Thermal Contact Conductance

Microscopic and macroscopic irregularities are present in all practical solid surfaces. Surface roughness is a measure of the microscopic irregularity, whereas the macroscopic errors of form include flatness deviations, waviness and, for cylindrical surfaces, out-of-roundness. Two solid surfaces apparently in contact, therefore, touch each other only at a few individual spots (Fig. 1.1). Even at relatively high contact pressures of the order of 10 MPa, the actual area of contact for most metallic surfaces is only about 1 to 2% of the nominal contact area (see, e.g., Bowden and Tabor, 1950). Since the heat flow lines are constrained to flow through the sparsely spaced actual contact spots, there exists an additional resistance to heat flow at a joint. This resistance manifests itself as a sudden temperature drop at the interface.

It was seen in Chapter 1 that the contact interface consists of a number of discrete and small actual contact spots separated by relatively large gaps. These gaps may be either evacuated or filled with a conducting medium such as gas. In the first case, all of the heat flow lines are constrained to pass through the contact spots. If the gaps are filled with a conducting medium, however, some of the heat flow lines are allowed to pass through the gaps, that is, they are less constrained and thus the constriction is alleviated to some extent.

When both sides of the contact spot are considered (Fig. 3.1), the total resistance is simply the sum of the resistances for each side of the contact. Therefore, if k ₁ and k ₂ are the thermal conductivities of the two solids in contact, then the resistance associated with a single contact spot is given by: where F is the constriction alleviation factor defined in chapter 2 and is the harmonic mean of the conductivities.

At low contact pressures (of the order of 10^-4 H or less), it can be shown that the heat transfer across a joint occurs mainly through the gas gap (Madhusudana, 1993). Boeschoten and van der Held (1957) had also made the qualitative observation that heat transfer was predominantly through the gas gap for “low (up to several kg/sq cm)” contact pressures. Furthermore, Lang (1962) pointed out that the convective heat transfer is usually negligible for gap widths of up to about 6 mm (corresponding to Grashof numbers of 2000 for air at atmospheric pressure of 101 kPa and temperature of 300 K). Since the mean separation between contacting engineering surfaces is some three orders of magnitude less than this dimension, it is clear that convection cannot be the mode of the heat transfer across the gas gap. Thus, the mode of heat transfer across the gas filling the voids between the actual contact spots, as also noted earlier, is principally by conduction.

Thermal conductance of joints may be determined experimentally in several ways. However, by far the most common method uses the axial flow apparatus in which two cylinders of similar or dissimilar materials are placed end to end as illustrated in Fig. 1.2 (Chapter 1). There have been other apparatus built for specific needs, for example, to determine contact conductance in concentric cylinders when the heat flow is radial; in periodic contacts; and in transient situations. In every case, before the heat transfer experiments are performed, it is necessary that profilometric measurements are made to characterize the surfaces. It is also necessary to determine the microhardness of the surfaces prior to the heat transfer tests.

As noted in Chapter 1, the actual solid-to-solid contact area, in most mechanical joints, is only a small fraction of the apparent area. The voids between the actual contact spots are usually occupied by some conducting substance such as air. Other interstitial materials may be deliberately introduced to control, that is, either to enhance or lessen, the thermal contact conductance: examples include foils, powders, wire screens, and epoxies. To enhance the conductance, the bare metal surfaces may also be coated with metals of higher thermal conductivity by electroplating or vacuum deposition. Greases and other lubricants also provide alternative means of enhancing thermal conductance of a joint.

The discussion, so far, has been concerned basically with the general nature of contact heat transfer. In this chapter, some specific problems in thermal contact conductance will be considered. These include special contact configurations, such as bolted or riveted joints, and cylindrical joints. The effect of the direction of heat flow and the loading history will be considered next in separate sections. This is followed by a discussion of packed beds and stacks of laminations. In these applications, the contact resistance plays a major role in controlling their effectiveness as insulators. Finally, in view of their particular significance, contact heat transfer in specific materials, such as nuclear fuel elements and other specific materials, and the contact conductance in the presence of oxide films, will be considered in some detail.

Having discussed the influence of various parameters, surface configurations and types of thermal and mechanical loading, it is now possible to review the means by which the TCC (or TCR) can be controlled to suit a given practical application. The first section of the present chapter summarizes the possible methods of control; for more specific details, reference may be made to the relevant sections in the earlier chapters.