Computational MHD Part III — Application to Electromagnetic Control of Convective Flows

  • Christian Karcher
  • Ulrich Lüdtke
  • Dietmar Schulze
  • Andre Thess
Part of the International Centre for Mechanical Sciences book series (CISM, volume 418)


Convective flow in a liquid metal heated locally at its upper surface and affected by an applied time-dependent magnetic field is investigated. The system under consideration serves as a physical model for the industrial process of electron beam evaporation of liquid metals. In this process, the strong energy input induces strong temperature gradients along the free surface and in the interior of the melt. Thus, the liquid metal is subject to both thermocapillary and natural convection. The vigorous convective motion within the melt leads to highly unwelcome heat losses through the walls of the crucible. The strong convective heat transfer limits the temperature rise in the hot spot and, therefore, the thermodynamic efficiency of the evaporation process. The present paper aims to demonstrate that the melt-flow can be effectively controlled by using external magnetic fields in order to considerably reduce the convective heat losses. As examples, we employ numerical simulations based on the finite element method to study the effects of both a traveling magnetic field and a rotating magnetic field.


Nusselt Number Liquid Metal Lorentz Force Electron Beam Evaporation Flux Line 
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  1. 1.
    S. Schiller, U. Heisig, S. Panzer: Electron beam technology Technik Verlag Berlin (1982).Google Scholar
  2. 2.
    S.H. Davis: Ann. Rev. Fluid Mech. 19 (1987), 403.CrossRefMATHGoogle Scholar
  3. 3.
    E.D. Siggia: Ann. Rev. Fluid Mech. 26 (1994), 137.MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Pumir, L. Blumenfeld: Phys. Rev. E54 (1997), 4528.Google Scholar
  5. 5.
    T. DebRoy, S.A. Davis: Rev. Mod. Phys. 67 (1995), 85.CrossRefGoogle Scholar
  6. 6.
    Ch. Karcher, R. Schaller, Th. Boeck, Ch. Metzner, A. Thess: Int. J. Heat Mass Transfer 43 (2000), 1759.Google Scholar
  7. 7.
    Ch. Karcher, R. Schaller, A. Thess: in Fluid flow phenomena in metals processing N. El-Kaddah, D.G.C. Robertson, S.T. Johansen, V.R. Voller (eds ), TMS Publication (1999).Google Scholar
  8. 8.
    R.Moreau: Magnetohydrodynamics, Kluwer, Dordrecht (1990).CrossRefMATHGoogle Scholar
  9. 9.
    Ch. Karcher, Y. Kolesnikov, O. Andreev, A. Thess: Eur. J. Mech. B/Fluids (submitted).Google Scholar
  10. 10.
    Ch. Karcher, U. Lüdtke, D. Schulze, A. Thess: Proc. 3rd Int. Symposium on Electromagnetis Processing of Materials, Nagoya (2000), 473–478.Google Scholar
  11. 11.
    Ch. Karcher, Y. Kolesnikov, U. Lüdtke, A. Thess: Proc. 4th Pamir Int. Conference, Presqu’île Giens (2000), (to appear).Google Scholar
  12. 12.
    K. J. Binns, P. J. Lawrensen, C. W. Trowbridge: The Analytical and Numerical Solution of Electric and Magnetic Fields, Wiley & Sons, New York (1992).Google Scholar
  13. 13.
    D. J. Jackson: Classical Electrodynamics, J. Wiley and Sons, New York (1999).MATHGoogle Scholar
  14. 14.
    U. Luedtke: Ilmenau University of Technology, PhD dissertation (1990).Google Scholar
  15. 15.
    O. C. Zienkiewicz, R. L. Taylor: The Finite Element Method, McGraw-Hill, London (1991).Google Scholar
  16. 16.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. B. Flannery: Numerical Recipes in Fortran 77, Cambridge University Press, New York (1992).MATHGoogle Scholar
  17. 17.
    S. Rinke, Ch. Karcher, and A. Thess: Report ILR/B977, Dresden University of Technology (1998).Google Scholar
  18. 18.
    J. Platten, J. Legros: Convection in Liquids, Springer, New York (1984).CrossRefMATHGoogle Scholar
  19. 19.
    D. A. Anderson, J. C. Tannehill, R. H. Plechter: Computational Fluid Mechanics and Heat Transfer, Taylor and Francis, Washington D. C., (1997).Google Scholar
  20. 20.
    E. J. Hopfinger (Ed.): Rotating Fluids in Geophysical and Industrial Applications, CISM Courses and Lectures No. 329, Springer, New York (1992).Google Scholar
  21. 21.
    A. Thess, D. Schulze: This volume.Google Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Christian Karcher
    • 1
  • Ulrich Lüdtke
    • 2
  • Dietmar Schulze
    • 2
  • Andre Thess
    • 1
  1. 1.Department of Mechanical EngineeringIlmenau University of TechnologyGermany
  2. 2.Department of Electrical EngineeringIlmenau University of TechnologyGermany

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