## 4 Results and Investigations
### Cooling Analysis Characteristics
The overall trends were similar to when uni-directional cooling was performed with water, but relatively even cooling was achieved by using bi-directional cooling, and the cooling was quick compared to when nitrogen was used. During cooling, a maximum temperature deviation of 4 degrees occurred, and a deviation of less than 0.2 degrees was maintained after 300 s. Compared to uni-directional cooling, there was no marked difference in temperature deviation, unlike when nitrogen was used. In the case of bidirectional cooling, even when nitrogen was used, a temperature difference of less than 2 degrees was achieved at a rate of 10 m/s. When water was used, a temperature difference of less than 2 degrees was not achieved in less than 5 s regardless of the rate. Figure 14: Temperature distribution in Figure 13 except for the fact that the flows in all of the cooling holes are uni-directional. Figure 15: Variation of the maximum temperature difference on the hot plate surface estimated from Figure 14.  
In an actual small hot plate, sufficient cooling is only possible through direct cooling with a cooling fluid. Up to this point, the results for direct cooling have been described. The results for indirect cooling are as follows. For the hot plate model that uses a heat pipe, the loss was less than 10% of the total supplied heat in the results found by using Equation (3). As such, the calculations were performed assuming that 90% cooling was performed using the heat pipe and assuming that the supplied heat was 150 W. It can be determined that the emitted heat was excessive. However, the heat pipe case was the same as the case in which cooling was performed on a 340 mm long portion at 200 mm using 15 \({}^{\circ}\)C air at 30 m/s. The cooling time was calculated for up to 200 s. The measurement points were P1 and P6 from the same 9 points shown in Figure 11:0 Figure 18 shows the abnormal temperature behavior at 6 points. Since the end of the heat pipe is cooled by convection, it showed an overall monotone decrease. Figure 19 shows the difference between the maximum and minimum temperatures over time in order to quantitatively analyze the temperature difference shown in Figure 11:1 Overall, the temperature difference between the maximum and minimum temperatures over time in order to quantitatively analyze the temperature difference shown in Figure 18 is much smaller than the temperature difference. Figure 11:2 The legends are the same as in Figure 12 except for the fact that the flows in all the cooling holes are bi-direction. Figure 11:3 Variation of the maximum temperature difference on the hot plate surface estimated from Figure 11:4  
difference at the hot plate's upper surface was maintained at less than 6.5 \({}^{\circ}\)C over time. In order to observe the temperature field of the upper surface in areas outside of the measurement points, Figure 20 shows the upper surface temperature at a cooling time of 200 s. It can be seen that the overall temperature field has a temperature deviation of less than 2.55 \({}^{\circ}\)C. The analysis that was performed up to this point has confirmed the usability of the hot plate heating model that uses the proposed controller and the hot plate cooling model that uses a heat pipe. Figure 11:5 Variation of the maximum temperature difference on the hot plate surface estimated from Figure 11:6  
Figure 11:7 Time-dependent evolution of the temperature at the 6 points on the upper surface of Al hot plate by indirect cooling using heat pipes. The heat release is 135 W.