Phonon-boundary scattering and second-order boundary conditions: Application to the heat transfer in one-dimensional nanosystems

At nanoscale, wherein several conceptual questions still remain unanswered, it is currently well-known that the regime of heat transfer can be strictly related to the ratio between the phonon mean-free path and the characteristic size of the system, i.e., the so-called Knudsen number. The phonons, in fact, undergo different scattering mechanisms throughout the heat propagation in nanosystems. The analysis of the role played by the phonon-boundary scattering, for different values of the Knudsen number, in particular is an interesting research playground. In this paper we therefore propose enhanced boundary conditions in order to suitably account for the phonon-boundary scattering when heat is flowing in a one-dimensional nanosystem (e.g., a nanowire, a nanotube, a nanorod, etc.).