ORIGINAL PAPER
Eddy current loss behavior of hollow circular cylinder due to time varying electro-magnetic field
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1
Mathematics, Department of Mathematics, RTM Nagpur University, India
2
Mathematics, J.M.Patel Arts, Commerce & Science College, Bhandara-441904, Maharashtra, India, India
Submission date: 2024-08-02
Final revision date: 2024-09-13
Acceptance date: 2024-12-30
Online publication date: 2025-03-06
Publication date: 2025-03-06
Corresponding author
G. D. Kedar
Mathematics, Department of Mathematics, RTM Nagpur University, Wadi Road, Nagpur, 440033, Nagpur, India
International Journal of Applied Mechanics and Engineering 2025;30(1):1-20
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ABSTRACT
The purpose of this study is to investigate the effects of a time-varying electromagnetic field on the quasi-static thermoelastic behavior of a finitely conducting hollow circular cylinder. As a consequence of a time-varying electromagnetic field, conducting currents, also known as eddy currents, are induced inside the cylinder. We treat the Joule heat that the induced eddy currents generate due to resistive heating as a thermal loading of the cylinder. The cylinder thickness is considered negligible in comparison to the magnetic field's penetration depth, and the problem is considered one-dimensional. The convection-type boundary conditions are applied across the curved surface of the cylinder. The intensity of Joule heat in terms of current density and eddy current loss is obtained in quasi-static form using integral transform techniques, which include the finite Hankel transform, the Marchi Zgrablich transform, and the Laplace transform. The quasi-static solutions of thermal stresses, displacement, non-dimensional temperature, eddy current loss, and magnetic field fluctuations are obtained in terms of electrical conductivity, magnetic permeability, frequency, and magnetic intensity of the electromagnetic field applied and are illustrated graphically using MATLAB software.
REFERENCES (35)
1.
Paria G. (1967): Magneto-elasticity and magneto-thermo-elasticity.– Advances in Applied Mechanics, vol.10, pp.73-112.
2.
Zhou Y.H. and Zheng X.J. (1999): Electromagnetic solid structural mechanics.– Science Press, Peking.
3.
Bai X.Z. (2006): Magnetic Base Plate and Shell Elasticity.– Science Press, Peking.
4.
Wang X. (1995): Thermal shock in a hollow cylinder caused by rapid arbitrary heating.– Journal of Sound Vibrations,vol.18, pp.899-906.
5.
Xing Y. and Liu B. (2010): A differential quadrature analysis of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field.– International Journal of Engineering Science, vol.48, pp.1944-1960.
https://doi.org/10.1016/j.ijen....
6.
Higuchi M., Kawamura R. and Tanigawa Y. (2007): Magneto-thermo-elastic stresses induced by a transient magnetic field in a conducting solid circular cylinder.– International Journal of Solids and Structures, vol.44, No.16, pp.5316-5335.
7.
Higuchi M., Kawamura R. and Tanigawa Y. (2008): Dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field.– International Journal of Mechanical Sciences, vol.50, No.3, pp.365-379,
https://doi.org/10.1016/j.ijme....
8.
Moon F.C. and Chattopadhyay S. (1974): Magnetically induced stress waves in a conducting solid-theory and experiment.– Journal of Applied Mechanics, Transactions ASME, vol.41, pp.641-646.
9.
Chian C.T. and Moon F.C. (1981): Magnetically induced cylindrical stress waves in a thermoelastic conductor.– International Journal of Solids and Structures, vol.17, pp.1021-1035.
10.
Wauer J. (1995): Parametric vibrations in a magneto-thermo-elastic layer of finite thickness.– In Proceedings of the 1995 Design Engineering Technical Conferences, vol.3A. New York, ASME, p.407-414.
11.
Pantelyat M.G. and Fe´liachi M. (2002): Magneto-thermo-elastic-plastic simulation of inductive heating of metals.– The European Physical Journal Applied Physics, vol.17, No.1, pp.29-33.
12.
Sinha G. and Prabhu S.S. (2011): Analytical model for estimation of eddy current and power loss in conducting plate and its application.– Phys, Rev, Accel, Beams, vol.14, p.062401.
13.
Cen S. and Xu J. (2018): Analysis of thermo-magneto elastic nonlinear dynamic response of shallow conical shells.– Engineering, vol.10, pp.837-850.
14.
Plotnikov S.M. (2021): Determination of eddy-current and hysteresis losses in the magnetic circuits of electrical machines.– Measurement Techniques, vol.63, pp.904-909, DOI:10.1007/s11018-021-01866-9.
15.
