Summary
An exact parametric solution for the planar solidification of a liquid metal occupying the infinite half-space is presented. The metal is assumed to exhibit nonlinear thermal characteristics of the Storm type. Both the idealized one phase and the full two phase problems are considered. For both problems an approximate analysis of the underlying coupled transcendental equations is presented which provides initial estimates for use in a numerical scheme. Typical numerical results are given which illustrate the monotonic nature of the solution.
Zusammenfassung
Eine genaue Lösung für die ebene Solidifizierung eines flüssigen Metalls, das in einem unendlichen Halbraum liegt, wird dargestellt. Es wird angenommen, daß das Metall nonlineare thermale Elgenschaften der Stormschen Art aufweist. Das idealisierte Einphasen-Problem wie auch das voile Zweiphasen-Problem werden betrachtet. Für beide Probleme wird eine ungefähre Analyse der zugrundeliegenden gekuppelten transzendentalen Gleichungen gegeben, die Anfangswerte zur Verwendung in einer numerischen Darstellung liefert. Es werden typische Zahlenwerte gegeben, die die Monotonie der Lösung illustrieren.
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Hill, J.M., Hart, V.G. The Stefan problem in nonlinear heat conduction. Z. angew. Math. Phys. 37, 206–229 (1986). https://doi.org/10.1007/BF00945083
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DOI: https://doi.org/10.1007/BF00945083