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- 10.1007/s11071-022-07734-7
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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).
Journal
Nonlinear Dynamics – Springer Journals
Published: Nov 1, 2022
Keywords: Multiple timescales; Stefan problem; Time-dependent heat flux; 35K55; 35R37; 35C20; 80A22; 35B20