Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

Matthew G. Hennessy*, Tim G. Myers

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Abstract

Thermoreflectance experiments involve heating the surface of a solid using a high-frequency laser. The small length and time-scales associated with this rapid heating lead to the onset of heat conduction mechanisms that cannot be captured using Fourier’s law. We propose a model for thermoreflectance experiments based on the Guyer–Krumhansl equation of heat conduction. We show that heat conduction occurs in the form of two distinct modes that are analogous to pressure and shear waves in linear viscoelastic materials. We present analytical solutions to the model that can be used to calculate the three-dimensional temperature and flux profiles in the heated solid as well as the phase difference between the laser and the surface temperature oscillations. Using the Laplace transform, we show how the solution can be extended to account for laser pulses with an arbitrary dependence on time.

Original languageEnglish
Title of host publicationSEMA SIMAI Springer Series
PublisherSpringer Science and Business Media Deutschland GmbH
Pages21-34
Number of pages14
DOIs
Publication statusPublished - 2021

Publication series

NameSEMA SIMAI Springer Series
Volume11
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

Bibliographical note

Funding Information:
This project has received funding from the European Union?s Horizon 2020 research and innovation programme under grant agreement no. 707658. MC acknowledges that the research leading to these results has received funding from ?la Caixa? Foundation. TM acknowledges financial support from the Ministerio de Ciencia e Innovaci?n grant MTM2017-82317-P. The authors have been partially funded by the CERCA Programme of the Generalitat de Catalunya.

Funding Information:
Acknowledgments This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 707658. MC acknowledges that the research leading to these results has received funding from ‘la Caixa’ Foundation. TM acknowledges financial support from the Ministerio de Ciencia e Innovación grant MTM2017-82317-P. The authors have been partially funded by the CERCA Programme of the Generalitat de Catalunya.

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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