Slip boundary condition of heat flux in Knudsen layers

Abstract

In a Knudsen layer with thickness comparable to the mean free path, collisions between heat carriers and solid walls play an important role in nanoscale heat transports. An interesting question is that whether these collisions also induce the slip of heat flow similar to the velocity slip condition of the rarefied gases on solid walls. In this work based on the discrete Boltzmann transport equation, the slip boundary condition of heat flux on solid walls in the Knudsen layer is established. This result is exemplified by the slip boundary condition of heat flux in nanowires, which has been proposed in a phenomenological way.

Transient in-plane thermal transport in nanofilms with internal heating

“…As t → 0, equation (3.9) tends to beT 10) in which the effective thermal conductivity, k eff , has been cancelled out. Equation ( 3.10) indicates that the modification of the effective thermal conductivity for the heat diffusion model to reflect the boundary effect cannot work at the initial heating stage, which explains the reason why the heat diffusion model with the effective thermal conductivity significantly under-predicts the temperature rise at the initial stage.…”

“…In the modelling work about the in-plane effective thermal conductivity of the nanofilms, a nanofilm is generally assumed to be in contact with two phonon baths of different temperatures and the temperature difference induces the heat flow [9][10][11][12][13]. Then the effective thermal conductivity can be calculated using Fourier's law.…”

“…Analytical effective thermal conductivity models were derived based on the steady-state phonon Boltzmann transport equation [9,10], extended irreversible thermodynamics [11] and phonon hydrodynamics [12,13]. Besides, the molecular dynamics [14] and MC [15] simulations were also employed to investigate the effective thermal conductivity.…”

“…Great efforts have focused on the reduction of in-plane effective thermal conductivity in the nanofilms [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and tried to characterize the thermal transport with phonon-boundary scattering by the modification of effective thermal conductivity [24][25][26]. Analytical effective thermal conductivity models were derived based on the steady-state phonon Boltzmann transport equation [9,10], extended irreversible thermodynamics [11] and phonon hydrodynamics [12,13].…”

Effective phonon mean-free path and slip heat flow in rarefied phonon hydrodynamics

“…However, this may lead to a too strong reduction of the associated thermal conductivity in this regime in terms of the characteristic size of the system. In order to improve the agreement with experimental observations and with theoretical analysis of kinetic theory of rarefied gases, it has been proposed to consider a slip (i.e., nonvanishing) heat flow along the walls [7,8,10,[22][23][24][25].…”