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TECHNICAL PAPERS: Melting and Freezing

Phase Change in a Cylinder and a Cylindrical Shell Heated With an Axisymmetric Front Moving in the Axial Direction

[+] Author and Article Information
C. K. Hsieh

Mechanical Engineering Department, University of Florida, Gainesville, FL 32611-6300e-mail: doughsieh@aol.com

M. Leung

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Konge-mail: memleung@cityu.edu.hk

J. Heat Transfer 123(3), 476-485 (Nov 07, 2000) (10 pages) doi:10.1115/1.1370499 History: Received June 19, 2000; Revised November 07, 2000
Copyright © 2001 by ASME
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References

Rosenthal,  D., 1946, “The Theory of Moving Sources of Heat and its Applications to Metal Treatments,” Trans. ASME, 68, pp. 840–866.
Grosh,  R. J., Trabant,  E. A., and Hawkins,  G. A., 1955, “Temperature Distribution in Solids of Variable Thermal Properties Heated by Moving Heat Sources,” Quarterly Appl. Math., 13, pp. 161–167.
Watts,  R. G., 1969, “Temperature Distributions in Solid and Hollow Cylinders Due to a Moving Circumferential Ring Heat Source,” ASME J. Heat Transfer, 91, pp. 465–470.
DesRuisseaux,  N. R., and Zerkle,  R. D., 1970, “Temperature in Semi-Infinite and Cylindrical Bodies Subjected to Moving Heat Sources and Surface Cooling,” ASME J. Heat Transfer, 92, pp. 456–464.
Yuen,  W. Y. D., 1987, “A New Formulation of Heat Transfer Between Two Moving Bodies in Contact Over a Finite Region with Different Bulk Temperatures,” Mathematical Engineering in Industry, 1, pp. 1–19.
Landau,  H. G., 1950, “Heat Conduction in a Melting Solid,” Quarterly Appl. Math., 8, pp. 81–94.
Jackson,  F., 1965, “Moving Heat Sources with Change of Phase,” ASME J. Heat Transfer, 87, pp. 329–332.
Hsieh,  C. K., 1995, “Exact Solution of Stefan Problems for a Heat Front Moving at Constant Velocity in a Quasi-Steady State,” Int. J. Heat Mass Transf., 38, pp. 71–79.
Hsieh,  C. K., 1995, “Exact Solution of Stefan Problems Related to a Moving Line Heat Source in a Quasi-Stationary State,” ASME J. Heat Transfer, 117, pp. 1076–1079.
Crank, J., 1984, Free and Moving Boundary Problems, Clarendon, London.
Yao,  L. S., and Prusa,  J., 1989, “Melting and Freezing,” Adv. Heat Transfer, 19, pp. 1–95.
Hsieh,  C. K., and Choi,  C.-Y., 1992, “Solution of One- and Two-Phase Melting and Solidification Problems Imposed with Constant or Time-Variant Temperature and Flux Boundary Conditions,” ASME J. Heat Transfer, 114, pp. 524–528.
Hsieh,  C. K., and Choi,  C.-Y., 1992, “A General Analysis of Phase Change Energy Storage for Solar Energy Applications,” ASME J. Sol. Energy Eng., 114, pp. 203–211.
Whittaker, E. T., and Watson, G. N., 1934, Modern Analysis (Fourth Edition), Cambridge University Press, London.
Carslaw, H. S., 1950, An Introduction to the Theory of Fourier’s Series and Integrals (Third Revised Edition), Dover Publications, New York.
Finlayson, B. A., 1972, The Method of Weighted Residuals and Variational Principles, Academic Press, New York.
Patel,  P. D., 1968, “Interface Condition in Heat Conduction Problems with Change of Phase,” AIAA J., 6, pp. 2454–2456.
Boley,  B. A., and Pagoda,  H. P., 1969, “The Starting Solution for Two-Dimensional Heat Conduction Problems With Change of Phase,” Quarterly Appl. Math., 27, pp. 223–246.
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Figures

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Coordinate systems used for analysis and temperature profiles as a result of the presence of source and sink in a medium
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Division of the domain into six regions in the moving coordinates
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Temperature curves in an insulated cylinder without phase change
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Isotherms for the cylinder studied in Fig. 3
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Curves and equations used to model interfaces
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Limiting position of the interface and evaluated interface position for the cylinder (Zm=1.6) studied in Fig. 3
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Temperature distribution curves for phase change in the cylinder (Zm=1.6) studied in Fig. 3
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Limiting position of the interface and evaluated interface position for the cylinder (Zm=2.1) studied in Fig. 3
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Comparison of surface temperature distribution with and without phase change for the cylinder (Zm=2.1) studied in Fig. 3
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Temperature distribution curves for phase change in the cylinder (Zm=2.1) studied in Fig. 3
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Limiting position of the interface and evaluated interface position for a cylindrical shell (Zm=3.2)
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Temperature distribution curves for phase change in a cylindrical shell (Zm=3.2)
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Temperature distribution curves for phase change in a cylindrical shell (Zm=2.8)

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