By using a phonon hydrodynamics model for heat flow complemented with boundary conditions for smooth or rough boundaries, we study the influence of boundary conditions on the longitudinal thermal conductivity for several kinds of nanowires (single, tubular, and core-shell). The effects of the boundaries are seen to be extremely important.
Issue Section:
Micro/Nanoscale Heat Transfer
1.
Wang
, J.
, and Wang
, J. -S.
, 2006, “Carbon Nanotube Thermal Transport: Ballistic to Diffusive
,” Appl. Phys. Lett.
0003-6951, 88
, p. 111909
.2.
Fujii
, M.
, Zhang
, X.
, Xie
, H.
, Ago
, H.
, Takahashi
, K.
, Ikuta
, T.
, Abe
, H.
, and Shimizu
, T.
, 2005, “Measuring the Thermal Conductivity of a Single Carbon Nanotube
,” Phys. Rev. Lett.
0031-9007, 95
, p. 065502
.3.
Jou
, D.
, Casas-Vázquez
, J.
, Lebon
, G.
, and Grmela
, M.
, 2005, “A Phenomenological Scaling Approach for Heat Transport in Nano-Systems
,” Appl. Math. Lett.
0893-9659, 18
, pp. 963
–967
.4.
Cahill
, D. C.
, Ford
, W. K.
, Goodson
, K. E.
, Mahan
, G. D.
, Majumdar
, A.
, Maris
, H. J.
, Merlin
, R.
, and Phillpot
, S. R.
, 2003, “Nanoscale Thermal Transport
,” J. Appl. Phys.
0021-8979, 93
, pp. 793
–818
.5.
Chen
, G.
, 2001, “Ballistic-Diffusive Heat-Conduction Equations
,” Phys. Rev. Lett.
0031-9007, 86
, pp. 2297
–2300
.6.
Hao
, Z.
, Zhichao
, L.
, Lilin
, T.
, Zhimin
, T.
, Litian
, L.
, and Zhijian
, L.
, 2007, “Measurement of Thermal Conductivity of Ultra-Thin Single Crystal Silicon Film Using Symmetric Structure
,” Chin. J. Semicond.
0253-4177, 27
, pp. 1961
–1965
.7.
Liu
, W.
, and Asheghi
, M.
, 2005, “Thermal Conduction in Ultrathin Pure and Doped Single-Crystal Silicon Layers at High Temperatures
,” J. Appl. Phys.
0021-8979, 98
, p. 123523
.8.
Liu
, W.
, and Asheghi
, M.
, 2004, “Phonon-Boundary Scattering in Ultrathin Single-Crystal Silicon Layers
,” Appl. Phys. Lett.
0003-6951, 84
, pp. 3819
–3821
.9.
Asheghi
, M.
, Kurabayashi
, K.
, Kasnavi
, R.
, and Goodson
, K. E.
, 2002, “Thermal Conduction in Doped Single-Crystal Silicon Films
,” J. Appl. Phys.
0021-8979, 91
, pp. 5079
–5088
.10.
Kim
, P.
, Shi
, L.
, Majumdar
, A.
, and McEuen
, P. L.
, 2001, “Thermal Transport Measurements of Individual Multiwalled Nanotubes
,” Phys. Rev. Lett.
0031-9007, 87
, p. 215502
.11.
Ju
, Y. S.
, and Goodson
, K. E.
, 1999, “Phonon Scattering in Silicon Films With Thickness of Order 100 nm
,” Appl. Phys. Lett.
0003-6951, 74
, pp. 3005
–3007
.12.
Asheghi
, M.
, Leung
, Y. K.
, Wong
, S. S.
, and Goodson
, K. E.
, 1997, “Phonon-Boundary Scattering in Thin Silicon Layers
,” Appl. Phys. Lett.
0003-6951, 71
, pp. 1798
–1800
.13.
Li
, D.
, Wu
, Y.
, Kim
, P.
, Shi
, L.
, Yang
, P.
, and Majumdar
, A.
, 2003, “Thermal Conductivity of Individual Silicon Nanowires
,” Appl. Phys. Lett.
0003-6951, 83
, pp. 2934
–2936
.14.
Chen
, R.
, Hochbaum
, A. I.
, Murphy
, P.
, Moore
, J.
, Yang
, P.
, and Majumdar
, A.
, 2008, “Thermal Conductance of Thin Silicon Nanowires
,” Phys. Rev. Lett.
0031-9007, 101
, p. 105501
.15.
Hochbaum
, A. I.
, Chen
, R.
, Delgado
, R. D.
, Liang
, W.
, Garnett
, E. C.
, Najarian
, M.
, Majumdar
, A.
, and Yang
, P.
, 2008, “Enhanced Thermoelectric Performance of Rough Silicon Nanowires
,” Nature (London)
0028-0836, 451
, pp. 163
–167
.16.
Boukai
, A. I.
, Bunimovich
, Y.
, Tahir-Kheli
, J.
, Yu
, J. -K.
, Goddard
, W. A.
, III, and Heath
, J. R.
, 2008, “Silicon Nanowires as Efficient Thermoelectric Materials
,” Nature (London)
0028-0836, 451
, pp. 168
–171
.17.
Alvarez
, F. X.
, and Jou
, D.
, 2007, “Memory and Nonlocal Effects in Heat Transports: From Diffusive to Ballistic Regimes
,” Appl. Phys. Lett.
0003-6951, 90
, p. 083109
.18.
Jou
, D.
, Casas-Vázquez
, J.
, and Lebon
, G.
, 2001, Extended Irreversible Thermodynamics
, 3rd ed., Springer-Verlag
, Berlin
.19.
Joshi
, A. A.
, and Majumdar
, A.
, 1993, “Transient Ballistic and Diffusive Phonon Heat Transport in Thin Films
,” J. Appl. Phys.
0021-8979, 74
, pp. 31
–39
.20.
Guyer
, R. A.
, and Krumhansl
, J. A.
, 1966, “Solution of the Linearized Phonon Boltzmann Equation
,” Phys. Rev.
0031-899X, 148
, pp. 766
–778
.21.
Guyer
, R. A.
, and Krumhansl
, J. A.
, 1966, “Thermal Conductivity, Second Sound and Phonon Hydrodynamic Phenomena in Nonmetallic Crystals
,” Phys. Rev.
0031-899X, 148
, pp. 778
–788
.22.
Martin
, P.
, Aksamija
, Z.
, Pop
, E.
, and Ravaioli
, U.
, 2009, “Impact of Phonon-Surface Roughness Scattering on Thermal Conductivity of Thin Si Nanowires
,” Phys. Rev. Lett.
0031-9007, 102
, p. 125503
.23.
Mingo
, N.
, 2003, “Calculation of Si Nanowire Thermal Conductivity Using Complete Phonon Dispersion Relations
,” Phys. Rev. B
0556-2805, 68
, p. 113308
.24.
Alvarez
, F. X.
, Jou
, D.
, and Sellitto
, A.
, 2009, “Phonon Hydrodynamics and Phonon-Boundary Scattering in Nanosystems
,” J. Appl. Phys.
0021-8979, 105
, p. 014317
.25.
Prasher
, R.
, 2006, “Thermal Conductivity of Tubular and Core/Shell Nanowires
,” Appl. Phys. Lett.
0003-6951, 89
, p. 063121
.26.
Yang
, R.
, Chen
, G.
, and Dresselhaus
, M. S.
, 2005, “Thermal Conductivity of Simple and Tubular Nanowire Composites in the Longitudinal Direction
,” Phys. Rev. B
0556-2805, 72
, p. 125418
.27.
Lebon
, G.
, Jou
, D.
, and Casas-Vázquez
, J.
, 2008, Understanding Nonequilibrium Thermodynamics
, Springer
, Berlin
.28.
Jou
, D.
, and Casas-Vázquez
, J.
, 1990, “Nonequilibrium Absolute Temperature, Thermal Waves and Phonon Hydrodynamics
,” Physica A
0378-4371, 163
, pp. 47
–58
.29.
Cimmelli
, V. A.
, and Frischmuth
, K.
, 2007, “Gradient Generalization to the Extended Thermodynamic Approach and Diffusive-Hyperbolic Heat Conduction
,” Physica B
0921-4526, 400
, pp. 257
–265
.30.
Lacroix
, D.
, Joulain
, K.
, Terris
, D.
, and Lemonnier
, D.
, 2006, “Monte Carlo Simulation of Phonon Confinement in Silicon Nanostructures: Application to the Determination of the Thermal Conductivity of Silicon Nanowires
,” Appl. Phys. Lett.
0003-6951, 89
, p. 103104
.31.
Sellitto
, A.
, Alvarez
, F. X.
, and Jou
, D.
, 2010, “Second Law of Thermodynamics and Phonon-Boundary Conditions in Nanowires
,” J. Appl. Phys.
0021-8979, 107
, p. 064302
.32.
Ferry
, D. K.
, and Goodnick
, S. M.
, 2009, Transport in Nanostructures
, 2nd ed., Cambridge University Press
, Cambridge
.33.
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.
0021-8979, 107
, p. 114312
.34.
Landau
, L. D.
, and Lishitz
, E. M.
, 1985, Mechanics of Fluids
, Pergamon
, Oxford
.35.
Duan
, Z.
, and Muzychka
, Y. S.
, 2008, “Slip Flow Heat Transfer in Annular Microchannels With Constant Heat Flux
,” ASME J. Heat Transfer
0022-1481, 130
, p. 092401
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