https://doi.org/10.1140/epjs/s11734-022-00521-w
Regular Article
Exact analytical solutions of a steady-state mushy layer model containing heat exchange with the environment
1
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
2
Nosov Magnitogorsk State Technical University, Lenin st. 38, 455000, Magnitogorsk, Russian Federation
Received:
17
July
2021
Accepted:
3
March
2022
Published online:
10
March
2022
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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
