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 multiplescale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closedform 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:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1426455
Journal ID: ISSN 0307904X
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Published Article
 Journal Name:
 Applied Mathematical Modelling
 Additional Journal Information:
 Journal Volume: 40; Journal Issue: 4; Journal ID: ISSN 0307904X
 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
 OSTI Identifier:
 1225114
 Alternate Identifier(s):
 OSTI ID: 1398906
Jankowski, Todd Andrew, Pawley, Norma Helen, Gonzales, Lindsey Michal, Ross, Craig A., and Jurney, James D.. Approximate analytical solution for induction heating of solid cylinders. United States: N. p.,
Web. doi:10.1016/j.apm.2015.10.006.
Jankowski, Todd Andrew, Pawley, Norma Helen, Gonzales, Lindsey Michal, Ross, Craig A., & Jurney, James D.. Approximate analytical solution for induction heating of solid cylinders. United States. doi:10.1016/j.apm.2015.10.006.
Jankowski, Todd Andrew, Pawley, Norma Helen, Gonzales, Lindsey Michal, Ross, Craig A., and Jurney, James D.. 2015.
"Approximate analytical solution for induction heating of solid cylinders". United States.
doi:10.1016/j.apm.2015.10.006.
@article{osti_1225114,
title = {Approximate analytical solution for induction heating of solid cylinders},
author = {Jankowski, Todd Andrew and Pawley, Norma Helen and Gonzales, Lindsey Michal and Ross, Craig A. and Jurney, James D.},
abstractNote = {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 multiplescale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closedform 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.},
doi = {10.1016/j.apm.2015.10.006},
journal = {Applied Mathematical Modelling},
number = 4,
volume = 40,
place = {United States},
year = {2015},
month = {10}
}