Effects of Multiple Sources in the Contact Conductance Theory

An analysis of regularly spaced disk sources on the surface of a semi-infinite body is given and related to steady-state contact conductance theory. It is shown that simple superposition utilizing the steady-state temperature distribution for a single typical disk source is not valid since a steady state does not exist for the temperature resulting for an infinite number of regularly spaced sources on the surface of a semi-infinite solid. A novel analysis is presented that treats the transient surface temperature in such a manner that a steady-state conductance is derived. The conductance results are compared with those obtained by Yovanovich who use a complementary analysis. The method of analysis can be applied to other disk spacings and to random distribution of contacts. Also considered is the case of contact radius being a uniformly-distributed random variable which yielded the results of increased contact resistance compared to that using the average contact radius.