The starting solution for two-dimensional heat conduction problems with change of phase
Authors:
Bruno A. Boley and Harvey P. Yagoda
Journal:
Quart. Appl. Math. 27 (1969), 223-246
DOI:
https://doi.org/10.1090/qam/99828
MathSciNet review:
QAM99828
Full-text PDF Free Access
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Additional Information
Abstract: A short-time solution for two-dimensional change-of-phase problems for a half space is developed. The problems are such that melting starts at a point of the surface and spreads both along the surface and towards the interior of the body. Heating is applied by an analytic but otherwise general heat input.
G. Lamé and B. P. E. Clapeyron, Memoire sur la solidification par refroidissement d’un globe liquide, Ann. Chimie Phys. 47, 250–256 (1831)
F. Neumann, Unpublished lectures (1835–40?) reported by H. Weber in Die partiellen Differential-Gleichungen der mathematischen Physik, nach Riemann’s Verlesungen, Braunwshweig, 4th ed., Vol. II, 1901, pp. 118–122
J. Stefan, Ueber einige Probleme der Theorie des Wärmeleitung, Sitzungaberichte Kais. Akad. Wissenschaften, Vienna, 98, part II, pp. 473—484, 1889
M. Brillouin, Sur quelques problèmes non résolus de la physique mathématique classique: propagation de la fusion, Ann. Inst. H. Poincaré1, 285 (1931)
D. L. Sikarskie and B. A. Boley, The solution of a class of two-dimensional melting and solidification problems, Int. J. of Solids and Structures 1(2), 207–234 (April 1965) and Technical Report No. 25, Contract No. Nonr 266(20), Department of Civil Engineering and Engineering Mechanics, Columbia University, May 1964
- Bruno A. Boley, A method of heat conduction analysis of melting and solidification problems, J. Math. and Phys. 40 (1961), 300–313. MR 141376
B. A. Boley, “The analysis of problems of heat conduction and melting,” High temperature structures and materials: Proc. of Symp. on Naval Structural Mechanics, Pergamon Press, Oxford, 1964, pp. 260–315
J. C. Muehlbauer and J. E. Sunderland, Heat conduction with freezing or melting, Appl. Mech. Rev. 18 (12), 951–959 (1965)
B. A. Boley, A general starting solution for melting and solidifying slabs, Int. J. Eng. Sci. 6, 89–111 (1968)
- Ting-shu Wu and Bruno A. Boley, Bounds in melting problems with arbitrary rates of liquid removal, SIAM J. Appl. Math. 14 (1966), 306–323. MR 213105, DOI https://doi.org/10.1137/0114028
- Bruno A. Boley, Upper and lower bounds in problems of melting or solidifying slabs, Quart. J. Mech. Appl. Math. 17 (1964), 253–269. MR 165844, DOI https://doi.org/10.1093/qjmam/17.3.253
- S. J. Citron, On the conduction of heat in a melting slab, Proc. 4th U.S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) Amer. Soc. Mech. Engrs., New York, 1962, pp. 1221–1228. MR 0159568
E. Friedman and B. A. Boley, Design estimates of stresses and deformations in melting plates, Technical Report No. 29, Contract No. Nonr 4259(07), Department of Civil Engineering and Engineering Mechanics, Columbia University, June 1965
B. Chalmers, Principles of solidification, Wiley, New York, 1964
G. Horvay and J. Cahn, Dendritic and spheroidal growth, Acta Metallurgica 9, 695–705 (1961)
W. A. Tiller, “Alloy Crystal Growth,” Growth and Perfection of Crystals, Proc. of an Int. Conf. on Crystal Growth, General Electric Company, 1958
W. A. Tiller, Grain size control during ingot solidification, Part II: Columnar-equiaxed transition, Trans. of the Metallurgical Soc. of A. I. M. E. 224, 448–459 (1962)
- Bruno A. Boley and Jerome H. Weiner, Theory of thermal stresses, John Wiley & Sons, Inc., New York London, 1960. MR 0112414
- H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. MR 0022294
B. A. Boley, Estimate of errors in approximate temperature and thermal stress calculations, Proc. of the Eleventh Int. Cong. of Applied Mechanics, Munich, 1964, pp. 586–596
- N. N. Lebedev, Special functions and their applications, Revised English edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. Translated and edited by Richard A. Silverman. MR 0174795
