Journal of Engineering Mathematics

, Volume 114, Issue 1, pp 65–86 | Cite as

Electromagnetic heating control via high-frequencyresonance of a triple-layer laminate

  • J. M. Gaone
  • B. S. TilleyEmail author
  • V. V. Yakovlev


Beamed energy transport requires the use of heat exchangers to collect the thermal energy produced from the absorption of electromagnetic radiation. To explore the high-frequency effects of wave–geometry interactions on this heat transfer, we consider a central dielectric layer, possessing a temperature-dependent loss factor, surrounded by two fluid channels filled with a lossless dielectric fluid. Considering an asymptotically thin domain, we derive a diffusion–reaction equation, assuming no flow in the fluid. We show that the high-frequency effects generate a new energy balance leading to a previously unknown steady-state solution. A characterization of the steady-state-dependent parameters is performed in an effort to determine a mechanism to control the nonlinear heating. Diffusive effects are shown to produce regions of the power response where steady-state solutions are replaced by traveling-wave solutions. These regions are also location to the greatest heating efficiency. Analytical approximations to the wave speed and location of these regions are found using boundary layer theory.


Microwave heating Photonic crystal Thermal runaway 



The authors are grateful for the support from the Air Force Office of Scientific Research; Award FA9550-15-0476 and the National Science Foundation MRI Grant DMS-1337943 for high performance computing. This work was funded by AFOSR Award FA9550-15-0476 and NSF MRI Grant DMS-1337943 for high performance computing.

Supplementary material


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center for Industrial Mathematics and Statistics, Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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