Mathematical Modeling and Analysis of Thermal Regimes in a Steel Shaft During Induction Heat Treatment
Abstract
A physical and mathematical model is formulated to determine the axial component of the magnetic field
intensity vector and the specific density of Joule heat in a non-ferromagnetic steel shaft during its induction
heat treatment under an unsteady electromagnetic field. The initial-boundary relationships for the
electrodynamic problem of the shaft are recorded. The axial component of the magnetic field intensity vector
is selected as the governing function. To find the solution, a cubic approximation with respect to the radial
coordinate for the distribution of the governing function along the radius of the shaft is applied. As a result,
the initial-boundary problem for the governing function is reduced to a Cauchy problem in time for the
integral characteristics of the governing function in terms of the radial variable. Using the Laplace integral
transform, expressions for the integral characteristics and the axial component of the magnetic field intensity
vector are derived. The expressions for the governing function and Joule heat in the shaft under induction
heating in a unsteady electromagnetic field are obtained. A numerical analysis is performed on the time
evolution and radial distribution of the axial component of the magnetic field intensity vector and Joule heat,
depending on the duration of the unsteady electromagnetic field.
References
Asai S. Electromagnetic Processing of Materials. Springer, Netherlands (2012). https://doi.org/10.1007/978-94-007-2645-1
Rudnev, V.; Loveless, D.; Cook, R. Handbook of Induction Heating; CRC Press: London, UK; Taylor and Francis Group: Abingdon, UK, 2018.
Bobart, G.F. Induction heating. AccessScience. 2020.
Areitioaurtena, M., Segurajauregi, U., Akujärvi, V. et al. A semi-analytical coupled simulation approach for induction heating. Adv. Model. and Simul. in Eng. Sci. 8, 14 (2021).
Gantsevich, S.; Gurevich, V. Joule heat release during current flow through a nanowire. Phys. Solid State 2016, 58, 1711-1715. https://doi.org/10.1134/S1063783416080126
Musii, R.; Pukach, P.; Kohut, I.; Vovk; M.; Šlahor, Ľ. Determination and Analysis of Joule's Heat and Temperature in an Electrically Conductive Plate Element Subject to Short-Term Induction Heating by a Non-Stationary Electromagnetic Field. Energies 2022, 15, 525 https://doi.org/10.3390/en15020525
Musii R., Pukach P., Melnyk N., Vovk M., Šlahor L. Modeling of the temperature regimes in a layered bimetallic plate under short-term induction heating // Energies. - 2023. - Vol. 16, iss. 13.
Musii R., Melnyk N., Drohomyretska K., Melnyk M. Investigation of the heating regimes of a steel strip by a quasi-steady electromagnetic field // Direct and inverse problems of electromagnetic and acoustic wave theory : proceedings of 2023 IEEE XXVIIIth International seminar/workshop DIPED-2023 (Tbilisi, September 11-13, 2023). - 2023. - C. 229-232. https://doi.org/10.5406/21601267.13.2.22
Copyright (c) 2024 Роман Мусій, Наталія Мельник, Богдан Бандирський, Інга Свідрак (Автор)
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