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Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films.

Authors :
Chiloyan, Vazrik
Lingping Zeng
Huberman, Samuel
Maznev, Alexei A.
Nelson, Keith A.
Gang Chen
Source :
Journal of Applied Physics. 2016, Vol. 120 Issue 2, p025103-1-025103-7. 7p. 1 Diagram, 3 Graphs.
Publication Year :
2016

Abstract

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find 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 phononmediated 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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00218979
Volume :
120
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Applied Physics
Publication Type :
Academic Journal
Accession number :
116832906
Full Text :
https://doi.org/10.1063/1.4955164