Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers

Abstract

Owing to the heat propagation, in nano-systems the phonons always undergo to different scattering mechanisms. The particular regime of heat transfer, instead, strictly depends on the ratio between the phonon mean-free path and the characteristic size of the system, i.e., the so-called Knudsen number. At nano-scale, wherein several conceptual questions still remain unanswered, the analysis of the role played by the phonon-boundary scatterings, for different values of the Knudsen number, in particular is an interesting research playground. We therefore here propose an enhanced model of boundary conditions in order to suitably address the problem of the correct tackling of the phonon-boundary scatterings when heat is flowing in a thin layer.