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The Stefan problem for a slightly wavy wall. (English) Zbl 0727.73001

In the paper a fully two-dimensional Stefan problem is solved by a regular perturbation method for the case of a general slight deviation of wall geometry. An approximate solution is obtained in terms of linearized two-dimensional perturbations of a one-dimensional case. Three particular examples are given, namely, a sinusoidal corrugation on the wall (as is seen in refrigerator freezer compartments), a slight hump, and a plane wall rotated very slightly.

MSC:

74A15 Thermodynamics in solid mechanics
80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
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