Ekergård B. and Leijon M. (2021): Eddy current losses in solid pole shoes in a two-pole permanent magnet motor.– Engineering, vol.13, pp.536-543, DOI: 10.4236/eng.2021.1310038.
16.
Wang J.Q., Wang K. and Sun J.R. (2020): Numerical calculation and test of eddy current loss of magnetic coupling.– J. Journal of Drainage and Irrigation Machinery Engineering, vol.38, No.03, pp.230-235.
17.
Golebiowski M. (2017): Calculation of eddy current and hysteresis losses during transient states in laminated magnetic circuits.– COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol.36, No.3, pp.665-682,
https://doi.org/10.1108/COMPEL....
18.
Kumar N. and Kamdi D.B. (2020): Thermal behavior of a finite hollow cylinder in the context of fractional thermoelasticity with convection boundary conditions.– J. Therm. Stress, vol.43, pp.1189-1204.
19.
Lamba N. (2023): Impact of the memory-dependent response of a thermoelastic thick solid cylinder.– Journal of Applied and Computational Mechanics, vol.9, No.4, pp.1135-1143, DOI: 10.22055/jacm.2023.43952.4149.
20.
Srinivas V.B., Manthena V.R., Warbhe S.D., Kedar G.D. and Lamba N.K. (2024): Thermal stresses associated with a thermosensitive multilayered disc analyzed due to point heating.– International Journal of Applied Mechanics and Engineering, vol.29, No.2, pp.118-137, doi:10.59441/ijame/187051.
21.
Biswas S. (2019): Eigenvalue approach to a magneto-thermoelastic problem in the transversely isotropic hollow cylinder: comparison of three theories.– Waves in Random and Complex Media,
https://doi.org/10.1080/174550....
22.
Gao Y., Li K., Wang Y. and He Y. (2016): Eddy current pulsed thermography with different excitation configurations for metallic material and defect characterization.– Sensors, vol.16, pp.843, doi:10.3390/s16060843.
23.
Li X., Liu Z., Jiang X., and Lodewijks G. (2016): Method for detecting damage in carbon-fibre reinforced plastic-steel structures based on eddy current pulsed thermography.– Nondestructive Testing and Evaluation, vol.33, No.1, pp.1-19, doi:10.1080/10589759.2016.1254213.
24.
Lotfy Kh., El-Bary A. and Tantawi R.S. (2019): Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory.– The European Physical Journal Plus, vol.134, doi:10.1140/epjp/i2019-12631-1.
25.
Abo-Dahab S.M. and Lotfy Kh. (2015): Generalized magneto-thermoelasticity with fractional derivative heat transfer for a rotation of a fibre-reinforced thermoelastic.– Journal of Computational and Theoretical Nanoscience, doi:12. 10.1166/jctn.2015.3972.
26.
Lotfy Kh. (2012): Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem.– Chinese Physics B, vol.21, p.014209, doi:10.1088/1674-1056/21/1/014209.
27.
Lotfy Kh. and Tantawi R.S. (2020): Photo-thermal-elastic interaction in a functionally graded material (FGM) and magnetic field.– Silicon, vol.12, doi:10.1007/s12633-019-00125-5.
28.
Abo-Dahab S.M., Lotfy Kh. and Gohaly A. (2015): Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary.– Mathematical Problems in Engineering, pp.1-15, doi:10.1155/2015/671783.
29.
Marchi E. and Zgrablich G. (1964): Vibration in a hollow circular membrane with elastic support.– Bull. Calcutta Math. Soc., vol.22, No.1, pp.73-76.
30.
Garg M., Rao A. and Kalla S.L. (2007): On a generalized finite Hankel transform.– Applied Mathematics and Computation, vol.190, pp.705-711, doi:10.1016/j.amc.2007.01.076.
31.
Sneddon I.N. (1993): The Use of Integral Transforms.– McGraw-Hill, New York.
32.
Debnath L. and Bhatta D. (2007): Integral Transforms and Their Applications.– second ed., Chapman and Hall/CRC Press, Boca Raton, FL.
33.
Sneddon I.N. (1946): III. Finite Hankel transforms.– The London, Edinburgh and Dublin, Philosophical Magazine and Journal of Science: Series 7, vol.37, No.264, pp.17-25, DOI: 10.1080/14786444608521150.
34.
Das P., Kar A. and Kanoria M. (2013): Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect.– Journal of Thermal Stresses, vol.36, No.3, pp.239-258, DOI:10.1080/01495739.2013.765180.
35.
Milošević M.V. (2003): Temperature and stress fields in thin metallic partially fixed plate induced by harmonic electromagnetic wave.– FME Transactions, vol.31, pp.49-54.