Analysis of heat transfer between solids at low temperatures

A detailed analysis is given of the acoustic mismatch formulation first given by Little for the thermal contact resistance between solids for the case of phonon transport in a Debye model. Extrema in the heat transfer coefficients as a function of the refractive index of the interface are shown to be due to either impedance matching conditions or to the presence of the critical cone. Detailed numerical tables are presented which permit rapid evaluation of the heat transfer coefficient to an accuracy of 5% or better.