Abstract
The boundary element method is developed for the solution of Stefan problems in a semi-infinite domain with constant properties and imposed with constant or timevariant temperature and flux boundary conditions. The medium may or may not be superheated or subcooled and the boundary element results are obtained with a dissection method. Numerical data indicate that the boundary element results are almost as accurate as those of a source-and-sink method which has demonstrated to be highly accurate in previous studies. The advantages of the boundary element method are also given in the paper.
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Landau, H.G. ‘Heat Conduction in a Melting Solid’ Q. Appl. Math. Vol. VIII, No. 1, pp. 81 - 94, 1950.
Furzeland, R.M. ‘A Comparative Study of Numerical Methods for Moving Boundary Problems’ J. Inst. Math. Appl. Vol. 26, pp. 411 - 429, 1980.
Murray, W.D. and Landis, F. ‘Numerical and Machine Solutions of Transient Heat Conduction Problems Involving Melting or Freezing; Part I—Method of Analysis and Sample Solutions’ J. Heat Transfer, Vol. 81, pp. 106 - 112, 1959.
Heinlein, M., Mukherjee, S. and Richmond, O. ‘A Boundary Element Method Analysis of Temperature Fields and Stresses During Solidification’ Acta Mechanica, Vol. 59, pp. 59 - 81, 1986.
Hong, C.P., Umeda, T. and Kimura, Y. ‘Numerical Models for Casting Solidification: Part I. The Coupling of the Boundary Element and Finite Difference Methods for Solidification Problems’ Metallurgical Trans. B, Vol. 15B, pp. 91 - 99, 1984.
Hong, C.P., Umeda, T. and Kimura, Y. ‘Numerical Models for Casting Solidification: Part II. Application of the Boundary Element Method to Solidification Problems’ Metallurgical Trans. B, Vol. 15B, pp. 101 - 107, 1984.
O’Neill, K. ‘Boundary Integral Equation Solution of Moving Boundary Phase Change Problems’ Int. J. Numer. Meth. Eng., Vol. 19, pp. 1825 - 1850, 1983.
Sadegh, A.M., Jiji, L.M. and Weinbaum, S. ‘Boundary Integral Equation Technique with Application to Freezing Around a Buried Pipe’ Int. J. Heat Mass Transfer, Vol. 30, No. 2, pp. 223 - 232, 1987.
Zabaras, N. and Mukherjee, S. ‘An Analysis of Solidification Problems by the Boundary Element Methods’ Int. J. Numer. Meth. Eng., Vol. 24, pp. 1879 - 1900, 1987.
Yao, L.S. and Prusa, J. ‘Melting and Freezing’ Advances in Heat Transfer (Editors: J.P. Harntett and T.F. Irvine, Jr.) Vol. 19, pp. 1 - 95, 1989.
Hsieh, C.K. and Choi, C.-Y. ‘Solution of One- and Two-Phase Melting and Solidification Problems Imposed with Constant or Time-Variant Temperature and Flux Boundary Conditions’ J. Heat Transfer (in Press).
Choi, C.-Y. and Hsieh, C.K. ‘Solution of Stefan Problems Imposed with Cyclic Temperature and Flux Boundary Conditions’ Int. J. Heat Mass Transfer (in press).
Hsieh, C.K. and Choi, C.-Y. ‘A General Analysis of Phase Change Energy Storage for Solar Energy Applications’ J. Solar Energy Eng. (in press).
Hsieh, C.K. and Akbari, M. ‘Solution of Inverse Stefan Problems by a Source-and-Sink Method’ Submitted to Int. J. Numer. Meth. Heat Fluid Flow.
Morse, P.M. and Feshbach, H. Methods of Theoretical Physics, McGraw-Hill, New York, 1953.
Choi, C.-Y. Exact and Numerical Solution of One- and Two-phase Melting and Solidification Problems Imposed with Constant or Time-variant Temperature and Flux Conditions, Ph.D. Dissertation, University of Florida, 1991.
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© 1992 Computational Mechanics Publications
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Hsieh, C.K., Choi, CY., Kassab, A.J. (1992). Solution of Stefan Problems by a Boundary Element Method. In: Brebbia, C.A., Ingber, M.S. (eds) Boundary Element Technology VII. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2872-8_32
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DOI: https://doi.org/10.1007/978-94-011-2872-8_32
Publisher Name: Springer, Dordrecht
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