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Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment

Hua, Chengyun and Lindsay, Lucas and Chen, Xiangwen and Minnich, Austin J. (2019) Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment. Physical Review B, 100 (8). Art. No. 085203. ISSN 2469-9950. doi:10.1103/PhysRevB.100.085203.

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Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. However, debate exists over the appropriate constitutive law that defines thermal conductivity in the nondiffusive regime. Here, we derive a generalized Fourier's law that links the heat flux and temperature fields, valid from ballistic to diffusive regimes and for general geometries, using the Peierls-Boltzmann transport equation within the relaxation time approximation. This generalized Fourier's law predicts that thermal conductivity not only becomes nonlocal at length scales smaller than phonon mean free paths but also requires the inclusion of an inhomogeneous nonlocal source term that has been previously neglected. We provide evidence for the validity of this generalized Fourier's law through direct comparison with time-domain thermoreflectance measurements in the nondiffusive regime without adjustable parameters. Furthermore, we show that interpreting experimental data without the generalized Fourier's law can lead to inaccurate measurement of thermal transport properties.

Item Type:Article
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URLURL TypeDescription
Hua, Chengyun0000-0003-3587-8342
Minnich, Austin J.0000-0002-9671-9540
Additional Information:© 2019 American Physical Society. Received 26 February 2019; revised manuscript received 24 June 2019; published 21 August 2019. C.H. and L.L. acknowledge support from the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy. A.J.M. acknowledges support from the National Science Foundation under Grant No. CBET CAREER 1254213. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-05CH11231
Issue or Number:8
Record Number:CaltechAUTHORS:20190821-092908240
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98068
Deposited By: Tony Diaz
Deposited On:21 Aug 2019 18:46
Last Modified:16 Nov 2021 17:36

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