Modeling Thermal Contact Resistance: A Scale Analysis Approach

Abstract

A compact analytical model is developed for predicting thermal contact resistance (TCR) of nonconforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach is taken by employing the “scale analysis method.” It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable for an applicable range of contact pressure. It is shown that the surface curvature and contact pressure distribution have no effect on the effective microthermal resistance. The present model allows TCR to be predicted over the entire range of nonconforming rough contacts from conforming rough to smooth Hertzian contacts. A new nondimensional parameter, i.e., ratio of the macro- over microthermal resistances, is introduced as a criterion to identify three regions of TCR. The present model is compared to collected TCR data for SS304 and showed excellent agreement. Additionally, more than 880 experimental data points, collected by many researchers, are summarized and compared to the present model, and relatively good agreement is observed. The data cover a wide range of materials, mechanical and thermophysical properties, micro- and macrocontact geometries, and similar and dissimilar metal contacts.