A unified macroscopic and microscopic approach to contact conduction heat transfer

A close look at the literature on contact heat transfer reveals that the work on thermal boundary resistance (R b) arising due to the acoustic mismatch of phonons at the interface of two dissimilar materials, and thermal contact resistance (R c) arising due to incomplete contact at the interface of two materials, tends to be independent of each other, and at times there seems to be some confusion as to what is the origin of thermal contact resistance, especially at cryogenic temperatures. Since R b is present even if the interfaces are geometrically perfect, it is reasonable to expect that even in the case of imperfect interfaces, R b still plays a role in contact heat transfer. In this paper a unified model is developed, which bridges the gap between the macroscopic models based on incomplete area of contact, and the microscopic models based on acoustic mismatch in phonon transfer across the interface. A comparison between the model's predictions and cryogenic experimental data from the literature reveals that only the unified model correctly predicts the trend of the data.