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Technical Brief

A Generalized Enhanced Fourier Law

[+] Author and Article Information
Ashok T. Ramu

Department of Electrical and Computer Engineering,
University of California Santa Barbara,
Santa Barbara, CA 93106-9560
e-mail: ashok.ramu@gmail.com

John E. Bowers

Department of Electrical and Computer Engineering,
University of California Santa Barbara,
Santa Barbara, CA 93106-9560
e-mail: bowers@ece.ucsb.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 27, 2016; final manuscript received August 31, 2016; published online November 16, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 139(3), 034501 (Nov 16, 2016) (4 pages) Paper No: HT-16-1426; doi: 10.1115/1.4034796 History: Received June 27, 2016; Revised August 31, 2016

A generalized enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables is derived from the Boltzmann transport equation. It generalizes the previously reported EFL from a gray phonon population to an arbitrary quasi-ballistic phonon mode population, the chief advantage being its formulation in terms of observables like the heat flux and temperature, in a manner akin to the Fourier law albeit rigorous enough to describe quasi-ballistic phonon transport.

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References

Figures

Grahic Jump Location
Fig. 1

Suppression functions of Maznev et al. [4] and this work(see Eq. (8)) match very closely over a large range of values of χΛ

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