Fractal Network Model for Contact Conductance

[+] Author and Article Information
A. Majumdar

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287

C. L. Tien

Office of the Chancellor, University of California, Berkeley, CA 94720

J. Heat Transfer 113(3), 516-525 (Aug 01, 1991) (10 pages) doi:10.1115/1.2910594 History: Received May 16, 1990; Revised January 12, 1991; Online May 23, 2008


The topography of rough surfaces strongly influences the conduction of heat and electricity between two surfaces in contact. Roughness measurements on a variety of surfaces have shown that their structure follows a fractal geometry whereby similar images of the surface appear under repeated magnification. Such a structure is characterized by the fractal dimension D , which lies between 2 and 3 for a surface and between 1 and 2 for a surface profile. This paper uses the fractal characterization of surface roughness to develop a new network model for analyzing heat conduction between two contacting rough surfaces. The analysis yields the simple result that the contact conductance h and the real area of contact At are related as h ~ At D/2 where D is the fractal dimension of the surface profile. Contact mechanics of fractal surfaces has shown that At varies with the load F as At ~ Fη where η ranges from 1 to 1.33 depending on the value of D . This proves that the conductance and load are related as h ~ Fη D/2 and resolves the anomaly in previous investigations, which theoretically and experimentally obtained different values for the load exponent. The analytical results agreed well with previous experiments although there is a tendency for overprediction.

Copyright © 1991 by The American Society of Mechanical Engineers
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