On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition
A. F. Ihsan (Institut Teknologi Bandung, TU Delft - Electrical Engineering, Mathematics and Computer Science)
W. T. van Horssen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J. M. Tuwankotta (TU Delft - Electrical Engineering, Mathematics and Computer Science, Institut Teknologi Bandung)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.