https://doi.org/10.1140/epjs/s11734-024-01379-w
Regular Article
On the theory of non-stationary dendritic growth in a channel
Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000, Ekaterinburg, Russian Federation
Received:
10
September
2024
Accepted:
17
October
2024
Published online:
4
November
2024
The paper is concerned with the analytical solution to the problem of heat transfer around a non-stationary growing dendritic crystal in a channel. This problem is solved in the form of boundary integral equation governing such a growth mode of a dendrite. A new boundary integral equation is derived using the Green’s function technique and analyzed for the cases of a flat solid–liquid interface and stationary solidification. The boundary integral equation is used to select a stable mode of growth velocity for the parabolic dendrite. This technique allows me to obtain the dendrite tip diameter as a function of melt undercooling only. The prospects for the development of the theory of the boundary integral and its use are also discussed in the paper.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
