Effects of variations in magnetic Reynolds number on magnetic field distribution in electrically conducting fluid under magnetohydrodynamic natural convection

Document Type : Full Lenght Research Article


Islamic Azad University, Pardis Branch


In this study the effect of magnetic Reynolds number variation on magnetic distribution of natural convection heat transfer in an enclosure is numerically investigated. The geometry is a two dimensional enclosure which the left wall is hot, the right wall is cold and the top and bottom walls are adiabatic. Fluid is molten sodium with Pr=0.01 and natural convection heat transfer for Rayleigh number, Ra=105 , and magnetic Reynolds numbers 10-1, 10-3 and 10-5 are considered and the governing equations including continuum, momentum, energy and magnetic induction are solved together concurrent. The numerical method finite volume and simpler algorithm for coupling the velocity and pressure is used. The results show for high magnetic Reynolds number the non-dimensional magnetic field in X and Y directions approximately are constant because diffusion of magnetic Reynolds number is more than advection but as magnetic Reynolds number increases the magnetic field in enclosure is not equal to applied magnetic field and is not constant and deviation from one is increased so that for Rem=10-1 the non-dimensional magnetic field in X direction from 0.09 to 6.6 and in Y direction from -1.164 to 4.05 changes.


Main Subjects

[1].             G.M. Oreper and J. Szekely, “The effect of an externally imposed magnetic field on buoyancy driven flow in a rectangular cavity”, J. Cryst. Growth, 64, 505–515, (1983).
[2].             H. BenHadid, D. Henry, ‘‘Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 2. Three-dimensional flow’’, J. Fluid Mech., 333, 57–83, (1997).
[3].             R. Bessaiha, M. Kadja, Ph. Marty, ‘‘Effect of wall electrical conductivity and magnetic field orientation on liquid metal flow in a geometry similar to the horizontal Bridgman configuration for crystal growth’’, International Journal of Heat and Mass Transfer, 42, 4345-4362, (1999).
[4].             M. Ciofalo and F. Cricchio, ‘‘Influence of a magnetic field on liquid metal free convection in an internally heated cubic enclosure’’, International Journal of Numerical Methods for Heat & Fluid Flow, 12(6), 687-715, (2002).
[5].             I.D. Piazza, M. Ciofalo, ‘‘MHD free convection in a liquid metal filled cubic enclosure I. Differential heating’’, Int. J. Heat Mass Transfer 45, 1477–1492, (2002).
[6].             I.D. Piazza, M. Ciofalo, ‘‘MHD free convection in a liquid metal filled cubic enclosure II. Internal heating’’, Int. J. Heat Mass Transfer 45, 1493–1511, (2002).
[7].             M. Pirmohammadi, M. Ghassemi, ‘‘Effect of magnetic field on convection heat transfer inside a tilted square enclosure’’, International Communication in Heat and Mass Transfer, 36, 776–780, (2009).
[8].             M. Pirmohammadi, M. Ghassemi, A. Keshtkar, ‘‘Numerical study of hydromagnetic convection of an electrically conductive fluid with variable properties inside an enclosure’’, IEEE Transactions on Plasma Science, 39, 516–520, (2011).
[9].             N.M. Al-Najem, K.M. Khanafer, M.M. El-Rafaee, ‘‘Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field’’, Int. J. Numer. Meth. Heat Fluid Flow, 8, 651–672, (1998).
[10].           N. Rudraiah, R.M. Barron, M. Venkatachalappa, C.K. Subbaraya, ‘‘Effect of a magnetic field on free convection in a rectangular enclosure’’, Int. J. Eng. Sci., 33, 1075–1084, (1995).
[11].           F. Selimefendigil, H.F. Oztop, K. Al-Salem, Natural convection of ferrofluids in partially heated square enclosures, J. Magn. Magn. Mater., 372, , 122–133, (2014).
[12].           H. Heidary, R. Hosseini, M. Pirmohammadi, M. J. Kermani, ‘‘Numerical study of magnetic field effect on nano-fluid forced convection in a channel’’, Journal of Magnetism and Magnetic Matrials, 374, 11-17, (2014).
[13].           N.S. Bondareva, M.A. Sheremet, I. Pop, ‘‘Magnetic field effect on the unsteady natural convection in a right-angle trapezoidal cavity filled with a nanofluid’’, Int. J. Numer. Methods Heat. Fluid Flow., 25, 1924–1946, (2015).
[14].           I.V. Miroshnichenko, M.A. Sheremet, H.F. Oztopc, K. A-Salem, ‘‘MHD natural convection in a partially open trapezoidal cavity filled with a nanofluid’’, International Journal of Mechanical Sciences, 119, 294–302, (2016).
[15].           P.A. Davidson, ‘‘An Introduction to Magnetohydrodynamics’’, Cambridge University Press, Cambridge, 2001.
[16].           U. Müller, L. Bühler, ‘‘Magnetofluiddynamics in channels and containers’’, Springer, Wien, New York, (2001).
[17].           S.S. Sazhin, M. Makhlouf, ‘‘Solutions of magnetohydrodynamic problems based on a convectional computational fluid dynamic code’’, International Journal for Numerical Methods in Fluids, 21, 433-442, (1995).
[18].           E. Sarris , G. K. Zikos, A. P. Grecos, N.S. Vlachos, “On the Limits of Validity of the Low Magnetic ReynoldsNumber Approximation in MHD Natural-Convection HeatTransfer”, Numerical Heat Transfer (Part B), 50, 157-180, (2006).