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Zbl 0973.35202
King, J.R.; Riley, D.S.
Asymptotic solutions to the Stefan problem with a constant heat source at the moving boundary. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No.1997, 1163-1174 (2000). ISSN 1364-5021; ISSN 1471-2946/e

Summary: In [J. Fluid Mech. 198, 293-319 (1989; Zbl 0662.76072)] {\it H. E. Huppert} formulated mathematical models of the melting and/or freezing that occurs when a hot fluid begins to flow turbulently over a cold substrate. He solved the resulting Stefan problems numerically and presented certain asymptotic results. This note revisits one of his problems and adds to the mathematical analysis of its asymptotic structure. Generalizations and relationships with other results are also noted.

MSC 2000:: *35R35 Free boundary problems for PDE
80A22 Stefan problems, etc.
35K05 Heat equation

Keywords: Stefan problem; asymptotic methods; ablation; etching

Citations: Zbl 0662.76072

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