The starting solution for two-dimensional heat conduction problems with change of phase

Author:

Boley Bruno A.,Yagoda Harvey P.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Reference23 articles.

1. G. Lamé and B. P. E. Clapeyron, Memoire sur la solidification par refroidissement d’un globe liquide, Ann. Chimie Phys. 47, 250–256 (1831)

2. F. Neumann, Unpublished lectures (1835–40?)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

3. J. Stefan, Ueber einige Probleme der Theorie des Wärmeleitung, Sitzungaberichte Kais. Akad. Wissenschaften, Vienna, 98, part II, pp. 473—484, 1889

4. M. Brillouin, Sur quelques problèmes non résolus de la physique mathématique classique: propagation de la fusion, Ann. Inst. H. Poincaré1, 285 (1931)

5. 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

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