TECHNICAL PAPERS: Melting and Solidification

Melting of a Wire Anode Followed by Solidification: A Three-Phase Moving Interface Problem

[+] Author and Article Information
S. S. Sripada, Ira M. Cohen, P. S. Ayyaswamy

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315

J. Heat Transfer 125(4), 661-668 (Jul 17, 2003) (8 pages) doi:10.1115/1.1576811 History: Received May 22, 2002; Revised February 25, 2003; Online July 17, 2003
Copyright © 2003 by ASME
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Qin,  W., Cohen,  Ira. M., and Ayyaswamy,  P. S., 2000, “Charged Particle Distributions and Heat Transfer in a Discharge Between Geometrically Dissimilar Electrodes: From Breakdown to Steady State,” Phys. Plasmas, 7(2), pp. 719–728.
Yeung,  R. W., 1982, “Numerical Methods in Free-Surface Flows,” Annu. Rev. Fluid Mech., 14, pp. 395–442.
Tsai,  W. T., and Yue,  D. K. P., 1996, “Computation of Nonlinear Free-Surface Flows,” Annu. Rev. Fluid Mech., 28, pp. 249–278.
Shyy, W., Udaykumar, H. S., Rao, M. M., and Smith, R. W., 1996, Computational Fluid Dynamics With Moving Boundaries, Taylor & Francis, Washington, DC.
Finlayson, B. A., 1992, Numerical Methods for Problems With Moving Fronts, Ravenna Park Publishing, Inc., Seattle, WA.
Alexiades, V., and Solomon, A. D., 1993, Mathematical Modeling of Melting and Freezing Processes, Hemisphere, Bristol, PA.
Ryskin,  G., and Leal,  L. G., 1984, “Numerical Solution of Free-Boundary Problems in Fluid Mechanics. Part 1. The Finite-Difference Technique,” J. Fluid Mech., 148, pp. 1–17.
Kang,  I. S., and Leal,  L. G., 1987, “Numerical Solution of Axisymmetric, Unsteady Free-Boundary Problems at Finite Reynolds Number. I. Finite-Difference Scheme and Its Application to the Deformation of a Bubble in a Uniaxial Straining Flow,” Phys. Fluids, 30, pp. 1929–1940.
Juric,  D., and Tryggvason,  G., 1996, “A Front-Tracking Method for Dendritic Solidification,” J. Comput. Phys., 123, pp. 127–148.
Unverdi,  S. O., and Tryggvason,  G., 1992, “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flow,” J. Comput. Phys., 100, pp. 25–37.
Bonacina,  C., Comini,  G., Fasans,  A., and Primiceris,  M., 1973, “Numerical Solution of Phase Change Problems,” Int. J. Heat Mass Transfer, 16, pp. 1825–1832.
Huang,  L. J., Ayyaswamy,  P. S., and Cohen,  Ira. M., 1995, “Melting and Solidification of Thin Wires: A Class of Phase-Change Problems With a Mobile Interface-I. Analysis,” Int. J. Heat Mass Transfer, 38(9), pp. 1637–1645.
Yoo,  J., and Rubinsky,  B., 1983, “Numerical Computation Using Finite Elements for the Moving Interface in Heat Transfer Problems With Phase Change Transformation,” Numer. Heat Transfer, 6, pp. 209–222.
Bounds,  S., Moran,  G., Pericleous,  K., Cross,  M., and Croft,  T. N., 2000, “A Computational Model for Defect Prediction in Shape Castings Based on the Interaction of Free Surface Flow, Heat Transfer, and Solidification Phenomena,” Metall. Mater. Trans. B, 31(3), pp. 515–527.
Hsiao,  J. S., 1985, “An Efficient Algorithm for Finite-Difference Analysis of Heat Transfer With Melting and Solidification,” Numer. Heat Transfer, 8, pp. 653–666.
Shamsundar,  N., and Sparrow,  E., 1975, “Analysis of Multidimensional Phase Change via the Enthalpy Model,” ASME J. Heat Transfer, 19, pp. 333–340.
Cohen,  Ira. M., Huang,  L. J., and Ayyaswamy,  P. S., 1995, “Melting and Solidification of Thin Wires: A Class of Phase-Change Problems With a Mobile Interface-II. Experimental Confirmation,” Int. J. Heat Mass Transfer, 38(9), pp. 1647–1659.
