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.

References

References
1.
Bertman
,
B.
, and
Sandiford
,
D. J.
,
1970
, “
Second Sound in Solid Helium
,”
Sci. Am.
,
222
, pp.
92
101
.10.1038/scientificamerican0570-92
2.
Rogers
,
S. J.
,
1971
, “
Transport of Heat and Approach to Second Sound in Some Isotopically Pure Alkali-Halide Crystals
,”
Phys. Rev. B
,
3
, pp.
1440
1457
.10.1103/PhysRevB.3.1440
3.
Hardy
,
R. J.
,
1970
, “
Phonon Boltzmann Equation and Second Sound in Solids
,”
Phys. Rev. B
,
2
, pp.
1192
1207
.10.1103/PhysRevB.2.1193
4.
Jackson
,
H. E.
,
Walker
,
C. T.
, and
McNelly
,
T. F.
,
1970
, “
Second Sound in NaF
,”
Phys. Rev. Lett.
,
25
, pp.
26
28
.10.1103/PhysRevLett.25.26
5.
Narayana
,
V.
, and
Dynes
,
R. C.
,
1972
, “
Observation of Second Sound in Bismuth
,”
Phys. Rev. Lett.
,
28
, pp.
1461
1465
.10.1103/PhysRevLett.28.1461
6.
Brorson
,
S. D.
,
Fujimoto
,
J. G.
, and
Ippen
,
E. P.
,
1987
, “
Femtosecond Electron Heat-Transport HHHeat-Transport Dynamics in Thin Gold Film
,”
Phys. Rev. Lett.
,
59
, pp.
1962
1965
.10.1103/PhysRevLett.59.1962
7.
Ma
,
Y.
,
2012
, “
Heat Pulse Propagation Along Silicon Nanofilms
,”
ASME 2012 3rd Micro/Nanoscale Heat & Mass Transfer International Conference (MNHMT 2012)
, Mar. 3–6, 2012, Atlanta, GA.
8.
Ma
,
Y.
,
2013
, “
A Transient Ballistic–Diffusive Heat Conduction Model for Heat Pulse Propagation in Nonmetallic Crystals
,”
Int. J. Heat Mass Transfer
,
66
, pp.
592
602
.10.1016/j.ijheatmasstransfer.2013.06.069
9.
Ma
,
Y.
,
2013
, “
A Hybrid Phonon Gas Model for Transient Ballistic-Diffusive Heat Transport
,”
ASME J. Heat Transfer
,
135
, p.
044501
.10.1115/1.4023231
10.
Özisik
,
M. N.
, and
Tzou
,
D. Y.
,
1994
, “
On the Wave Theory in Heat Conduction
,”
ASME J. Heat Transfer
,
116
, pp.
526
535
.10.1115/1.2910903
11.
Guyer
,
R. A.
, and
Krumhansl
,
J. A.
,
1966
, “
Solution of the Linearized Phonon Boltzmann Equation
,”
Phys. Rev.
,
148
, pp.
766
778
.10.1103/PhysRev.148.766
12.
Fung
,
Y. C.
,
1965
,
Introduction to Solid Mechanics
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
13.
Tzou
,
D. Y.
,
1995
, “
A Unified Field Theory for Heat Conduction From Macro- to Micro-Scale
,”
ASME J. Heat Transfer
,
117
, pp.
8
16
.10.1115/1.2822329
14.
Tzou
,
D. Y.
,
1995
, “
The Generalized Lagging Response in Small-Scale and High-Rate Heating
,”
Int. J. Heat Mass Transfer
,
38
, pp.
3231
3240
.10.1016/0017-9310(95)00052-B
15.
Tzou
,
D. Y.
,
1997
,
Macro- to Microscale Heat Transfer: The Lagging Behavior
,
Taylor & Francis
,
Washington DC
.
16.
Sellitto
,
A.
,
Alvarez
,
F. X.
, and
Jou
,
D.
,
2010
, “
Temperature Dependence of Boundary Conditions in Phonon Hydrodynamics of Smooth and Rough Nanowires
,”
J. Appl. Phys.
,
107
, p.
114312
.10.1063/1.3431348
17.
Alvarez
,
F. X.
, and
Jou
,
D.
, and
Sellitto
,
A.
,
2009
, “
Phonon Hydrodynamics and Phonon-Boundary Scattering in Nanosystems
,”
J. Appl. Phys.
,
105
, p.
014317
.10.1063/1.3056136
18.
Tzou
,
D. Y.
,
2011
, “
Nonlocal Behavior in Phonon Transport
,”
Int. J. Heat Mass Transfer
,
54
, pp.
475
481
.10.1016/j.ijheatmasstransfer.2010.09.022
19.
Tzou
,
D. Y.
, and
Guo
,
Z. Y.
,
2010
, “
Nonlocal Behavior in Thermal Lagging
,”
Int. J. Therm. Sci.
,
49
, pp.
1133
1137
.10.1016/j.ijthermalsci.2010.01.022
20.
Cao
,
B. Y.
, and
Guo
,
Z. Y.
,
2007
, “
Equation of Motion of a Phonon Gas and Non-Fourier Heat Conduction
,”
J. Appl. Phys.
,
102
, p.
053503
.10.1063/1.2775215
21.
Guo
,
Z. Y.
, and
Hou
,
Q. W.
,
2010
, “
Thermal Wave Based on the Thermomass Model
,”
ASME J. Heat Transfer
,
132
, p.
072403
.10.1115/1.4000987
22.
Yih
,
C. S.
,
1977
,
Fluid Mechanics: A Concise Introduction to the Theory
,
West River Press
,
Ann Arbor, MI
.
23.
Guyer
,
R. A.
,
1994
, “
Phonon Gas: A Lattice Boltzmann Description
,”
Phys. Rev. E
,
50
, pp.
4596
4608
.10.1103/PhysRevE.50.4596
24.
Bertman
,
B.
, and
Sandiford
,
D. J.
,
1970
, “
Second Sound in Solid Helium
,”
Sci. Am.
,
222
, pp.
92
101
.10.1038/scientificamerican0570-92
25.
Khodusov
,
V. D.
, and
Blinkina
,
A. A.
,
2009
, “
Second Sound Waves in Orthodeuterium, Parahydrogen Quantum Crystals, and Neon Crystals
,”
Low Temp. Phys.
,
35
, pp.
349
355
.10.1063/1.3130962
26.
Guyer
,
R. A.
, and
Krumhansl
,
J. A.
,
1964
, “
Dispersion Relation for Second Sound in Solids
,”
Phys. Rev.
,
133
, pp.
A1411
A1417
.10.1103/PhysRev.133.A1411
You do not currently have access to this content.