Phononic heat transfer across an interface: thermal boundary resistance

We present a general theory of phononic heat transfer between two solids (or a solid and a fluid) in contact at a flat interface. We present simple analytical results which can be used to estimate the heat transfer coefficient (the inverse of which is usually called the 'thermal boundary resistance' or 'Kapitza resistance'). We present numerical results for the heat transfer across solid-solid and solid-liquid He contacts, and between a membrane (graphene) and a solid substrate (amorphous SiO2). The latter system involves the heat transfer between weakly coupled systems, and the calculated value of the heat transfer coefficient is in good agreement with the value deduced from experimental data.