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Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux

In: Integral Methods in Science and Engineering

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  • Otto G. Ruehr

Abstract

A solid, initially at the melting temperature, is heated by prescribing either the temperature or the heat flux at a fixed boundary; see [1]. Taking account of the heat of fusion, the position of a melting interface, X(t), is to be determined as well as the temperature in the liquid; we treat only one space dimension. We develop exact representations for the temperature as a functional of X(t). Integral or differential equations for the melting boundary, X(t), are then obtained. The integral equations facilitate solutions in special cases and the differential equations are used to calculate Taylor coefficients and, ultimately, numerical solutions for X(t). For the important special case of constant applied flux, the Maclaurin series for the melting boundary has zero radius of convergence; however, using continued fractions and other means of summability, we obtain very accurate results for all times with physical realizability.

Suggested Citation

  • Otto G. Ruehr, 2002. "Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux," Springer Books, in: Christian Constanda & Peter Schiavone & Andrew Mioduchowski (ed.), Integral Methods in Science and Engineering, chapter 34, pages 215-220, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0111-3_34
    DOI: 10.1007/978-1-4612-0111-3_34
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