## 3 Results
### Calculated Heat Transfer Coefficients  
Using the measured temperatures of both the wire samples and the lead bath, the heat transfer coefficients are calculated according to the approach described in Section 3.3. The resulting heat transfer coefficients as well as the measured and calculated temperature curves during cooling are shown in Figure 7. In this case, the results for sample 2 from Figures 5 and 6 are displayed. The calculated temperature curve shows good agreement with the measured one over the whole cooling duration. The maximum deviation between the two curves is in the range of 10 K. Since the influence of the phase transition is difficult to predict and the cool-down to the starting point of this transition leaves enough measurement points, only the data up to 2.5 s are displayed and used for the calculation of the heat transfer coefficient. The calculated heat transfer coefficient shows a steep rise as soon as the sample is submerged into the lead bath. During the transport through the protective atmosphere into the lead bath at t \(<\) 1 s, the heat transfer coefficient is 187 W/m\({}^{2}\)K. This rather high  
Figure 7: Measured and calculated temperature curves for sample 2 as well as heat transfer coefficients as a function of the trial duration. value is a result of the model setup, where radiation was neglected during the transport time. Therefore, the convective heat transfer is overestimated. This was done mainly for reasons of simplicity, since the precise calculation of the heat transfer coefficient during the transport is no objective of this work. The transport time was, nonetheless, included in the calculation to determine the start of the immersion in the lead bath correctly. After that, the heat transfer coefficient rises to 8000 W/m\({}^{2}\)K. This steep rise in the heat transfer coefficient starts a few fractions of a second before the temperature begins to fall at a steeper gradient. This offset is due to the fact that the heat transfer coefficient is calculated at the surface while the temperature is measured at the centre. Therefore, the heat must be conducted from the surface to the centre to cause a temperature change, which causes the offset between the two curves. The evaluation method was applied in the same way to all measurements conducted (see Table 1 in Appendix A). All in all, only four samples could not be evaluated. The main reasons for this inconvenience were thermocouples that slipped out of the sample during the experiments and problems during the sample transport into the lead bath, especially for larger sample diameters. For other samples, the evaluation was possible but resulted in unreasonably high heat transfer coefficients. This was mainly due to the thermocouple moving out of the sample during the trials, causing a discontinuous temperature curve. The calculated heat transfer coefficients for the other samples are shown in Figure 8 as a function of the sample diameter. Additionally, the different steel grades, carbon steel and SiCr-alloyed steel, are shown with different markers. The calculated heat transfer coefficients show a clear dependence on the sample diameter. The heat transfer coefficients increase with decreasing diameter. Therefore, the samples with a diameter of 1.8 mm show the highest heat transfer coefficients with about 12,800 W/m\({}^{2}\)K. On the other hand, the samples with a diameter of 15.0 mm have a heat transfer coefficient of only 3500 W/m\({}^{2}\)K. Overall, the heat transfer coefficients follow a regression curve that can be approximated using the reciprocal of the square root of the diameter, which is also shown in the figure. The biggest deviation from this can be seen for the samples with a diameter of 1.8 mm and 3.0 mm. Also, the samples for a diameter of 5.5 mm show a higher heat transfer coefficient than those with a diameter of 3.0 mm. The reason for this is not clear and most likely a result of slightly varying conditions at the industrial lead bath used for the measurements.