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Title: Approximate analytical solution for induction heating of solid cylinders

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and for the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.
Authors:
ORCiD logo [1] ; ORCiD logo [1] ;  [1] ;  [1] ;  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
1225114
Report Number(s):
LA-UR-14-26455
Journal ID: ISSN 0307-904X
Grant/Contract Number:
AC52-06NA25396
Type:
Published Article
Journal Name:
Applied Mathematical Modelling
Additional Journal Information:
Journal Volume: 40; Journal Issue: 4; Journal ID: ISSN 0307-904X
Publisher:
Elsevier
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Induction heating; Coupled multiphysics; Perturbation methods; Load signature analysis