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A Hybrid Phonon Gas Model for Transient Ballistic-Diffusive Heat Transport

[+] Author and Article Information
Yanbao Ma

School of Engineering,
University of California at Merced,
Merced, CA 95343
e-mail: yma5@ucmerced.edu

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received September 11, 2012; final manuscript received December 7, 2012; published online February 20, 2013. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 135(4), 044501 (Feb 20, 2013) (4 pages) Paper No: HT-12-1496; doi: 10.1115/1.4023231 History: Received September 11, 2012; Revised December 07, 2012

We present a continuum hybrid phonon gas model to describe transient ballistic-diffusive heat transport. In this model, heat energy is carried by a mixture of longitudinal and transverse phonon gases so that the distinction between longitudinal and transverse phonon excitations is taken into account. This new model is validated by the successful reconstruction of benchmark cases of heat-pulse experiments in NaF, which have never been completely reconstructed before. It is elucidated how thermal pulses are transmitted by longitudinal and transverse phonon gases. This model not only helps us yield new insight in transient ballistic-diffusive heat conduction mechanisms but also provides numerical tools to study transient ballistic-diffusive heat conduction in nanoelectronic and modern optoelectronics.

Copyright © 2013 by ASME
Topics: Heat , Waves , Phonons
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Grahic Jump Location
Fig. 1

Comparison of the numerical results with experimental results on pulse arrival times in very pure NaF [6]

Grahic Jump Location
Fig. 2

Comparison between numerical results and experimental observations of heat pulses. (a) Photographs of oscilloscope traces in experiments (redrawn based on Fig. 2 in Ref. [6]); (b) numerical heat pulses to fit (a); (c) photographs of oscilloscope traces in experiments (redrawn based on Fig. 4 in Ref. [7]); (d) numerical heat pulses to fit (c).

Grahic Jump Location
Fig. 3

(a)–(h) Distribution of internal energy at different times for a trapezoidal pulse (solid lines) and a parabolic pulse (dotted lines) in very pure NaF



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