To evaluate the impact of the important non-uniformity technological factor of the external electric current distribution on the low-temperature heating parameters of flat ferrite elements, taking into account the stressed state (strength characteristics), a model problem is considered to determine and study the thermomechanical behavior of the ferrite layer under the influence of a quasi-steady electromagnetic field created by the current flowing in the current-carrying plane, the density of which changes sinusoidally along the longitudinal coordinate. In accordance with the earlier results regarding the dependence of the heating process on the frequency of external electromagnetic influence, it is accepted that the circular carrier frequency of the electromagnetic field is outside the vicinity of the resonant ones (when the thermally stressed state has an almost quasi-static character). In this case, the calculation scheme consists of three stages for sequentially determining the parameters that describe the electromagnetic, temperature, and mechanical fields.
- Lucia O., Maussion P., Dede E., Burdio J. M. Induction heating technology and its applications: past developments, current technology, and future challenges. IEEE Trans. on Industrial Electronics. 61, 2509 (2013).
- Rudnev V., Loveless D., Cook R. L. Handbook of Induction Heating. CRC Press (2017).
- Rapoport E., Pleshivtseva Y. Optimal Control of Induction Heating Processes. CRC Press (2006).
- Hachkevych O. R., Ivas'ko R. O. Thermomechanics of ferrite solids in a quasi-steady electromagnetic field. Mat. Met. Fiz.-Mekh. Polya. 43, 161 (2000), (in Ukrainian).
- Hachkevych O. R., Ivas'ko R. O. Thermoelastic state of a ferritic layer in a quasistationary electromagnetic field. Materials Science. 41, 376 (2005).
- Hachkevych O. R., Ivas'ko R. O., Kasperski Z. Methodology for studying temperature fields and stresses in ferrite solids exposed to low electromagnetic fields of high frequency. Visn. Donets. un-tu. Ser. A. Pryrodnychi nauky. 1, 91 (2006).
- Hachkevych O. R., Ivas'ko R. O., Solodyak M. T., Szymura S. Methodology for predicting the thermomechanical behaviour of ferrite elements in electromagnetic devices while ensuring their functional properties. Tieor. i prikl. miekhanika. 43, 28 (2007).
- Hachkevych O., Ivas'ko R., Solodyak M., Szymura S. Modelling the thermally stressed state of ferrite solids exposed to low electromagnetic fields of high frequency. Mechanical Engineering. 5, 9 (2009), (in Ukrainian).
- Hachkevych O., Ivas'ko R., Stanik-Besler A. Selected Mathematical Problems of Thermomechanics of Ferrite Solids. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine (2022).
- Bronsztejn I. N., Siemiendiajew K. A., Musiol G., Muhlig H. Modern Compendium of Mathematics. PWN (2022), (in Polish).
- Korn G. A., Korn T. M. Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. Courier Corporation (2013).
- Hachkevych O. R. Thermomechanics of Electrically Conducting Solids Exposed to Quasi-Steady Electromagnetic Fields. Naukova dumka (1992).
- Hachkevych O., Kasperski Z. Mathematical Models and Methods in Boundary Problems of Thermomechanics of Conducting Solids. OWPO (1999), (in Polish).
- Materials in Instrumentation and Automation: Reference Book. Ed. by Yu. M. Piatin. Mashynostroieniie (1982).
- Sidorov I. N., Khristinin A. A., Skorniakov S. V. Small-Sized Magnetic Circuits and Cores. Reference Book. Radio i sviaz' (1989).
- Tables of Physical Quantities: Reference Book. Ed. by I. K. Kikoin. Atomizdat (1976).
- Ferrites and magnetodielectrics: Reference Book. Ed. by N. D. Gorbunov, G. A. Matvieiev. Sov. radio (1968).
- Von Hippel Arthur R. Dielectrics and Waves. Artech House (1995).
- Kuz'michov V. Ye. Laws and formulas of physics. Reference Book. Naukova dumka (1989).
- Pchel'nikov Yu. N., Sviridov V. T. Microwave Electronics. Radio i sviaz' (1981).