Modeling Thermal Contact Resistance

One difficulty in using cryocoolers is making good thermal contact between the cooler and the instrument being cooled. The connection is often made through a bolted joint. The temperature drop associated with this joint has been the subject of many experimental and theoretical studies. The low temperature behavior of dry joints have shown some anomalous dependence on the surface condition of the mating parts. There is also some doubts on how well one can extrapolate from the test samples to predicting the performance of a real system. Both finite element and analytic models of a simple contact system have been developed. The model assumes (a) the contact is dry (contact limited to a small portion of the total available area and the spaces in-between the actual contact patches are perfect insulators), (b) contacts are clean (conductivity of the actual contact is the same as the bulk), (c) small temperature gradients (the bulk conductance may be assumed to be temperature independent), (d) the absolute temperature is low (thermal radiation effects are ignored), and (e) the dimensions of the nominal contact area are small compared to the thickness of the bulk material (the contact effects are localized near the contact). The models show that in the limit of actual contact area much less than the nominal area (a much less than A), that the excess temperature drop due to a single point of contact scales as a(exp -1/2). This disturbance only extends a distance approx. A(exp 1/2) into the bulk material. A group of identical contacts will result in an excess temperature drop that scales as n(exp -1/2), where n is the number of contacts and n dot a is constant. This implies that flat rough surfaces will have a lower excess temperature drop than flat polished surfaces.