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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
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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
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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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