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research-article

# Effect of Surface Curvature on Contact Resistance between Cylinders

[+] Author and Article Information
Michael Mayer

Department of Mechanical Engineering, Tufts University, Medford, MA, USA
michael.mayer@tufts.edu

Dr. Marc Hodes

Department of Mechanical Engineering, Tufts University, Medford, MA, USA
marc.hodes@tufts.edu

Toby Kirk

Mathematical Institute, University of Oxford, Oxford, England
toby.kirk12@imperial.ac.uk

DARREN Crowdy

Department of Mathematics, Imperial College, London, England
d.crowdy@imperial.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4042441 History: Received July 24, 2018; Revised December 19, 2018

## Abstract

Abstract Due to the microscopic roughness of contacting materials, an additional thermal resistance arises from the constriction and spreading of heat near contact spots. Predictive models for contact resistance typically consider abutting semi-infinite cylinders subjected to an adiabatic boundary condition along their outer radius. At the nominal plane of contact an isothermal and circular contact spot is surrounded by an adiabatic annulus and the far-field boundary condition is constant heat flux. However, cylinders with flat bases do not mimic the geometry of contacts. To remedy this, we perturb the geometry of the problem such that, in cross section, the circular contact is surrounded by an adiabatic arc. When the curvature of this arc is small, we employ a series solution for the leading-order (flat base) problem. Then, Green's Second Identity is used to compute the increase in spreading resistance in a single cylinder, and thus the contact resistance for abutting ones, without fully resolving the temperature field. Complementary numerical results for contact resistance span the full range of contact fraction and protrusion angle of the arc. The results suggest as much as a 10-15% increase in contact resistance for realistic contact fraction and asperity slopes. When the protrusion angle is negative, the decrease in spreading resistance for a single cylinder is also provided.

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