On a multiple timescales perturbation approach for a stefan problem with a time-dependent heat flux at the boundary

A. F. Ihsan; W. T. van Horssen; J. M. Tuwankotta

doi:10.1007/s11071-022-07734-7

On a multiple timescales perturbation approach for a stefan problem with a time-dependent heat flux at the boundary

A. F. Ihsan, W. T. van Horssen, J. M. Tuwankotta^*

^*Corresponding author for this work

Mathematical Physics

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Abstract

In this paper, a classical Stefan problem is studied. It is assumed that a small, time-dependent heat influx is present at the boundary, and that the initial values are small. By using a multiple timescales perturbation approach, it is shown analytically (most likely for the first time in the literature) how the moving interface and its stability are influenced by the time-dependent heat influx at the boundary and by the initial conditions. Accurate approximations of the solution of the problem are constructed, which are valid on long timescales. The constructed approximations turn out to agree very well with solutions of problems for which similarity solutions are available (in numerical form).

Original language	English
Pages (from-to)	2673-2683
Number of pages	11
Journal	Nonlinear Dynamics
Volume	110
Issue number	3
DOIs	https://doi.org/10.1007/s11071-022-07734-7
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Multiple timescales
Stefan problem
Time-dependent heat flux

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abstract = "In this paper, a classical Stefan problem is studied. It is assumed that a small, time-dependent heat influx is present at the boundary, and that the initial values are small. By using a multiple timescales perturbation approach, it is shown analytically (most likely for the first time in the literature) how the moving interface and its stability are influenced by the time-dependent heat influx at the boundary and by the initial conditions. Accurate approximations of the solution of the problem are constructed, which are valid on long timescales. The constructed approximations turn out to agree very well with solutions of problems for which similarity solutions are available (in numerical form).",

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AB - In this paper, a classical Stefan problem is studied. It is assumed that a small, time-dependent heat influx is present at the boundary, and that the initial values are small. By using a multiple timescales perturbation approach, it is shown analytically (most likely for the first time in the literature) how the moving interface and its stability are influenced by the time-dependent heat influx at the boundary and by the initial conditions. Accurate approximations of the solution of the problem are constructed, which are valid on long timescales. The constructed approximations turn out to agree very well with solutions of problems for which similarity solutions are available (in numerical form).

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On a multiple timescales perturbation approach for a stefan problem with a time-dependent heat flux at the boundary

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Keywords

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