https://doi.org/10.1140/epjs/s11734-023-00851-3
Regular Article
The thermal field around a parabolic dendrite growing in inclined melt flow
1
Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
2
Laboratory of Multi-Scale Mathematical Modeling, Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
Received:
11
March
2023
Accepted:
25
April
2023
Published online:
17
May
2023
The solution to the boundary integral equation defining undercooling at the surface of a parabolic dendrite growing in an inclined melt flow is obtained. The temperature gradient with respect to dendrite’s normal direction and the isotherms in liquid around the dendritic tip are analytically found. We show that the undercooling at dendritic surface responsible for its growth rate can change about 5–7
in the presence of small flow slope. In addition, we show that the isotherms shift towards the incoming melt flow. This theoretically confirms favourable conditions for the growth of secondary patterns in the direction of liquid flow.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
