The effect of geometry on the contact conductance of contiguous interfaces

The analysis to determine the thermal resistance across contiguous, rough interfaces is presented. Numerical solutions using the finite element method are presented for a range of the government geometric and thermal parameters and for three interfacial configurations. The three interface shapes examined are the saw-tooth, the sine wave, and the square wave profiles. It is observed that in all cases the influence of the interface presence is to decrease the resistance below the one-dimensional, smooth interface value. This observation is supported through application of Elrod's two theorems to the problem configuration. Numerical solutions for the decrease in resistance, estimated to be within one percent of their true values, are presented for a range of conductivity ratios and interface amplitudes. It was observed that the effect of increasing both of these parameters is to increase the reduction in resistance due to the presence of the interface.