Analytical solution for constriction resistance with interstitial fluid in the gap

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 Kg less than or equal to 0.7. The resistance is observed to be a strong function of gap conductivity and gap thickness, especially at lower values of these parameters.