Numerical Study of turbulent free convection of liquid metal with constant and variable properties in the presence of magnetic field

Document Type : Full Lenght Research Article


Islamic Azad University, Pardis Branch


In this research, turbulent MHD convection of liquid metal with constant and variable properties is investigated numerically. The finite volume method is applied to model the fluid flow and natural convection heat transfer in a square cavity. The fluid flow and heat transfer were simulated and compared for two cases constant and variable properties. It is observed that for the case variable properties in high Hartmann numbers (Ha) the temperature slope near the hot wall is more than the cold wall. For both cases, the temperature gradient near the hot and cold walls is high. By applying magnetic field and increasing the Ha the temperature slope reduces so at Ha=800 the profile is linear. In the case constant properties, the slope of temperature profile near the vertical walls is the same and the temperature profiles pass from one point at the center of the cavity. However,in the case variable properties as it was expected the temperature profile doesn’t pass one point and the slope of temperature profile at high Hartmann numbers near the hot and cold walls is partly different. Furthermore, it is indicated that for the case constant properties the Nusselt number is less than the case variable properties.


Main Subjects

 [1] M. D, Sozou, R.F.D,Mirando, H.A Machado, Natural convection in enclosures with variable fluid properties, International Journal of Numerical Methods for Heat & Fluid Flow, 13(8), (2003).
[2] E. Leonardi, J.A Reizes, Convective flows in closed cavities with variable fluid properties, Wiley, New York, (1981).
[3] Z.Y., Zhong, , K.T. ,Yang, J.R., Lloyd, Variable property effects in laminar natural convection in a square enclosure, ASME J. Heat Trans. 107, 133– 138 (1985).
[4] M. A. Leal, H. A. Machado, R. M. Cotta, Integral transform solutions of transient natural convection in enclosures with variable fluid properties, Int. J. Heat Mass Trans. 43, 3977–3990 (2003).
[5] Y. Y. Jin, C. F. Chen, Natural convection of high Prandtl number fluids with variable viscosity in a vertical slot, Int. J. Heat Mass Trans., 39, 2663–2670(1966).
[6] S. Saravanan, P. Kandaswamy, Buoyancy convection in low Prandtl number liquids with large temperature variation, Meccanica, 37, 599–608 (2002).
[7] T. Pesso, S. Piva, ,Laminar natural convection in a square cavity: low Prandtl numbers and large density differences, Int. J. Heat Mass Transfer, 52, 1036–1043 ( 2009)
[8] M. Bahiraei, M. Hangi, Investigating the efficacy of magnetic nanofluid as a coolant in double-pipe heat exchanger in the presence of magnetic field Energy Conversion and Management, 76, 1125- 1133 (2013).
[9] Mehdi Bahiraei, Morteza Hangi, Automatic cooling by means of thermomagnetic phenomenon of magnetic nanofluid in a toroidal loop, Applied Thermal Engineering 107, 700– 708 (2016).
[10] Mehdi Bahiraei, Morteza Hangi, Flow and heat transfer characteristics of magnetic nanofluids: A review, Journal of Magnetism and Magnetic Materials 374, 125–138 (2015).
[11] Tlili, W.A. Khan, I. Khan. Multiple slips effects on MHD SA-Al2O3 and SA-Cu non-Newtonian nanofluids flow over a stretching cylinder in porous medium with radiation and chemical reaction. Results in Physics, 8, 213-22 (2018).
[12] Veera Krishna. M, G.Subba Reddy, A.J.Chamkha, “Hall effects on unsteady MHD oscillatory free convective flow of second grade fluid through porous medium between two vertical plates,” Physics of Fluids, 30, p. 023106 (2018).