Liu,  A., Voth,  T. E., and Bergman,  T. L., 1993, “Pure Material Melting and Solidification With Liquid Phase Buoyancy and Surface Tension Force,” Int. J. Heat Mass Transfer, 36, pp. 411–422.
Sadhal, S. S., Ayyaswamy, P. S., and Chung, J. N., 1997, Transport Phenomena With Bubbles and Drops, Springer, New York.
Ayyaswamy, P. S., Sripada, S. S., and Cohen, Ira. M., 1999, “Interfacial Motion of a Molten Layer Subject to Plasma Heating,” Fluid Dynamics at Interfaces, Wei Shyy and Ranga Narayanan, eds., Cambridge University Press, New York, pp. 320–338.
Sripada, Srinivas. S., 1999, “Fundamental Studies of Plasma Applications in Microelectronic Manufacturing and Flames: Fluid Mechanics, Phase-Change, and Heat Transfer,” Ph.D. thesis, Univ. of Pennsylvania.
Sripada,  Srinivas, S., Ayyaswamy,  P. S., and Cohen,  I. M., 1998, “Weakly Ionized Plasma Heat Transfer Between Geometrically Dissimilar Electrodes,” ASME J. Heat Transfer, 120(3), pp. 939–942.
Ryskin,  G., and Leal,  L. G., 1983, “Orthogonal Mapping,” J. Comput. Phys., 50, pp. 71–100.
Eca,  L., 1996, “2D Orthogonal Grid Generation With Boundary Point Distribution Control,” J. Comput. Phys., 125, pp. 440–453.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC.
de Zeeuw,  P. M., 1990, “Matrix-Dependent Prolongations and Restrictions in a Blackbox Multigrid Solver,” J. Comput. Appl. Math., 33, pp. 1–27.
de Zeeuw, P. M., 1997, “Acceleration of Iterative Methods by Coarse Grid Corrections,” Ph.D. thesis, Univ. of Amsterdam.
Raithby,  G. D., Galpin,  P. F., and Van Doormaal,  J. P., 1986, “Prediction of Heat and Fluid Flow in Complex Geometries Using General Orthogonal Coordinates,” Numer. Heat Transfer, 9, pp. 125–142.
Karki,  K. C., and Patankar,  S. V., 1988, “Calculation Procedure for Viscous Incompressible Flows in Complex Geometries,” Numer. Heat Transfer, 14, pp. 295–307.
Shyy, W., 1994, Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier, Amsterdam.
Bennon,  W. D., and Incropera,  F. P., 1988, “Numerical Analysis of Binary Solid-Liquid Phase-Change Using a Continuum Model,” Numer. Heat Transfer, 13(3), pp. 277–296.
Ferziger, J. H., and Peric, M., 1996, Computational Methods for Fluid Dynamics, Springer, New York.
Miller, R. R., 1952, Liquid-Metals Handbook, 2nd edition, R. N. Lyon et al.,eds., Office of Naval Research, Dept. of Navy, Washington, DC, pp. 38–102; Chpt. 2.
Ho,  C. Y., Powell,  R. W., and Liley,  P. E., 1974, “Thermal Conductivity of the Elements: a Comprehensive Review,” J. Phys. Chem. Ref. Data, 3, Suppl. 1.
Beer, S. Z., 1972, Liquid Metals: Chemistry and Physics, Marcel Dekker, Inc., New York.
Sripada, S. S., Cohen, I. M., and Ayyaswamy, P. S., “A Study of the Electronic Flame Off Discharge Process Used for Ball Bonding in Microelectronic Packaging,” 1996, Transport Phenomena in Materials Processing and Manufacturing, Proc. Int. Mech. Eng. Congress & Expo, HTD-336 , ASME, New York, pp. 129–136.


Grahic Jump Location
(ξ,η) grid system detail: all lengths normalized by wire diameter
Grahic Jump Location
Evolution of the free surface of the anode during melting: (a) Free surface at t*=2.53, (b) Free surface at t*=4.69, (c) Free surface at t*=9.56, (d) Free surface at t*=18.8, (e) Free surface at t*=28.3, and (f) Free surface at t*=45.2. Arrow denotes location of solid-liquid interface.
Grahic Jump Location
Isotherms at t*=200. Nondimensional temperature T*=T/T.



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