Vol. 14, No. 2, 2019

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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

Vol. 14 (2019), No. 2, 175–205
Abstract

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 A-ϕ 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 A-ϕ finite element method and show some numerical simulation results.

Keywords
induction hardening, nonlinear eddy current equations, potential field formulation, solvability, Rothe's method
Mathematical Subject Classification 2010
Primary: 35Q60, 35Q61
Milestones
Received: 9 August 2018
Revised: 22 April 2019
Accepted: 17 May 2019
Published: 4 October 2019
Authors
Tong Kang
Department of Applied Mathematics
School of Sciences
Communication University of China
Beijing
China
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