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TECHNICAL PAPERS: Heat Transfer in Manufacturing

Combined Effects of Rotating Magnetic Field and Rotating System on the Thermocapillary Instability in the Floating Zone Crystal Growth Process

[+] Author and Article Information
Nancy Ma

Department of Mechanical and Aerospace Engineering, Campus Box 7910, North Carolina State University, Raleigh, NC 27695

John S. Walker

Department of Mechanical and Industrial Engineering, 1206 West Green St., University of Illinois, Urbana, IL 61801

Laurent Martin Witkowski

LIMSI, BP133, F91403, Orsay Cedex, France

J. Heat Transfer 126(2), 230-235 (May 04, 2004) (6 pages) doi:10.1115/1.1666883 History: Received May 23, 2003; Revised December 02, 2003; Online May 04, 2004
Copyright © 2004 by ASME
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References

Dold,  P., Croll,  A., Lichtensteiger,  M., Kaiser,  Th., and Benz,  K. W., 2001, “Floating Zone Growth of Silicon in Magnetic Fields. IV. Rotating Magnetic Fields,” J. Cryst. Growth, 231, pp. 95–106.
Walker,  J. S., Martin Witkowski,  L., and Houchens,  B. C., 2003, “Effects of a Rotating Magnetic Field on the Thermocapillary Instability in the Floating Zone Process,” J. Cryst. Growth, 252, pp. 413–423.
Wanschura,  M., Shevtsova,  V. M., Kuhlmann,  H. C., and Rath,  H. J., 1995, “Convective Instability Mechanisms in Thermocapillary Liquid Bridges,” Phys. Fluids, 7, pp. 912–925.
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Fischer,  B., Friedrich,  J., Weimann,  H., and Muller,  G., 1999, “The Use of Time-Dependent Magnetic Fields for Control of Convective Flows in Melt Growth Configurations,” J. Cryst. Growth, 198/199, pp. 170–175.
Levenstam,  M., Amberg,  G., and Winkler,  C., 2001, “Instabilities of Thermocapillary Convection in a Half-Zone at Intermediate Prandtl Number,” Phys. Fluids, 13, pp. 807–816.
Dold,  P., and Benz,  K. W., 1999, “Rotating Magnetic Field: Fluid Flow and Crystal Growth Applications,” Prog. Cryst. Growth Charact. Mater., 38, pp. 7–38.
Martin Witkowski,  L., Walker,  J. S., and Marty,  Ph., 1999, “Nonaxisymmetric Flow in a Finite-Length Cylinder With a Rotating Magnetic Field,” Phys. Fluids, 11, pp. 1821–1826.
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Smith, B. T. et al., 1976, Matrix Eigensystem Routines—EISPACK Guide, Lecture Notes in Computer Science, Vol. 6, New York, Springer-Verlag.
Chen,  G., Lizee,  A., and Roux,  B., 1997, “Bifurcation Analysis of the Thermocapillary Convection in Cylindrical Liquid Bridges,” J. Cryst. Growth, 180, pp. 638–647.

Figures

Grahic Jump Location
Critical mode results for rotation of the crystal and feed rod without a rotating magnetic field: (a) Recr versus ReΩ; and (b) λI versus ReΩ
Grahic Jump Location
Base-flow streamlines for Tm=0,ReΩ=150 and Recr=3651.9:ψ0=2.0k for k=0 to 7 and ψ0=−0.2k, for k=1 to 5
Grahic Jump Location
Critical mode results versus −Tm for ReΩ=100; (a) Recr versus −Tm; and (b) λI versus −Tm
Grahic Jump Location
Base-flow streamlines for ReΩ=100,Tm=−5500 and Recr=2472.7:ψ0=2.0k, for k=0 to 8
Grahic Jump Location
Critical mode results for ReΩ=175: (a) Recr versus −Tm; and (b) λI versus −Tm
Grahic Jump Location
Base-flow results for ReΩ=175,Tm=−7000 and Recr=2297: (a) Streamlines for meridional flow: ψ0=2.0k, for k=0 to 7 and ψ0=−0.1k, for k=1 to 5; and (b) Lines of constant azimuthal velocity: vθ0=20k, k=0 to 8 and vθ0=−10k, k=1 to 7

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