Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

European Journal of Applied Mathematics

Volumn 11, Issue 2, 2000, Pages 153-169

  Lacey, A A ^a   Herraiz, L A ^a,b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346107443     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792599004027     Document Type: Article

References (7)

1. ATTHEY, D. R. (1974) A finite difference scheme for melting problems. J. Inst. Maths. Applics. 13, 353-366.
2. CHRISTIAN, J. W. (1965) The Theory of Transformations in Metals and Alloys: An Advanced Textbook in Physical Metallurgy. Oxford, Pergamon Press.
3. FIFE, P. C. & GILL, G. S. (1989) The phase-field description of mushy zones. Physica D. 35, 267-275.
4. FIFE, P. C. & GILL, G. S. (1991) Phase-transition mechanisms for the phase-field model under internal heating. Physical Rev. 43, 843-851.
5. LACEY, A. A. & SHILLOR, M. (1983) The existence and stability of regions with superheating in the classical two-phase one-dimensional Stefan problem with heat sources. IMA J. Appl. Maths. 30, 215-230.
6. LACEY, A. A. & TAYLER, A. B. (1983) A mushy region for a Stefan problem. IMA J. Appl. Math. 30, 303-313.
7. MULLINS, W. W. & SEKERKA, R. F. (1964) Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35, 444-451.