Analysis and simulations of multifrequency induction hardening
Analysis of PDEs
2014-01-10 v1
Abstract
We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of {\sl 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.
Cite
@article{arxiv.1401.2013,
title = {Analysis and simulations of multifrequency induction hardening},
author = {D. Hoemberg and T. Petzold and E. Rocca},
journal= {arXiv preprint arXiv:1401.2013},
year = {2014}
}