E. Goursat, Cours d’analyse mathematique, fifth ed., Vol. 3, Chapter 29, Gauthier-Villars, Paris, 1942
H. P. Yagoda, The starting solution for two-dimensional heat conduction problems with change of phase, Dissertation for the Eng. Sc. D. degree, Department of Civil Engineering and Engineering Mechanics, Columbia University, 1967
G. Lamé and B. P. E. Clapeyron, Memoire sur la solidification par refroidissement d’un globe liquide, Ann. Chimie Phys. 47, 250–256 (1831)
F. Neumann, Unpublished lectures (1835–40?) reported by H. Weber in Die partiellen Differential-Gleichungen der mathematischen Physik, nach Riemann’s Verlesungen, Braunwshweig, 4th ed., Vol. II, 1901, pp. 118–122
J. Stefan, Ueber einige Probleme der Theorie des Wärmeleitung, Sitzungaberichte Kais. Akad. Wissenschaften, Vienna, 98, part II, pp. 473—484, 1889
M. Brillouin, Sur quelques problèmes non résolus de la physique mathématique classique: propagation de la fusion, Ann. Inst. H. Poincaré1, 285 (1931)
D. L. Sikarskie and B. A. Boley, The solution of a class of two-dimensional melting and solidification problems, Int. J. of Solids and Structures 1(2), 207–234 (April 1965) and Technical Report No. 25, Contract No. Nonr 266(20), Department of Civil Engineering and Engineering Mechanics, Columbia University, May 1964
B. A. Boley, A method of heat-conduction analysis of melting and solidifying slabs, J. Math. Phys. 40 (4), 300–313 (1961)
B. A. Boley, “The analysis of problems of heat conduction and melting,” High temperature structures and materials: Proc. of Symp. on Naval Structural Mechanics, Pergamon Press, Oxford, 1964, pp. 260–315
J. C. Muehlbauer and J. E. Sunderland, Heat conduction with freezing or melting, Appl. Mech. Rev. 18 (12), 951–959 (1965)
B. A. Boley, A general starting solution for melting and solidifying slabs, Int. J. Eng. Sci. 6, 89–111 (1968)
Ting-Shu Wu and B. A. Boley, Bounds in melting problems with arbitrary rates of liquid removal, SIAM J. Appl. Math. 14(2) (1966)
B. A. Boley, Upper and lower bounds in problems of melting or solidifying slabs, Quart. J. Mech. Appl. Math. 7, 253–269 (1964)
S. J. Citron, On the conduction of heat in a melting slab, Proc. of the IVth U. S. Cong, of Applied Mechanics, A. S. M. E., June 1962, pp. 1221–1227
E. Friedman and B. A. Boley, Design estimates of stresses and deformations in melting plates, Technical Report No. 29, Contract No. Nonr 4259(07), Department of Civil Engineering and Engineering Mechanics, Columbia University, June 1965
B. Chalmers, Principles of solidification, Wiley, New York, 1964
G. Horvay and J. Cahn, Dendritic and spheroidal growth, Acta Metallurgica 9, 695–705 (1961)
W. A. Tiller, “Alloy Crystal Growth,” Growth and Perfection of Crystals, Proc. of an Int. Conf. on Crystal Growth, General Electric Company, 1958
W. A. Tiller, Grain size control during ingot solidification, Part II: Columnar-equiaxed transition, Trans. of the Metallurgical Soc. of A. I. M. E. 224, 448–459 (1962)
B. A. Boley and J. H. Weiner, Theory of thermal stresses, Wiley, New York, 1960
H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, 2nd ed., Clarendon Press, Oxford, 1959
B. A. Boley, Estimate of errors in approximate temperature and thermal stress calculations, Proc. of the Eleventh Int. Cong. of Applied Mechanics, Munich, 1964, pp. 586–596
N. N. Lebedev, Special functions and their applications, Prentice-Hall, Englewood Cliffs, N. J., 1965, pp. 60
E. Goursat, Cours d’analyse mathematique, fifth ed., Vol. 3, Chapter 29, Gauthier-Villars, Paris, 1942
H. P. Yagoda, The starting solution for two-dimensional heat conduction problems with change of phase, Dissertation for the Eng. Sc. D. degree, Department of Civil Engineering and Engineering Mechanics, Columbia University, 1967
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Article copyright:
© Copyright 1969
American Mathematical Society
