Guyer-Krumhansl heat conduction in thermoreflectance experiments

Conference item

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 which 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.

Authors: Hennessy, M; Myers, TG

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Host title: Multidisciplinary Mathematical Modelling
• Series: ICIAM 2019 SEMA SIMAI Spring Series
• Series number: 11
• Publication date: 2020-12-16
• Acceptance date: 2020-07-17
• Event title: International Congress on Industrial and Applied Mathematics 2019
• Event location: Valencia
• Event website: https://iciam2019.com/
• Event start date: 2019-07-15
• Event end date: 2019-07-19
• DOI: 10.1007/978-3-030-64272-3
• ISSN: 2662-7183
• EISBN: 978-3-030-64272-3
• ISBN: 978-3-030-64271-6
• Language: English
• Keywords: FFR