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On the convergence of the heat balance integral method. (English) Zbl 1151.80329
The authors apply the well-known Godmann’s approximate heat-balance method to the single-phase semi-infinite ice slab, whose exact solution is well-known and represents a special case of the Neumann general solution. The distance from the beginning of the slab \((x= 0)\) to the moving melt front \((x= s)\) is subdivided into \(n\) equal cells and the temperature is approximated at each node by a linear temperature profile. The further calculation is performed by the Godmann method. The authors demonstrated that the approximate solution obtained in such a way, is in good agreement with the exact solution. The study of the convergence of the approximate solution is accomplished in details.

MSC:
80M25 Other numerical methods (thermodynamics) (MSC2010)
80A22 Stefan problems, phase changes, etc.
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