Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 56
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lee, Jonghyun Matson, Douglas M. Binder, Sven Kolbe, Matthias Herlach, Dieter and Hyers, Robert W. 2014. Magnetohydrodynamic Modeling and Experimental Validation of Convection Inside Electromagnetically Levitated Co-Cu Droplets. Metallurgical and Materials Transactions B, Vol. 45, Issue. 3, p. 1018.

    Chen, J. Lengsdorf, R. Henein, H. Herlach, D.M. Dahlborg, U. and Calvo-Dahlborg, M. 2013. Microstructure evolution in undercooled Al–8wt%Fe melts: Comparison between terrestrial and parabolic flight conditions. Journal of Alloys and Compounds, Vol. 556, p. 243.

    Fautrelle, Yves Ernst, Roland and Moreau, René 2009. Magnetohydrodynamics applied to materials processing. International Journal of Materials Research, Vol. 100, Issue. 10, p. 1389.

    Li, Mingjun Nagashio, Kosuke Ishikawa, Takehiko Mizuno, Akitoshi Adachi, Masayoshi Watanabe, Masahito Yoda, Shinichi Kuribayashi, Kazuhiko and Katayama, Yoshinori 2008. Microstructure formation and in situ phase identification from undercooled Co–61.8at.% Si melts solidified on an electromagnetic levitator and an electrostatic levitator. Acta Materialia, Vol. 56, Issue. 11, p. 2514.

    Shatrov, Victor Gerbeth, Gunter and Hermann, Regina 2008. An Alternating Magnetic Field Driven Flow in a Spinning Cylindrical Container. Journal of Fluids Engineering, Vol. 130, Issue. 7, p. 071201.

    Shatrov, Victor Gerbeth, Gunter and Hermann, Regina 2008. Linear stability of an alternating-magnetic-field-driven flow in a spinning cylindrical container. Physical Review E, Vol. 77, Issue. 4,

    Li, Mingjun Ishikawa, Takehiko Nagashio, Kosuke Kuribayashi, Kazuhiko and Yoda, Shinichi 2007. Microtexture formation of Ni99B1 alloys solidified on an ESL and an EML—a study based on the EBSP technique. Materials Science and Engineering: A, Vol. 449-451, p. 684.

    Li, Mingjun Ishikawa, Takehiko Nagashio, Kosuke Kuribayashi, Kazuhiko and Yoda, Shinichi 2006. A comparative EBSP study of microstructure and microtexture formation from undercooled Ni99B1 melts solidified on an electrostatic levitator and an electromagnetic levitator. Acta Materialia, Vol. 54, Issue. 14, p. 3791.

    Bullard, C. Hyers, R.W. and Abedian, B. 2005. Spin-up instability of a levitated molten drop in magnetohydrodynamic-flow transition to turbulence. IEEE Transactions on Magnetics, Vol. 41, Issue. 7, p. 2230.

    Im, Kichang and Mochimaru, Yoshihiro 2005. Numerical analysis on magnetic levitation of liquid metals, using a spectral finite difference scheme. Journal of Computational Physics, Vol. 203, Issue. 1, p. 112.

    Hyers, R. W. Trapaga, G. and Abedian, B. 2003. Laminar-turbulent transition in an electromagnetically levitated droplet. Metallurgical and Materials Transactions B, Vol. 34, Issue. 1, p. 29.

    Shatrov, V. Priede, J. and Gerbeth, G. 2003. Three-dimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field. Physics of Fluids, Vol. 15, Issue. 3, p. 668.

    Ben Salah, Nizar Soulaimani, Azzeddine and Habashi, Wagdi G. 2001. A finite element method for magnetohydrodynamics. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue. 43-44, p. 5867.

    CIOCIRLAN, B.O. BEALE, D.G. and OVERFELT, R.A. 2001. SIMULATION OF MOTION OF AN ELECTROMAGNETICALLY LEVITATED SPHERE. Journal of Sound and Vibration, Vol. 242, Issue. 4, p. 559.

    Bojarevics, V. Pericleous, K. and Cross, M. 2000. Modeling the dynamics of magnetic semilevitation melting. Metallurgical and Materials Transactions B, Vol. 31, Issue. 1, p. 179.

    Ciocirlan, Bogdan O. and Marghitu, Dan B. 2000. Stability Analysis of a Levitated Droplet by Using Floquet Multipliers. Journal of Vibration and Acoustics, Vol. 122, Issue. 4, p. 399.

    Zhong, X. and Bayazitoghu, Y. 2000. Electromagnetic field and lifting capacity for longitudinal electromagnetic levitator. IEEE Transactions on Magnetics, Vol. 36, Issue. 5, p. 3746.

    Ben Salah, Nizar Soulaimani, Azzeddine Habashi, Wagdi G. and Fortin, Michel 1999. A conservative stabilized finite element method for the magneto-hydrodynamic equations. International Journal for Numerical Methods in Fluids, Vol. 29, Issue. 5, p. 535.

    Song, S. P. and Li, B. Q. 1999. A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes. International Journal for Numerical Methods in Engineering, Vol. 44, Issue. 8, p. 1055.

    Clemente, R. A. and Tessarotto, M. 1998. Minima of dissipated power in magnetic levitation. Journal of Applied Physics, Vol. 83, Issue. 1, p. 588.

  • Journal of Fluid Mechanics, Volume 117
  • April 1982, pp. 27-43

Magnetic levitation of liquid metals

  • A. J. Mestel (a1)
  • DOI:
  • Published online: 01 April 2006

The process of levitation melting of metals is examined analytically and numerically for the case of axisymmetric toroidal high-frequency currents. The governing equations for the mean-velocity field and associated free-surface shape are derived under the assumption of low magnetic Reynolds number and the neglect of thermal effects. The form of the solution for high Reynolds number is discussed in general, and particularized to the case of high surface tension, in which limit a perturbation analysis about a spherical shape is presented. Finite-difference techniques are used to solve the Navier–Stokes equations in the sphere, and the surface perturbation is calculated. The asymptotic behaviour of the potential vorticity is illustrated by the numerical experiments.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *