Phonon hydrodynamics and phonon-boundary scattering in nanosystems

We use phonon hydrodynamics with a surface slip flow as a simplified macroscopic model accounting for a reduction in lateral thermal conductivity in nanosystems. For high Knudsen numbers, the corresponding effective thermal conductivity decreases linearly with the radius or the width, in contrast with the quadratic dependence predicted by usual phonon hydrodynamics. The linear dependence is accounted for by the surface slip flow. The difference in the expressions for the surface tangential flow in the hydrodynamic and the diffusive regimes is commented on and the influence of boundary conditions on the form of the effective thermal conductivity is explored.

[1]  David Jou,et al.  Memory and nonlocal effects in heat transport: From diffusive to ballistic regimes , 2007 .

[2]  Mehdi Asheghi,et al.  Phonon–boundary scattering in ultrathin single-crystal silicon layers , 2004 .

[3]  R. Dingle,et al.  The electrical conductivity of thin wires , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  V. I. Roldugin,et al.  REVIEWS OF TOPICAL PROBLEMS: Non-equilibrium thermodynamics and kinetic theory of rarefied gases , 1998 .

[5]  W. Tian,et al.  Introduction to Microfluidics , 2008 .

[6]  David Jou,et al.  Understanding Non-equilibrium Thermodynamics , 2008 .

[7]  R. Chambers.  Anomalous Skin Effect in Metals , 1950, Nature.

[8]  K. Frischmuth,et al.  Gradient generalization to the extended thermodynamic approach and diffusive-hyperbolic heat conduction , 2007 .

[9]  G. Lebon,et al.  Extended irreversible thermodynamics , 1993 .

[10]  R. Guyer,et al.  Solution of the Linearized Phonon Boltzmann Equation , 1966 .

[11]  E. H. Sondheimer,et al.  The mean free path of electrons in metals , 1952 .

[12]  J. Ziman,et al.  In: Electrons and Phonons , 1961 .

[13]  R. G. Chambers,et al.  The conductivity of thin wires in a magnetic field , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Maynard,et al.  Phonon Poiseuille Flow in Quasi-One-Dimensional Single Crystals. , 1996, Physical review letters.

[15]  Robert A. Guyer,et al.  Thermal Conductivity, Second Sound, and Phonon Hydrodynamic Phenomena in Nonmetallic Crystals , 1966 .

[16]  Yiying Wu,et al.  Thermal conductivity of individual silicon nanowires , 2003 .

[17]  Maekawa,et al.  Quantum transport and surface scattering. , 1986, Physical review letters.

[18]  Kenneth E. Goodson,et al.  PHONON-BOUNDARY SCATTERING IN THIN SILICON LAYERS , 1997 .

[19]  D. Jou,et al.  Size and frequency dependence of effective thermal conductivity in nanosystems , 2008 .

[20]  Zhuomin M. Zhang.  Nano/Microscale Heat Transfer , 2007 .