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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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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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Funding

A.F. Ihsan’s research is supported by ITB post-graduate voucher scholarship. J.M Tuwankotta’s research is supported by Riset P2MI FMIPA ITB 2021.

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Authors and Affiliations

  1. Analysis and Geometry, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia

    A. F. Ihsan & J. M. Tuwankotta

  2. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    W. T. van Horssen

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  1. A. F. Ihsan
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  2. W. T. van Horssen
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  3. J. M. Tuwankotta
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All authors contributed to the study and the preparation of this paper. All authors read and approved the final manuscript.

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Correspondence to J. M. Tuwankotta.

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Ihsan, A.F., van Horssen, W.T. & Tuwankotta, J.M. On a multiple timescales perturbation approach for a stefan problem with a time-dependent heat flux at the boundary. Nonlinear Dyn 110, 2673–2683 (2022). https://doi.org/10.1007/s11071-022-07734-7

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