Thermal conductance of a rough elastic contact

From an existing theory of the elastic contact of an isotropically rough Gaussian surface in terms of moments of its power spectrum, limiting expressions for the number and average size of contact spots are derived and hence an upper-bound expression for the solid thermal contact conductance is obtained in terms of the separation of the contacting surfaces. It is shown that over a realistic range of loads, conductance and number of contacts are approximately proportional to the load and contact size is almost independent of load. Equivalent moments are defined such that the geometry of anisotropic surfaces can be represented by equivalent isotropic equations in good agreement with experiment. The problems of quantifying the moments are discussed and it is shown how equivalent moments may be obtained from simple measurements on two profiles at right angles.