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Research Papers: Micro/Nanoscale Heat Transfer

Longitudinal and Transverse Phonon Transport in Dielectric Crystals

[+] Author and Article Information
D. Y. Tzou

James C. Dowell Professor of Engineering,
Fellow ASME
Department of Mechanical
and Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: tzour@missouri.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 25, 2012; final manuscript received November 4, 2013; published online January 2, 2014. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 136(4), 042401 (Jan 02, 2014) (5 pages) Paper No: HT-12-1190; doi: 10.1115/1.4026005 History: Received April 25, 2012; Revised November 04, 2013

Longitudinal and transverse modes of thermal disturbances in isotopically pure alkali-halide crystals are derived from phonon hydrodynamics. Guyer-Krumhansl (GK) model of phonon scattering is first recovered by relating the first and second viscosity to the relaxation times. Helmholtz potentials are then introduced to split the two modes from the heat flux vector. It has been found that the scalar potential coincides with the heat equation in the dual-phase-lag model, while the vector potential describes dispersive transverse phonons and introduces a new type of equation in microscale heat transfer.

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References

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Figures

Grahic Jump Location
Fig. 1

(a) Longitudinal (F) and (b) transverse (Y) disturbances for z = 0.001 and βs = 0.01 at ξ = 0.01 (solid line), 0.03 (dashed line), and 0.05 (dotted line)

Grahic Jump Location
Fig. 2

Longitudinal and transverse disturbances at ξ = 0.05: z = 0.005; βs = 0.01. The oscilloscope trace is reproduced from Ref. [2] for LiF at 7.2K in the principal direction of [110].

Grahic Jump Location
Fig. 3

Longitudinal and transverse disturbances at ξ = 0.05: z = 0.01; βs = 0.01. The oscilloscope trace is reproduced from Ref. [2] for LiF at 7.2K and ts = 0.3 μs in the principal direction of [100].

Grahic Jump Location
Fig. 4

Longitudinal and transverse disturbances as β = 0.05: z = 0.01; βs = 0.01

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