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Exact analytical solutions of a steady-state mushy layer model containing heat exchange with the environment

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Abstract

A set of nonlinear equations describing the crystallization of a binary melt in the presence of a quasi-equilibrium mushy layer is analytically solved in the case of heat exchange with the environment. Solute concentration, temperature distributions, and a bulk fraction of the solid phase in a mushy region are found. In addition, the average interdendritic distance in the two-phase region, which characterizes the structural-phase transition and porosity of the material, was analytically determined. The mushy layer’s thickness was also found as a function of given the physical and operating parameters of the solidification process. The analytical solutions obtained are compared with experimental data.

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Acknowledgements

This work is supported by the Russian Science Foundation [project no. 21-19-00279].

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Authors and Affiliations

  1. Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin ave., 51, Ekaterinburg, 620000, Russian Federation

    Irina V. Alexandrova, Alexander A. Ivanov, Svetlana V. Bulycheva & Dmitri V. Alexandrov

  2. Nosov Magnitogorsk State Technical University, Lenin st. 38, Magnitogorsk, 455000, Russian Federation

    Svetlana V. Bulycheva

Authors
  1. Irina V. Alexandrova
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  2. Alexander A. Ivanov
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  3. Svetlana V. Bulycheva
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  4. Dmitri V. Alexandrov
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Correspondence to Irina V. Alexandrova.

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Alexandrova, I.V., Ivanov, A.A., Bulycheva, S.V. et al. Exact analytical solutions of a steady-state mushy layer model containing heat exchange with the environment. Eur. Phys. J. Spec. Top. 231, 1123–1128 (2022). https://doi.org/10.1140/epjs/s11734-022-00521-w

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