## 3 Results and Discussion
### Infrared Image Analysis and Calculations  
#### 3.2.1 Calculation of Zone Length and Molten Zone Thermal Gradient  
The obtained thermographic image by the infrared camera after applying the proper calibration (explained in Section 2.1) is a clear and quite precise view of the temperature distribution on the surface of the metallic bar. Figure 8 shows the molten zone region during the zone refining of the example metal, aluminum. By selecting the appropriate color schemes, the molten zone (showed within the dashed rectangle) was recognized. Therefore, a series of thermographic pictures was recorded throughout the entire zone refining process to obtain the temperature distribution in the region, the zone length across the bar, as well as the exact growth rate. The raw data measured through this system were recorded and later analyzed. The camera was adjusted to record one frame per minute during the whole zone refining process. A faster picture recording for the whole length of the bar would lead to too many data and make the process more complicated. Nonetheless, the number of the total frames is so big that they had to be captured and processed again by a MATLAB script. In Figure 9, the recorded thermographic images illustrate the molten zone at an hourly interval for a length of a 600-mm aluminum bar subjected to induction heating power (from 10-11 kW and a 0.8-mm min\({}^{-1}\) travel rate). This image sequence shows the changes in the molten zone, as well as the variation in the temperature profile alongside the bar. For every recorded frame, a temperature profile along the middle of the crucible (see the red line in Figure 9) is extracted from the thermographic image, and in each one of these frames, the information about the temperature distribution, as well as the molten zone length can be demonstrated, as shown in Figure 10. Here, based on the smoothed temperature profile, the intervals that are over the liquidus point of aluminum (660 \({}^{\circ}\)C) are determined as the length of the molten zone. These measured  
Figure 8: An infrared thermographic picture showing the zone length in the middle portion of the bar and the horizontal and vertical temperature profile at the middle of the molten zone. values correspond to the pixel interval from the IR image, which were later converted to millimeters in MATLAB. Additionally, the values of the temperature gradient (\(\Delta\)T/\(\delta\)x) between the freezing interface and the highest temperature value in the molten zone were calculated for every frame. The \(\Delta\)T value was calculated by subtracting the highest temperature within the zone length from the temperature at the freezing interface. The \(\delta\)x was the distance between the position where the highest temperature was and the freezing interface. Figure 11 illustrates how the temperature gradient varies along a bar of 600 mm in length, based on the example of Figure 9. It can be seen that the gradient is slightly decreasing while moving towards the middle of the bar, as it is departing from the massive graphite crucible sides, or stays quite low and constant in the middle part of the bar. Accepting the fact that a lower temperature gradient means a lower growth rate and as a consequence a higher removal efficiency, the application of an IR system can deliver the most profitable information to control the refining efficiency through such diagrams. However, whether this temperature gradient alone is the effective parameter to control a zone refining process or it is a mixture of many influencing factors such as changing the zone length, the absolute values of the growth rate, etc., are still not clear exactly. By all means, the IR camera system can be useful to investigate these terms, as well, as explained in the following subsections. Figure 9: Thermographic image of every hour from start to finish of one pass of zone refining. The temperature measured by the IR camera refers to the surface temperature according to the calibration performed (see Table 1).