Thermal contact resistance

Imagine two solid bars brought into contact as indicated in Fig. 2-14, with the sides of the bars insulated so that heat flows only in the axial direction. The materials may have different thermal conductivities, but if the sides are insulated, the heat flux must be the same through both materials under steady-state conditions. Experience shows that the actual temperature profile through the two materials varies approximately as shown in Fig. 2-14b. The temperature 

The physical mechanism of contact resistance may be better understood by examining a joint in more detail, as shown in Fig. 2-15. The actual surface roughness is exaggerated to implement the discussion. No real surface is perfectly smooth, and the actual surface roughness is believed to play a central role in determining the contact resistance. There are two principal contributions to the heat transfer at the joint  

The conduction through entrapped gases in the void spaces created by the contact 

The second factor is believed to represent the major resistance to heat flow, because the thermal conductivity of the gas is quite small in comparison to that of the solids. 

Designating the contact area by A, and the void area by Ar, we may write for the heat flow across the joint 

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Gardner, K A. and T. C. Carnavas, Thermal-Contact Resistance to Pinned Tubing, Trans, of ASMEJour, of Heat Transfer, Paper No. 59-A-135. 

In 1959, Little [69] extended the acoustic mismatch model to interfaces between solids. The experiments have revealed that in this case, the thermal contact resistance between solids is higher than that evaluated from the model and that data are less reproducible. 

In 1987, Swartz [73] measured the thermal boundary resistance between metal films and the dielectric substrates onto which the films were deposited, in the range 0.6-200 K. A typical example is the measurement of the thermal contact resistance between indium and sapphire [72]. To minimize the dependence on surface irregularities, indium was vacuum deposited onto the sapphire rods the two surfaces were then pressed together and annealed. Analogous measurements have been carried out also with lead and aluminium. In all these cases, it has been clear that the contact resistance was strongly dependent on the sample preparation. In particular, obtained data suggest that the contact between the two materials was not complete. 

Fig. 4.4. Thermal contact resistance Rk multiplied by A T3 between liquid helium and various solids and also...

A system reaches the thermal equilibrium in a time that depends on its heat capacity, on the thermal conductance of the various parts and on the thermal contact resistance. The latter contribution becomes more important as the temperature decreases. The ideal... 

Mechanical properties of the sample In the simplest case, the sample stands alone (it is fixed by a screw as in measure of Section 11.5.2), or a support may be necessary as in the examples of Section 11.3.2 and Section 11.4.2. In the latter case, the support represents again a thermal conductance in parallel with the sample. Such shunt conductance must be taken into account for low-conductance samples. Contractions (or dilatations, see Chapter 13), which take place when the sample is cooled, not only change the geometrical factor, but also influence the mechanical joints and hence the thermal contact resistance. Various mechanical solutions, some of them very exotic , have been used in the measure of the thermal conductivity [2-4]. 

It should be noted that it is difficult to obtain models that can accurately predict thermal contact resistance and rapid solidification parameters, in addition to the difficulties in obtaining thermophysical properties of liquid metals/alloys, especially refractory metals/al-loys. These make the precise numerical modeling of flattening processes of molten metal droplets extremely difficult. Therefore, experimental studies are required. However, the scaling of the experimental results for millimeter-sized droplets to micrometer-sized droplets under rapid solidification conditions seems to be questionable if not impossible,13901 while experimental studies of micrometer-sized droplets under rapid solidification conditions are very difficult, and only inconclusive, sparse and scattered data are available. 

Figure 3.6 Thermal contact resistance between two solid surfaces.

If the thermal conductivity of the fluid is less than that of the two solids, then the interface between the two solids acts as a resistance to heat flow. This resistance is referred to the thermal contact resistance . It can be rather significant if the contact between the two solid surfaces is poor, and/or the fluid conductivity is much less than the conductivities of the solids. 

Note that the temperature drop ( Tla - Tib ) is caused by the thermal contact resistance between the surfaces of rod A and rod B. 

Fig. 2-14 Illustrations of thermal- contact-resistance effect (a) physical situation (b) temperature profile.

Fig. 2-15 Joint-roughness model for analysis of thermal contact resistance.

A very complete survey of the contact-resistance problem is presented in Refs. 4, 6, 7, and 10. Unfortunately, there is no satisfactory theory which will predict thermal contact resistance for all types of engineering materials, nor have experimental studies yielded completely reliable empirical correlations. 

For design purposes the contact conductance values given in Table 2-2 may be used in the absence of more specific information. Thermal contact resistance can be reduced markedly, perhaps as much as 75 percent, by the use of a thermal grease like Dow 340. 

What is meant by thermal contact resistance Upon what parameters does this resistance depend ... 

Moore, C. J., Jr., H. A. Blum, and H. Atkins Subject Classification Bibliography for Thermal Contact Resistance Studies, ASME Pap. 68-WA/HT-18, December 1968. 

A typical experimental setup for the determination of thermal contact resistance (from Song et al.). 

When two such surfaces are pressed against each other, the peaks form good material contact but the valleys form voids filled with air. As a result, an interface contains numerous air gaps of varying sizes that act as insulation because of the low thermal conductivity of air. Thus, an interface offers some resistance to heat transfer, and this resistance per unit interface area is called the thermal contact resistance, R. The value of is determined experimentally using a setup like the one shown in Fig. 3-15, and as expected, there is considerable scatter of data because of the difficulty in characterizing the surfaces. 

That is, thermal contact resistance is the inverse of thermal contact conductance. Usually, thermal contact conductance is reported in the jiterature, but the concept of thermal contact resistance serves as a better vehicle for explaining the effect of interface on heat transfer. Note that represents thermal contact resistance per unit area. The thermal resistance for the entire interface is obtained by dividing by the apparent interface area/t. 

When w c analyze heat transfer ifi a medium consisting of two or more layers, the first thing we need to know is whether the thermal contact resistance is significant or not. We can answer this question by comparing the magiii-tudes of th thermal resistances of the layers with typical values of thermal contact resistance. For example, the thermal resistance of a 1-cm-thick layer of an insulating material per unit surface area is... 

Comparing the values above with typical values of thermal contact resistance, we conclude that thermal contact resistance is significant and can even dominate the heat transfer for good heat conductors such as metals, but can be... 

Another way to minimize the contact resistance is to insert a soft metallic foil such as tin, silver, copper, nickel, or aluminum between the two surfaces. Experimental studies show that the thermal contact resistance can be reduced by a factor of up to 7 by a metallic foil at the interface. For maximum effectiveness, the foils must be very thin. The effect of metallic coatings on thermal contaci conductance is shown in Fig. 3-16 for various metal surfaces. 

SOLUTION The thickness of the aluminum plate whose thermal resistance is equal to the thermal contact resistance is to be determined. 

Analysis Noting that thermal contact resistance is the inverse of thermal contact conductance, the thermal contact resistance is... 

Discussion Note that the interface between the two plates offers as much re-sistanc to heat transfer as a 2.15-cm-thick aluminum plate. It is interesting that the thermal contact resistance in this case is greater than the sum of the thermal resistances of both plates. 

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