A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering
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When a junction is formed by pressing two similar or dissimilar metallic materials together, only a small fraction of the nominal surface area is actually in contact because of the nonflatness and roughness of the contacting surfaces. If a heat flux is imposed across the junction, the uniform flow of heat is generally restricted to conduction through the contact spots, as shown in Figure 1. The limited number and size of the contact spots results in an actual contact area which is significantly smaller than the apparent contact area. This limited contact area causes a thermal resistance, the contact resistance or thermal contact resistance.

The presence of a fluid or solid interstitial medium between the contacting surfaces may contribute to or restrict the heat transfer at the junction, depending upon the thermal conductivity, thickness, and hardness (in the case of a solid) of the interstitial medium. If there is a significant temperature difference between the surfaces composing the junction, heat exchange by radiation also may occur across the gaps between the contacting surfaces.

When a metallic junction is placed in a vacuum, conduction through the contact spots is the primary mode of heat transfer, and the contact resistance is generally greater than when the junction is in the presence of air or other fluid. In a vacuum, the temperature distribution in the contacting materials, with the resulting temperature difference at the junction, is shown in Figure 2 for both flat and cylindrical junctions.

This temperature difference is used to define the contact resistance at the junction, such that:

(1)

where T1 and T2 are the temperatures of the bounding contact surfaces, S is the area across which the heat is transferred, and ac is the heat transfer coefficient for the junction, or the thermal contact conductance. This contact conductance or joint conductance is often reported in the literature and is defined as:

(2)

The magnitude of the contact conductance is a function of a number of parameters including the thermophysical and mechanical properties of the materials in contact, the characteristics of the contacting surfaces, the presence of gaseous or nongaseous interstitial media, the apparent contact pressure, the mean junction temperature, and the conditions surrounding the junction, as noted by Fletcher (1988).

In view of the significant number of parameters affecting the contact conductance or contact resistance, it has not been possible to develop a single analytical expression for the prediction of the contact resistance at a junction between two materials, except for cases of highly idealized single and multiple contacts. An overview of the idealized models has been reported by Sridhar and Yovanov-ich (1994). An analytical expression for predicting the contact conductance of nonflat or machined metallic surfaces in contact has been developed by Lambert and Fletcher (1995) for a wide range of metallic materials and test conditions. Despite the availability of these models, a majority of the. contact resistance information is determined experimentally in order to provide a measure of the thermal performance of a specific configuration or system.

Most experimental contact resistance data are obtained using a traditional cut-bar, vertical column test facility in a vacuum or ambient environment over a range of steady-state test conditions. More specialized test facilities have been developed for use with such configurations as bolted joints, periodic or sliding contacts, concentric cylinders, and full scale or partial scale models, while some configurations are studied by electrolytic analogue techniques. Essentially all of these experimental facilities may be used for evaluation of metallic and nonmetallic materials in contact, or metallic and nonmetallic materials with gaseous or nongaseous interstitial media between the contacting surfaces, over a wide range of test parameters.

The force applied to the nominal contact area of the junction provides the apparent contact pressure on the junction. The mean junction temperature, Tm, is the average of the contacting surface temperatures. The apparent contact pressure and the mean junction temperature, combined with the thermophysical and mechanical properties of the contacting materials and the surface characteristics, are the primary factors in determining the magnitude of the contact resistance. High junction loads and high temperatures result in low contact resistances, whereas light junction loads and low temperatures lead to high contact resistances.

The surface finish, or roughness and flatness of the contacting surfaces, can significantly affect the magnitude of the contact resistance. If the axial force on the contacting surfaces is increased, the surface roughness peaks or asperities may deform plastically or elastically, depending upon the material properties, leading to increased contact area and decreased contact resistance. An elevated temperature at the junction may also cause plastic and/or elastic deformation of the roughness asperities, especially for softer materials, with an associated increase in the actual contact area and a decrease in the contact resistance. Typical contact resistance values for Aluminum 2024-T4 samples in contact at moderate test conditions in a vacuum environment are shown in Figure 3, to demonstrate the effect of surface finish and mean junction temperature on contact resistance [Fletcher (1991)].

Some additional factors which may affect the contact resistance are the direction of the heat flux, surface scratches or cracks, nonuniform loading which causes uneven contact pressure, relative motion or slipping between the surfaces, and the presence of oxides or contaminants on the contacting surfaces.

The use of interstitial or thermal control materials for thermal enhancement or thermal isolation of metallic junctions further effects the contact resistance. Although there are variations in material thickness and composition, the contact resistance for representative interstitial materials is shown in Figure 4. These interstitial materials have been categorized as greases and oils; metallic foils and screens; ceramic composites and cements; and synthetic and natural sheets [Fletcher (1972)]. While metallic foils and greases are often used for thermal enhancement, most of the interstitial materials are generally used for thermal isolation.

Surface treatments, or coatings and films, may also be used for thermal enhancement or thermal isolation. Metallic coatings provide modest to significant thermal enhancement, depending upon the metal used and the method of application. Ceramic coatings provide modest to excellent thermal isolation depending upon the choice of material. Ceramic coatings may also provide hard, corrosion resistant coatings that are not electrically conducting. Care must be taken to assure that galvanic corrosion will not occur with the choice of materials for some applications.

#### REFERENCES

Fletcher, L. S. (1972) A review of thermal control materials for metallic junctions, A1AA Journal of Spacecraft and Rockets, 9, 12, 849–850.

Fletcher, L. S. (1988) Recent developments in contact conductance heal transfer. ASME Journal of Heat Transfer, 110, 4B, 1059–1070.

Fletcher, L. S. (1991) Conduction in solids—Imperfect metal-to-metal contacts: Thermal contact resistance, Section 502.5, Heat Transfer and Fluid Mechanics Data Books, Genium Publishing Company, Schenectady, New York.

Lambert, M. A. and Fletcher, L. S. (1995) Thermal Contact Conductance of Spherical Rough Metals: Theory and Comparison to Experiment, Proceedings of the ASME/JSME Thermal Engineering Joint Conference, Maui, Hawaii, March 19–24.

Sridhar, M. R. and Yovanovich, M. M. (1993) Critical Review of Elastic and Plastic Contact Conductance Models and Comparison with Experiment, AIAA Paper 93-2776, A1AA Thermophysics Conference, Orlando, Florida, July 6–9.

#### References

1. Fletcher, L. S. (1972) A review of thermal control materials for metallic junctions, A1AA Journal of Spacecraft and Rockets, 9, 12, 849â€“850. DOI: 10.2514/3.61809
2. Fletcher, L. S. (1988) Recent developments in contact conductance heal transfer. ASME Journal of Heat Transfer, 110, 4B, 1059â€“1070.
3. Fletcher, L. S. (1991) Conduction in solidsâ€”Imperfect metal-to-metal contacts: Thermal contact resistance, Section 502.5, Heat Transfer and Fluid Mechanics Data Books, Genium Publishing Company, Schenectady, New York.
4. Lambert, M. A. and Fletcher, L. S. (1995) Thermal Contact Conductance of Spherical Rough Metals: Theory and Comparison to Experiment, Proceedings of the ASME/JSME Thermal Engineering Joint Conference, Maui, Hawaii, March 19â€“24.
5. Sridhar, M. R. and Yovanovich, M. M. (1993) Critical Review of Elastic and Plastic Contact Conductance Models and Comparison with Experiment, AIAA Paper 93-2776, A1AA Thermophysics Conference, Orlando, Florida, July 6â€“9.