Analysis of Varying Temperature Regimes in a Conductive Strip during Induction Heating under a Quasi-Steady Electromagnetic Field

Roman Musii, Marek Lis, Petro Pukach, Andriy Chaban, Andrzej Szafraniec, Myroslava Vovk () and Nataliia Melnyk
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Roman Musii: Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine
Marek Lis: Faculty of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland
Petro Pukach: Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine
Andriy Chaban: Faculty of Transport, Electrical Engineering, and Computer Science, University of Radom, 26-600 Radom, Poland
Andrzej Szafraniec: Faculty of Transport, Electrical Engineering, and Computer Science, University of Radom, 26-600 Radom, Poland
Myroslava Vovk: Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine
Nataliia Melnyk: Institute of Computer Sciences and Information Technologies, Lviv Polytechnic National University, 79013 Lviv, Ukraine

Energies, 2024, vol. 17, issue 2, 1-17

Abstract: Transition processes in a steel conductive strip are analyzed during its induction heating under a quasi-steady electromagnetic field. In particular, the temperature field in the strip is studied. A method of solving corresponding initial boundary problems in a two-dimensional mathematical model for differential equations of electrodynamics and heat conduction is developed. The Joule heat and the temperature are determined with a high level of accuracy. The defining functions are the temperature and component of the magnetic field intensity vector tangent to the bases and end planes of the strip. To find them, we use cubic approximation of the defining functions’ distribution along the thickness coordinate. The original two-dimensional initial boundary value problems for the defining functions are reduced to one-dimensional initial boundary value problems on their integral characteristics. General solutions for these problems are obtained using the finite integral transformation by the transverse variable and the Laplace transform of the integral by time. Integral characteristics’ expressions are represented as convolutions for functions that describe homogeneous solutions of one-dimensional initial boundary value problems and limiting values of defining functions on the bases and end planes of the strip. The change of temperature under a varying regime in the dimensionless Fourier time and temperature distribution over the strip cross-section in a steady state depending on the parameters of induction heating and the Biot number are numerically analyzed. Varying and constant temperature regimes of the strip under conditions of the near-surface and continuous induction heating are studied.

Keywords: quasi-steady electromagnetic field; electro-conductive strip; induction heating; varying temperature regime (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
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