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A cubic heat balance integral method for one-dimensional melting of a finite thickness layer. (English) Zbl 1140.80389
Summary: The work in this paper concerns the one-dimensional melting of a finite thickness layer. An asymptotic series solution describes the temperature in the melt regions. In the solid region the thermal boundary layers are approximated by a cubic polynomial. Results are compared with the exact solution for a semi-infinite block, and shown to agree to within less than 1%. The method is then applied to a situation where no analytical solution is available. A finite thickness frozen solid is placed on a warm substrate in a warm environment: initially the base of the solid heats to the melting temperature when a single melted region develops and subsequently a second melting front appears on the top boundary. We also present an example relevant to heating an ice layer from below, which occurs with de-icing systems.
MSC:
80A22Stefan problems, phase changes, etc.
80M25Other numerical methods (thermodynamics)