Thermal conductance of metallic contacts

Across a contact joint, different modes of heat transfer take place, namely, by conduction through the metallic junctions, by conduction of the fluid through the interstitial space and by radiation. They are in reality interrelated so that any solution to the problem must take into account the inter-dependent nature of these three modes. The greatest obstacle to the seeking of a satisfactory solution lies in the uncertainty of the size and distribution of metallic junctions engaged in contact and of the exact dimensions of the interstitial space which is usually filled with a fluid of a lower thermal conductivity than that of the metal. Under these circumstances, it is necessary to introduce an idealised contact model for the convenience of obtaining a mathematical solution. In this model the contact members are represented by two circular cylindrical blocks while the irregularities on the surfaces which are engaged in contact are represented by two protuberant junctions of cylindrical shape with a diameter smaller than that of the main blocks. The thermal resistance of these junctions, however small it may be, is considered to have a governing effect on the heat transfer characteristics of a contact joint and it is included in the formulation of the theory. The theory thus obtained can be conveniently extended to cover contact models other than the idealised one with cylindrical junctions. Since the shape of the asperities on a surface resembles a cone more than a circular cylinder, it is suggested that a more realistic contact model could be one having its contact junctions represented by a pair of conic frusta. By taking an appropriate equivalent thermal conductivity of the junctions, the theory derived from the idealised contact model can be applied without any modification. A simplified method for the solution of a contact problem is also suggested. This method under certain conditions yields results very close to those obtained by the analytical method. The merit of this method lies in its comparative ease of formulation. Experiments were carried out for the study of the fundamental phenomena of heat transfer across a metallic contact. In order to achieve this object it was necessary to eliminate some of the governing factors for others to be observed. To overcome the obscurity of the matching condition at a contact interface an artificial contact joint was introduced. This was done by inserting small steel balls and small aluminium discs between the contact surfaces for different experiments. The contact thermal conductance was measured under conditions in vacuum and with argon and helium gases, while the inserted objects were subjected to an applied load of various magnitudes. The test results agree favourably with the calculated values. They also confirm that the thermal conductance of a contact cannot be reliably determined from electrical measurements. The hysteresis phenomenon observed by a number of investigators was found to be due to the seizure of the contact junctions as well as due to the irreversible deformation of the material. The primary governing factors of heat transferred through the fluid path and through the solid path are the fluid contact parameter Kf, the solid contact parameter Ks and the contact area parameter X. By specifying the magnitudes of these parameters, it is possible to estimate the heat transfer rate through each path. By altering their values, it may also be possible to control the thermal contact conductance for a given purpose