Theory of thermal resistance between solids with randomly sized and located contacts

Linear superposition method is used to determine an analytical solution of the thermal constriction resistance adapted to random contacts. The contact area is constituted of numerous disks which have different radii and are randomly distributed over a square or circular area. The developed solution is easy to use and allows to consider numerous contacts at a reasonable computing time. The disks can be distributed in entire contact surface or located in a specific region. The results are in an excellent agreement with available data in the literature for identical and regular contacts. The model is used to study the thermal constriction resistance evolution as a function of contact disorders, number and sizes of disks and relative contact size area. The results are compared to the model of regular contacts.