A model of thermal contact conductance at high real contact area fractions

Thermal contact conductance (TCC) is studied in the whole range of real contact area fractions between zero and unity. For this purpose, a two-scale model is developed in which the effective (macroscopic) TCC coefficient is obtained from the solution of the heat conduction problem at the scale of asperities. Additional thermal resistance at the real contact spots is included in the model. The model is applied for several real 3D roughness topographies for which the effective TCC coefficient is determined as a function of the real contact area fraction and the local TCC coefficient at real contact spots. An analytical function is found which approximates this relationship in the whole range of parameters, and a characteristic length-scale parameter is introduced which characterizes the effective TCC properties of a rough surface.