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.
|Titolo:||Analysis and simulations of multifrequency induction hardening|
ROCCA, ELISABETTA (Ultimo)
|Parole Chiave:||finite element simulations; heat equation; Maxwell's equations; multifrequency induction hardening; stability estimates; well-posedness of the initial boundary value problem; analysis; applied mathematics; computational mathematics; engineering (all); medicine (all); economics, econometrics and finance (all)2001 economics, econometrics and finance (miscellaneous)|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2015|
|Digital Object Identifier (DOI):||10.1016/j.nonrwa.2014.07.007|
|Appare nelle tipologie:||01 - Articolo su periodico|