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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

Author

Listed:
  • Roman Musii

    (Department of Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine)

  • Petro Pukach

    (Department of Computational Mathematics and Programming, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine)

  • Ihor Kohut

    (Department of Computational Mathematics and Programming, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine)

  • Myroslava Vovk

    (Department of Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 79013 Lviv, Ukraine)

  • Ľudomír Šlahor

    (Faculty of Management, Comenius University Bratislava, 82005 Bratislava, Slovakia)

Abstract

We propose a mathematical model that allows us to determine the temperature field of a parallel-sided electrically conductive plate element subject to uniform non-stationary electromagnetic action. We formulate initial-boundary value problems to determine the parameters of the non-stationary electromagnetic field (NEMF) and the temperature. We develop a methodology to solve these initial-boundary value problems using the approximation of determining functions by cubic polynomials over thickness of the plate element. General solutions for the related Cauchy problems at uniform non-stationary electromagnetic action are obtained. Based on these solutions, the temporal variation of Joule’s heat and temperature in the plate element, subject to short-term induction heating by an NEMF in the mode of impulse modulating signal (MIMS), is analyzed. Temperature dependencies on the different values of electromagnetic field stress and on the different time duration were obtained. The choice of the carrier frequency of electromagnetic field oscillations is explained for the frequencies mostly used in industrial devices for inductive heating.

Suggested Citation

  • Roman Musii & Petro Pukach & Ihor Kohut & Myroslava Vovk & Ľudomír Šlahor, 2022. "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, MDPI, vol. 15(14), pages 1-11, July.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:14:p:5250-:d:866997
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    Citations

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    Cited by:

    1. Huabin Song & Youhua Wang & Jiangpai Peng & Chengcheng Liu, 2022. "Study on the Uniformity of Temperature Distribution of Transverse Flux Induction Heating Based on a New Magnetic Pole," Energies, MDPI, vol. 15(19), pages 1-15, October.
    2. Stanisław Ledakowicz & Olexa Piddubniak, 2023. "Temperature Distribution in a Finite-Length Cylindrical Channel Filled with Biomass Transported by Electrically Heated Auger," Energies, MDPI, vol. 16(17), pages 1-23, August.
    3. Roman Musii & Petro Pukach & Nataliia Melnyk & Myroslava Vovk & L’udomír Šlahor, 2023. "Modeling of the Temperature Regimes in a Layered Bimetallic Plate under Short-Term Induction Heating," Energies, MDPI, vol. 16(13), pages 1-12, June.
    4. Roman Musii & Marek Lis & Petro Pukach & Andriy Chaban & Andrzej Szafraniec & Myroslava Vovk & Nataliia Melnyk, 2024. "Analysis of Varying Temperature Regimes in a Conductive Strip during Induction Heating under a Quasi-Steady Electromagnetic Field," Energies, MDPI, vol. 17(2), pages 1-17, January.

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