Thermal constriction resistance between two solids for random distribution of contacts

Abstract

An infinite interface of randomly distributed contacts is modeled as a finite square region with randomly placed contacts inside it. The contacts outside the region are treated as continuum of contacts. The continuum approximation allows for an interaction between the contacts within the square and those outside it. An analytical solution is obtained for the temperature field, and the contact resistance is analyzed for randomness effects. This is the first such analytical model developed to study random distribution of contacts. The result shows an excellent agreement when tested against the the available analytical solution for the case of periodic arrangement of contacts. For the random case, the resistance is observed to be a strong function of the area fraction of contact.