Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

Matthew G. Hennessy; Tim G. Myers

doi:10.1007/978-3-030-64272-3_2

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 proceeding › Chapter in a book

2 Citations (Scopus)

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 language	English
Title of host publication	SEMA SIMAI Springer Series
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	21-34
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-030-64272-3_2
Publication status	Published - 2021

Publication series

Name	SEMA SIMAI Springer Series
Volume	11
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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title = "Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments",

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{\textquoteright}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.",

author = "Hennessy, \{Matthew G.\} and Myers, \{Tim G.\}",

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{\textquoteright}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 {\textquoteleft}la Caixa{\textquoteright} Foundation. TM acknowledges financial support from the Ministerio de Ciencia e Innovaci{\'o}n grant MTM2017-82317-P. The authors have been partially funded by the CERCA Programme of the Generalitat de Catalunya. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

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AU - Hennessy, Matthew G.

AU - Myers, Tim G.

N1 - 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.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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DO - 10.1007/978-3-030-64272-3_2

M3 - Chapter in a book

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BT - SEMA SIMAI Springer Series

PB - Springer Science and Business Media Deutschland GmbH

ER -

Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

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