Analysis and simulations of multifrequency induction hardening

被引：22

作者：

Hoemberg, Dietmar ^{[1
]}

Petzold, Thomas ^{[1
]}

Rocca, Elisabetta ^{[1
,2
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[2] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 22卷

基金：

欧洲研究理事会;

关键词：

Multifrequency induction hardening; Heat equation; Maxwell's equations; Well-posedness of the initial boundary value problem; Stability estimates; Finite element simulations; MODEL;

D O I：

10.1016/j.nonrwa.2014.07.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：84 / 97

页数：14

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