J., Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field, Numer. Heat Tranfer A Appl., 69 (2016), pp. 11891200.
[21] Chen H., Ding Y. and Lapkin A. et al., Rheological behaviour of ethylene glycol-titanate nanotube nanofluids, J. Nanopart. Res., 11 (2009), pp. 15131520.
[22] Phuoc T. X., Massoudi M., Experimental observations of the effects of shear rates and particle concentration on the viscosity of Fe2O3-deionized water nanofluids, Int. J. Therm. Sci., 48 (2009), pp. 12941301.
[23] Ellahi R., The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions, Appl. Math. Model., 37 (2013), pp. 14511467.
[24] Kefayati Gh. R., FDLBM simulation of mixed convection in a lid-driven cavity filled with non-Newtonian nanofluid in the presence of magnetic field, Int. J. Therm. Sci., 95 (2015), pp. 2946.
[25] Li B. T., Lin Y. H., Zhu L. L. and Zhang W., Effects of non-Newtonian behaviour on the thermal performance of nanofluids in a horizontal channel with discrete regions of heating and cooling, Appl. Therm. Eng., 94 (2016), pp. 404412.
[26] Wakitani S., Formation of cells in natural convection in a vertical slot at large Prandtl number, J. Fluid Mech., 314 (1996), pp. 299314.
[27] Succi S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2001.
[28] Guo Z. L. and Shu C., Lattice Boltzmann Method and Its Applications in Engineering, World Scientific, 2013.
[29] Chai Z. H., Huang C. S., Shi B. C. and Guo Z. L., A comparative study on the lattice Boltzmann models for predicting effective diffusivity of porous media, Int. J. Heat Mass Transfer, 98 (2016), pp. 687696.
[30] Kang Q., Lichtner P. C. and Janecky D. R., Lattice Boltzmann method for reacting flows in porous media, Adv. Appl. Math. Mech., 2 (2010), pp. 545563.
[31] Hu Y., Niu X. D. and Shu S. et al., Natural convection in a concentric annulus: a lattice Boltzmann method study with boundary condition-enforced immersed boundary method, Adv. Appl. Math. Mech., 5 (2013), pp. 321336.
[32] Yang L. M., Shu C. and Wu J., Development and comparative studies of three non-free parameter lattice Boltzmann models for simulation of compressible flows, Adv. Appl. Math. Mech., 4 (2012), pp. 454472.
[33] Huang C. S., Chai Z. H. and Shi B. C., Non-Newtonian effect on hemodynamic characteristics of blood flow in stented cerebral aneurysm, Commun. Comput. Phys., 13 (2013), pp. 916928.
[34] Luo L. S. and Girimaji S. S., Theory of the lattice Boltzmann method: two-fluid model for binary mixtures, Phys. Rev. E, 67 (2003), 036302.
[35] Du R., Liu W. W., A new multiple-relaxation-time lattice Boltzmann method for natural convection, J. Sci. Comput., 56 (2013), 122130.
[36] Chai Z. H., Shi B. C. and Guo Z. L., A multiple-relaxation-time lattice Boltzmann model for general nonlinear anisotropic convection-diffusion equations, J. Sci. Comput., 69 (2016), pp. 355390.
[37] Kamyar A., Saidur R. and Hasanuzzaman M., Application of computational fluid dynamics (CFD) for nanofluids, Int. J. Heat Mass Transfer, 55 (2012), pp. 41044115.
[38] Sheikholeslami M. and Ellahi R., Simulation of ferrofluid flow for magnetic drug targeting using the lattice Boltzmann method, Z. Naturfors. A, 70 (2015), pp. 115124.
[39] Wang L., Chai Z. H. and Shi B. C., Regularized lattice Boltzmann simulation of double-diffusive convection of power-law nanofluids in rectangular enclosures, Int. J. Heat Mass Transfer, 102 (2016), pp. 381395.
[40] Xuan Y. and Roetzel W., Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer, 43 (2000), pp. 37013707.
[41] Sheikholeslami M., KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel, Phys. Lett. A, 378 (2014), pp. 33313339.
[42] Sheikholeslami M., Effect of uniform suction on nanofluid flow and heat transfer over a cylinder, 37 (2015), pp. 16231633.
[43] Wang X. Q. and Mujumdar A. S., Heat transfer characteristics of nanofluids: a review, Int. J. Therm. Sci., 46 (2007), pp. 119.
[44] Rea U., McKrell T. and Hu L. et al., Laminar convective heat transfer and viscous pressure loss of aluminaCwater and zirconia-water nanofluids, Int. J. Heat Mass Transfer, 52 (2009), pp. 20422048.
[45] Maxwell-Garnett J. C., Colours in metal glasses and in metallic films, Philos. Trans. R. Soc. A, 203 (1904), pp. 385420.
[46] Brinkman H. C., The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20 (1952), pp. 571571.
[47] Neofytou P., A 3rd order upwind finite volume method for generalised Newtonian fluid flows, Adv. Eng. Software, 36 (2005), pp. 664680.
[48] Chai Z. H., Shi B. C. and Guo Z. L. et al., Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows, J. Non-Newton. Fluid Mech., 166 (2011), pp. 332342.
[49] He N. Z., Wang N. C. and Shi B. C. et al., A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow, Chin. Phys., 13 (2002), 40.
[50] Guo Z. L., Shi B. C. and Wang N. C., Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165 (2000), pp. 288306
[51] Guo Z. L., Zheng C. G. and Shi B. C., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65 (2002), 046308.
[52] Chai Z. H. and Zhao T. S., Lattice Boltzmann model for the convection-diffusion equation, Phys. Rev. E, 87 (2013), 063309.
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