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Asymptotic solutions to the Stefan problem with a constant heat source at the moving boundary. (English) Zbl 0973.35202
Summary: In [J. Fluid Mech. 198, 293-319 (1989; Zbl 0662.76072)] 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:
35R35Free boundary problems for PDE
80A22Stefan problems, phase changes, etc.
35K05Heat equation