A three-dimensional fractal theory based on thermal contact conductance model of rough surfaces

Abstract

The thermal contact conductance is an important problem in the field of heat transfer. In this research, a three-dimensional fractal theory based on the thermal contact conductance model is presented. The topography of the contact surfaces was fractal featured and determined by fractal parameters. The asperities in the microscale were considered as elastic, elastic-plastic, or plastic deformations. The real contact area of the asperities could be obtained based on the Hertz contact theory. It was assumed that the rough contact surface was composed of numerous discrete and parallel microcontact cylinders. Consequently, the thermal contact conductance of the surface roughness was composed of the thermal constriction conductance of microcontacts and the air medium thermal conductance of microgaps. The thermal contact conductance of rough surfaces could be calculated by the microasperities integration. An experimental set-up with annular interface was designed to verify the presented thermal contact conductance model. Three materials were used for the thermal contact conductance analysis with different fractal dimensions D and fractal roughness parameters G. The numerical results demonstrated that the thermal contact conductance could be affected by the elastic-plastic deformation of the asperities and the gap thermal conductance should not be ignored under the lower contact load. The presented model would provide a theoretical basis for thermal transfer engineering application.