On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

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

doi:10.1016/j.nonrwa.2023.103961

On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

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 with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.

Original language	English
Article number	103961
Number of pages	18
Journal	Nonlinear Analysis: Real World Applications
Volume	75
DOIs	https://doi.org/10.1016/j.nonrwa.2023.103961
Publication status	Published - 2024

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 time-scales
Stefan problem
Time-dependent boundary temperature

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10.1016/j.nonrwa.2023.103961

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title = "On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition",

abstract = "In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.",

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AU - van Horssen, W. T.

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N1 - 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.

PY - 2024

Y1 - 2024

N2 - In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.

AB - In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.

KW - Multiple time-scales

KW - Stefan problem

KW - Time-dependent boundary temperature

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DO - 10.1016/j.nonrwa.2023.103961

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JO - Nonlinear Analysis: Real World Applications

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On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

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