Experimental data of thermal contact conductance (TCC) between two metallic rough surfaces versus the applied load (pressure) distinctly exhibit non-linear behavior that can be split into two regimes with two distinct slopes. When the load is small, the rate of change of TCC with load is linear with a small slope. At intermediate loads, this slope increases. A third slope has been exhibited in some cases at extremely high loads — one in which the slope decreases again. In this study, two types of analysis are conducted on a simplified model system comprised of a single asperity compressed by two flat surfaces. The first analysis assumes one-dimensional heat conduction across the asperity, resulting in a fin-equation type model. In the second analysis, two-dimensional heat conduction through the asperity is considered, and the governing steady state heat conduction equation is solved numerically. Results show that the first two slopes at low and intermediate loads can be captured by both models. However, when the asperity is significantly depressed (high load regime) and deformed, the experimental behavior of the third reduced slope can only be captured by the two-dimensional numerical model. This implies that when the asperity deforms significantly, multi-dimensional heat transport becomes a critical limiting factor for the TCC.

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