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Solution to the 1D Stefan problem using the unified transform method

Dozoka, Toni ; Plümacher, Dominik ; Smuda, Martin ; Jegust, Christian ; Oberlack, Martin (2021):
Solution to the 1D Stefan problem using the unified transform method. (Publisher's Version)
In: Journal of Physics A: Mathematical and Theoretical, 54 (37), IOP Publishing, ISSN 1751-8113, e-ISSN 1751-8121,
DOI: 10.26083/tuprints-00019502,

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Status: Publisher's Version
Title: Solution to the 1D Stefan problem using the unified transform method
Language: English

In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing the heat distribution in each phase. For this the unified transform method has been employed which provides a method via a global relation, by which these problems can be solved using integral representations. To do this, the underlying partial differential equation is rewritten into a certain divergence form, which enables to treat the boundary values as part of the integrals. Classical analytical methods fail in the case of the Stefan problem due to the moving interface. From the resulting non-linear integro-differential equations the one for the position of the phase change can be solved in a first step. This is done numerically using a fix-point iteration and spline interpolation. Once obtained, the temperature distribution in both phases is generated from their integral representation.

Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Volume of the journal: 54
Issue Number: 37
Publisher: IOP Publishing
Collation: 22 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Date Deposited: 10 Sep 2021 12:24
Last Modified: 01 Oct 2021 07:01
DOI: 10.26083/tuprints-00019502
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-195026
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19502
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