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Potential field
formulation based on decomposition of the electric field for
a nonlinear induction hardening model
Tong Kang, Ran Wang and Huai Zhang |
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Vol. 14 (2019), No. 2, 175–205
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Abstract |
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In this paper we investigate a mathematical model of induction heating including eddy current equations coupled with a nonlinear heat equation. A nonlinear law between the magnetic field and the magnetic induction field in the workpiece is assumed. Meanwhile the electric conductivity is temperature dependent. We present a potential field formulation (the - method) based on decomposition of the electric field for the electromagnetic part. Using the theory of monotone operator and Rothe’s method, we prove the existence of a weak solution to the coupled nonlinear system in the conducting domain. Finally, we solve it by means of the - finite element method and show some numerical simulation results. |
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Keywords
induction hardening, nonlinear eddy current equations,
potential field formulation, solvability, Rothe's method
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Mathematical Subject Classification 2010
Primary: 35Q60, 35Q61
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Milestones
Received: 9 August 2018
Revised: 22 April 2019
Accepted: 17 May 2019
Published: 4 October 2019
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Authors |
| Tong Kang | |
| Department of Applied
Mathematics School of Sciences Communication University of China Beijing China |
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| Ran Wang | |
| Department of Applied
Mathematics School of Sciences Communication University of China Beijing China |
Key Laboratory of Computational
Geodynamics University of Chinese Academy of Sciences Beijing China |
| Huai Zhang | |
| Key Laboratory of Computational
Geodynamics University of Chinese Academy of Sciences Beijing China |
Laboratory for Marine Mineral
Resources Qingdao National Laboratory for Marine Science and Technology Qingdao China |
