A–ϕ formulation of a mathematical model for the induction hardening process with a nonlinear law for the magnetic field

Maxwell's equations; Minty–Browder; Monotone operators; Rothe's method; Scalar potential; Vector potential; Induction heating; Magnetic fields; Magnetism; Maxwell equations; Magnetic induction field; Mathematical analysis; Nonlinear relations; Temperature dependent; Hardening

Abstract :

[en] We derive and analyze a mathematical model for induction hardening. We assume a nonlinear relation between the magnetic field and the magnetic induction field. For the electromagnetic part, we use the vector–scalar potential formulation. The coupling between the electromagnetic and the thermal part is provided through the temperature-dependent electric conductivity and the joule heating term, the most crucial element, considering the mathematical analysis of the model. It acts as a source of heat in the thermal part and leads to the increase in temperature. Therefore, in order to be able to control it, we apply a truncation function. Using Rothe's method, we prove the existence of a global solution to the whole system. The nonlinearity in the electromagnetic part is handled by the theory of monotone operators. To supplement our theoretical results we provide a numerical simulation using real physical constants. © 2017 Elsevier B.V.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Chovan, Jaroslav; Department of Mathematical Analysis, Ghent University, Ghent, Belgium

Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)

Slodička, Marian; Department of Mathematical Analysis, Ghent University, Ghent, Belgium

Language :

English

Title :

A–ϕ formulation of a mathematical model for the induction hardening process with a nonlinear law for the magnetic field

Publication date :

2017

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier B.V.

Volume :

321

Pages :

294-315

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

UGent - Universiteit Gent

Available on ORBi :

since 22 April 2021

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Bibliography

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