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Application of standard and refined heat balance integral methods to one-dimensional Stefan problems. (English) Zbl 1188.80004

The authors study the conventional and refined heat balance integral method for phase change problems. To approximate the temperature values, functions of different profiles are used: quadratic, cubic and exponential. The derived results are comparable with the exact and numerical solutions.

In particular, the authors ponder over the use of the discussed methods to the approximate solution of the problem of melting a semi-infinite solid that is initially at the solidus with a Dirichlet boundary condition or with Robin boundary condition. Likewise, a problem of melting a semi-infinite block that is initially below the melting temperature is considered. The Authors briefly describe how to apply the methods to the process of melting a finite block, and to the ablation of a finite media.

MSC:
80A22Stefan problems, phase changes, etc.
35K05Heat equation