Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films
Author(s)Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel C.; Maznev, Alexei; Nelson, Keith Adam; Chen, Gang; ... Show more Show less
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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 distribution of materials via transient grating experiments.
DepartmentMassachusetts Institute of Technology. Department of Chemistry; Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal of Applied Physics
American Institute of Physics (AIP)
Chiloyan, Vazrik et al. “Variational Approach to Solving the Spectral Boltzmann Transport Equation in Transient Thermal Grating for Thin Films.” Journal of Applied Physics 120, 2 (July 2016): 025103 © 2016 Author(s)