An analytical model of thermal contact resistance based on the Weierstrass—Mandelbrot fractal function

Abstract

Abstract

A fractal model for analysing the thermal contact resistance (TCR) of rough surfaces is presented; it is based on the classical heat conduction theory and fractal geometry for the surface topography description, elastic—plastic deformation of contacting asperities, and size-dependent constriction resistance. Relations for the TCR in terms of contact load are obtained for heat conductive surfaces with known material properties and surface topography. With the real contact area being approximately 1 per cent of the apparent contact area or less, the microcontact area distribution has a dominant influence on the TCR. Useful design guidelines for heat contacts are extracted from the numerical results. The analytical results agree well with previous experiments.