Kapitza resistance and thermal transport across boundaries in superfluidHe3

Abstract

We calculate the temperature and normal fluid velocity of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ between parallel plates in the presence of a stationary heat flow normal to the plates. The system is modeled by a Landau-Boltzmann equation and a diffuse scattering mechanism at the boundaries. In the hydrodynamic regime the temperature jump at the wall turns out to be small. The three Onsager surface coefficients proposed recently by Grabinski and Liu are determined. In the Knudsen regime the thermal boundary resistance is found to increase exponentially with decreasing temperature.