Microscopic and macroscopic thermal contact resistances of pressed mechanical contacts

Contact heat transfer at mechanical pressed contacts between two materials is very important in many applications. There are two types of thermal contact resistance at the interface of two solids. One of them is due to the constriction of heat flow lines at the interface, commonly known as thermal contact resistance, and the engineering literature has extensively dealt with this macroscopic phenomenon. The other type of constriction resistance is instead microscopic in nature. If the characteristic dimension of the constriction becomes comparable to the mean free path of the heat carriers (i.e., electrons and phonons), then there is a ballistic component to the constriction resistance. For different materials on the two sides, thermal boundary resistance due to phonon acoustic mismatch and to electron-phonon interaction in the case of metals becomes important. Here a unified model is developed which bridges the gap between the macroscopic constriction resistance and the microscopic contact resistance for pressed mechanical contacts. The model predictions are in good agreement with experimental data for a mechanically pressed Cu/Si interface.