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A Broad Range of Phonon Mean Free Paths Is Important for Heat Conduction

[+] Author Affiliations
C. Dames

University of California at Riverside, Riverside, CA

Paper No. MNHT2008-52270, pp. 41-42; 2 pages
doi:10.1115/MNHT2008-52270
From:
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer, Parts A and B
  • Tainan, Taiwan, June 6–9, 2008
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 0-7918-4292-4 | eISBN: 0-7918-3813-7
  • Copyright © 2008 by ASME

abstract

The thermal conductivity is modeled with a spectral form of kinetic theory

k = 13CωνLdω    (1)
where ω is the angular frequency, is the specific heat per unit frequency, ν = ∂ω/∂q is the group velocity, and L is the effective mean free path (MFP) which combines bulk and boundary scattering using Matthiessen’s rule:
Cω = ħω DOS ∂f/∂T    (2)
L−1 = Lbulk−1 + Lboundary−1.    (3)
Here q is the wavevector, DOS is the density of states (acoustic modes only), T is the temperature, and f is the Bose-Einstein distribution function.

Copyright © 2008 by ASME

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