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

Journal article (2022)

Authors

A.F. Ihsan Institute of Technology Bandung
W. T. van Horssen Mathematical Physics
J.M. Tuwankotta Institute of Technology Bandung, Mathematical Physics
Research Group
Mathematical Physics
Copyright: © 2022 A. F. Ihsan, W.T. van Horssen, J.M. Tuwankotta
DOI: https://doi.org/10.1007/s11071-022-07734-7
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Published Date

2022

Language

English

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Research Group

Mathematical Physics

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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