A. Introduction

When two similar or dissimilar solid materials at different temperatures are brought into contact, energy is transferred across the interface of contact. If the two surfaces could be obtained free of contamination and brought into perfect contact without any gaps at the interface, the resistance to the flow of heat would be negligible. However, this condition is not one obtainable in practice. Hard surfaces, including metals, even when highly polished and apparently flat, show appreciable contact resistance to heat flow. This resistance is caused by a lack of complete contact between the mating surfaces: i.e., when two surfaces are pressed together, contact is actually made only at a few discrete points due to the individual surface roughness and microscopic asperities, as illustrated in Figure 1. As the interface is approached, heat flux lines tend to converge to the direct solid-to-solid contact points since this path offers less resistance than the gaps which may be filled with air or evacuated. The result is the formation of a temperature discontinuity at the interface.

Figure 1 Imperfect mating of contacting solid surfaces

For metal surfaces, the solid-to-solid contact area between the surfaces is generally a small fraction of the apparent area over which they meet. The direct contact area may be less than 1 percent of the total and generally exceeds 10 percent only when bonding agents or surface enhancements are used. When the pressure on the contact is increased, the peaks in contact will deform and the contact points will increase in both size and number. For dissimilar metals, the irregularities of the softer surface may undergo full plastic deformation while the peaks of the harder metal embed in the softer.

Thermal contact resistance (TCR) is defined as