# Experimental Investigation of Thermal Contact Conductance in a Bundle of Flat Steel Bars
## 3 Calculations and Results
Using the maximum values of the radiation conductance and joint conductance for each sample a percentage share of the thermal radiation  
Using the maximum \(h_{rd}\) values from Figure 7 for each of the analysed samples the contact conductance \(h_{ct}\) has been calculated:  
\[h_{ct}=h_{j}-h_{rd}, \tag{21}\]  
Calculation results of \(h_{ct}\) conductance for individual samples are presented in Figure 9. When analysing the results from Figure 9 it must be mentioned that in this case \(h_{ct}\) conductance expresses quantitatively the heat transferred across the joint both by conduction through microcontacts and conduction within the gas which fills the gaps. Due to the lack of information on the parameters describing the geometry of microcontacts in the joints of the analysed samples, it is not possible to express the above-mentioned mechanisms of heat transfer separately. However, in terms of practical application such a separation is not particularly important since for modelling of the heat transfer in bar bundles the most important point is the information on the global heat transfer through the joints. Figure 6:0 Calculated values of the percentage share of radiation in the joints: (**a**) results obtained for samples made of 5 \(\times\) 20 mm bars; (**b**) results obtained for samples made of 10 \(\times\) 40 mm bars. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & \(\mathbf{X_{rd-arc}}\) \% & \(\mathbf{X_{rd-arc}}\) \% \\ \hline
5 \(\times\) 20 TR & 8.8 & 21.7 \\
5 \(\times\) 20 PA & 19.1 & 45.0 \\
5 \(\times\) 20 MI & 17.5 & 41.5 \\
10 \(\times\) 40 TR & 14.7 & 36.9 \\
10 \(\times\) 40 MI & 22.0 & 50.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average and maximum values of \(X_{rd}\) parameter obtained for individual samples. Figure 7: Calculation results of the radiation conductance depending on the contact coefficient and surface emissivity. Contrary to joint conductance, the changes of contact conductance in the temperature function are not linear. The functions which can be used to describe temperature changes \(h_{ct}\) for all the samples are second degree polynomials:  
\[h_{ct}(t)=B_{5}\,t^{2}+B_{6}\,t+B_{7}, \tag{22}\]  
The values of \(B_{5}\), \(B_{6}\), \(B_{7}\) and \(R^{2}\) coefficients obtained for individual samples are collated in Table 6.  
For most samples the maximum value of contact conductance \(h_{ct}\) occurs in the temperature range from 300 \({}^{\circ}\)C to 400 \({}^{\circ}\)C. Table 7 presents the minimum, average and maximum \(h_{ct}\) values. The obtained character of the temperature changes of the \(h_{ct}\) coefficient is difficult to explain unambiguously at the present stage of the investigation. This results from the fact that the intensity of thermal contact conductance is influenced by many factors, such as: mechanical and thermal properties of bulk materials, the geometrical structure of the surfaces, the interstitial medium and the mean temperature of the joint [29]. The basic parameters of a geometrical structure of the surface, which determine the thermal contact conductance are: the root mean square (r.m.s) deviation of surface height \(\sigma_{p}\), and r.m.s. slope \(\sigma^{\prime}\) of the roughness [39]. For the given contacting solids, the amount of heat transferred by conduction depends on the number and size of the contact spots and the effective gap's thickness. This joint microgeometry results not only from microgeometry of both surfaces creating contact but also from the mechanical properties of the solids as well. The mechanical properties that influence thermal contact conductance are: [PERSON]'s modulus \(E\), [PERSON]'s ratio \(\
u\), the surface microhardness \(H_{c}\) (higher than hardness of bulk material) and the yield strength \(Y\). The listed factors depend on temperature and are often mutually connected. Therefore, at the current stage of investigation it is not possible to