Heat fluctuations and phonon hydrodynamics in nanowires

Abstract

We evaluate the second moments of the fluctuations of the total longitudinal heat flux in cylindrical nanowires described by phonon hydrodynamics with boundary conditions accounting for phonon boundary collisions. It is found that the second moments exhibit an explicit dependence on the boundary conditions and, therefore, may provide a suitable tool for analyzing phonon boundary collisions. Furthermore, an analogous dependence is also manifested in the relative probability of forward and backward fluctuations of the heat flux in a nonequilibrium steady state, thus providing a complementary tool of research for phonon boundary collisions.

Thermomass Theory: A Mechanical Pathway to Analyze Anomalous Heat Conduction in Nanomaterials

“…However, the experiments indicated that the effective thermal conductivity is approximately linear to the characteristic size rather than the square of size. It is thereby further elucidated that the boundary velocity slip would happen in case of large Kn [29,31]. By introducing the slip boundary condition into the governing equation, the linear size-dependent effective thermal conductivity can be achieved.…”

“…The phonon hydrodynamics [26][27][28][29][30][31] is another pathway to model the nanoscale heat conduction. It originates from the solving of linearized Boltzmann equation.…”

Slip boundary condition of heat flux in Knudsen layers

“…the heat conduction of nanowires was investigated in [24,25,27,28]. They proposed that the phonon flow exhibits a similar behaviour as rarefied gas flows or microscale flows in microchannels with the rarefied effect.…”

“…They proposed that the phonon flow exhibits a similar behaviour as rarefied gas flows or microscale flows in microchannels with the rarefied effect. As the velocity on the walls of microchannels satisfies the slip boundary condition, analogously the slip boundary condition of heat flux for the phonon flow in nanowires was assumed in [24,25,27,28]. However, the legitimacy of this slip boundary condition of heat flux on the boundary surface of nanowires needs to be proved.…”

“…However, they cannot reflect the non-local effect of nanoscale heat conductions, for example the size effect, which has been observed experimentally [8][9][10][11][12]. The Guyer-Krumhansl model accommodates both the lagging and non-local effects [21][22][23][24][25][26], which is expressed as follows:…”