Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films
Abstract
The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find here a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1388413
- Alternate Identifier(s):
- OSTI ID: 1421258
- Grant/Contract Number:
- SC0001299; FG02-09ER46577
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Applied Physics
- Additional Journal Information:
- Journal Volume: 120; Journal Issue: 2; Journal ID: ISSN 0021-8979
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., and Chen, Gang. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films. United States: N. p., 2016.
Web. doi:10.1063/1.4955164.
Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., & Chen, Gang. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films. United States. https://doi.org/10.1063/1.4955164
Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., and Chen, Gang. Mon .
"Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films". United States. https://doi.org/10.1063/1.4955164. https://www.osti.gov/servlets/purl/1388413.
@article{osti_1388413,
title = {Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films},
author = {Chiloyan, Vazrik and Zeng, Lingping and Huberman, Samuel and Maznev, Alexei A. and Nelson, Keith A. and Chen, Gang},
abstractNote = {The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find here a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.},
doi = {10.1063/1.4955164},
journal = {Journal of Applied Physics},
number = 2,
volume = 120,
place = {United States},
year = {Mon Jul 11 00:00:00 EDT 2016},
month = {Mon Jul 11 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
Thermal transport in suspended silicon membranes measured by laser-induced transient gratings
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