Analytical solution for constriction resistance with interstitial fluid in the gap

Abstract

An analysis of the thermal constriction resistance between two semi-infinite solids in contact has been carried out to study the effects of the interstitial medium. The thermal contact is modeled as a three-media problem with finite resistivities for each medium, together with complete interfacial coupling between the solids and the interstitial fluid. Analytical solutions are obtained for a periodic array of two-dimensional gaps of circular segment profiles flanked by flat contacting surfaces. A corrective-iterative technique is used to account for the interaction between the gaps to obtain a closed form expression for the contact resistance in terms of known parameters. For the special case of zero-thickness adiabatic gaps, the present solution compares very well with the available analytical solution for gap fraction values of the κ _g ≤0.7. The resistance is observed to be a strong function of gap conductivity and gap thickness, especially at lower values of these parameters.