Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
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.
- Research Organization:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- SC0001299; FG02-09ER46577
- OSTI ID:
- 1388413
- Alternate ID(s):
- OSTI ID: 1421258
- Journal Information:
- Journal of Applied Physics, Vol. 120, Issue 2; ISSN 0021-8979
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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