[13] V. Krishna.M and G.S. Reddy, Unsteady MHD convective flow of Second grade fluid through a porous medium in a 0 100 200 300 400 500 600 700 800 1 2 3 4 5 6 7 8 9 10 Const. Properties Variab. Properties M. Pirmohammadi / JHMTR 6 (2019) 133-141 141 Rotating parallel plate channel with temperature dependent source, IOP Conf. Series: Materials Science and Engineering, 149, p. 012216 (2016).
[14] V. Krishna.M., M. Gangadhara Reddy, A.J.Chamkha, Heat and mass transfer on MHD free convective flow over an infinite non-conducting vertical flat porous plate, Int. Jour. of Fluid Mech. Res., 45(5), 1-25 (2018).
[15] Z. A. Khan, S. U. Haq, T. S. Khan, I. Khan, Unsteady MHD flow of a Brinkman Type fluid between two side walls perpendicular to an infinite plate, Results in Physics, 9, 1602-1608 ( 2018).
[16] N. S. Bondareva, et al., Magnetic Field Effect on the Unsteady Natural Convection in a Right-Angle Trapezoidal Cavity Filled with a Nanofluid, International Journal of Numerical Methods for Heat Fluid Flow, 25, 1924– 1946 (2015)
[17] M. A. Sheremet, et al., Magnetic Field Effect on the Unsteady Natural Convection in a Wavy-Walled Cavity Filled with a Nanofluid: Buongiorno's Mathematical Model, Journal of the Taiwan Institute of Chemical Engineers, 61, 211–22 (2016).
[18] M. Pirmohammadi, M. Ghassemi, Effect of Magnetic Field on Convection Heat Transfer Inside a Tilted Square Enclosure, International Communications in Heat and Mass Transfer, 36, 776-780 (2009).
[19] M. Pirmohammadi, et al., 2011, Numerical Study of Hydromagnetic Convection of an Electrically Conductive Fluid with Variable Properties inside an Enclosure, IEEE Transactions on Plasma Science, 39, 516 - 520.
[20] J. M. Jalil, K. A. Al-Tae'y ,The Effect of Nonuniform Magnetic Field on Natural Convection in an Enclosure, Numerical Heat Transfer, Part A , 51, 899–917 (2007)
[21] S. C. Kakarantzas, et al., ,Natural Convection of Liquid Metal in a Vertical Annulus with Lateral and Volumetric Heating in the Presence of a Horizontal Magnetic Field, International Journal of Heat and Mass Transfer, 45, 3347-3356 (2011).
[22] X. Liu, et al., Effects of Static Magnetic Fields on Thermal Fluctuations in the Melt of Industrial CZ-Si Crystal Growth", Journal of Crystal Growth, 360, 38-42 (2012).
[23] S.Kakarantzas et al., Magnetohydrodynamic Natural Convection of Liquid Metal Between Coaxial Isothermal Cylinders due to Internal Heating, Numerical Heat Transfer, Part A, 65, 401–418 (2014).
[24] X. Zhang, O. Zikanov, Two-Dimensional Turbulent Convection in a Toroidal Duct of a Liquid Metal Blanket, Journal of. Fluid Mechanics, 779, 36-5 2(2015).
[25] H. Sajjadi, GH. R. Kefayati, ,MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method, Heat Transfer—Asian Research, 45 ,8, 795- 814 (2016).
[26] Enayati, et al., Numerical Simulations of Transitional and Turbulent Natural Convection in Laterally Heated Cylindrical Enclosures for Crystal Growth, Numerical Heat Transfer, Part A, 70(11), 1195–1212 (2016).
[27] H. Versteeg, W. Malalaskera, An Introduction to Computational Fluid Dynamics", Longman scientific & technical (1995).
[28] U. Müller, L. Bühler, Magnetofluid dynamics in channels and containers, Springer, Wien, New York (2001).
[29] Jayatilleke, C. L. V, The Influence of Prandtl Number and Surface Roughness on the Resistance of Laminar Sublayer to Momentum and Heat Transfer", heat and mass transfer, 1,193(1969).
[30] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC (1980)