1. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films
- Author
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Gang Chen, Samuel Huberman, Lingping Zeng, Keith A. Nelson, Alexei Maznev, Vazrik Chiloyan, Massachusetts Institute of Technology. Department of Chemistry, Massachusetts Institute of Technology. Department of Mechanical Engineering, Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel C., Maznev, Alexei, Nelson, Keith Adam, and Chen, Gang
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Mean free path ,Monte Carlo method ,FOS: Physical sciences ,General Physics and Astronomy ,02 engineering and technology ,Grating ,021001 nanoscience & nanotechnology ,01 natural sciences ,Boltzmann equation ,Computational physics ,Thermal conductivity ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Heat transfer ,Heat equation ,Closed-form expression ,010306 general physics ,0210 nano-technology - 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 phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path (MFP) distribution of materials via transient grating experiments., Comment: 19 pages, 4 figures
- Published
- 2016
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