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.