Article (Scientific journals)
A–ϕ formulation of a mathematical model for the induction hardening process with a nonlinear law for the magnetic field
Chovan, Jaroslav; Geuzaine, Christophe; Slodička, Marian
2017In Computer Methods in Applied Mechanics and Engineering, 321, p. 294-315
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Keywords :
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 [BE]
Available on ORBi :
since 22 April 2021

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