## 3 Results and Discussion
### Transient Performance under High Heat Flux Millisecond Pulses
#### 3.2.2 The Effects of the Thickness of the Metallic PCM Layer  
Metallic PCM can serve as a thermal buffer under heat pulses, but the effects of the PCM thicknesses on the cooling performance need to be further studied. When the filling thickness of PCM (\(\delta\)) is 1 mm, the variations of \(T_{\rm max}\) and the average phase change percentage of PCM (\(\gamma\)) are shown in Figure 9. It can be seen that during the calculation time, \(T_{\rm max}\) rises to the mean temperature of the phase change (\(T_{m}\) = 58 \({}^{\circ}\)C), and is temporarily maintained around \(T_{m}\), but then rises to a higher temperature quickly. The increase in the maximum \(T_{\rm max}\) slows down as it increases beyond 110 \({}^{\circ}\)C, but \(\gamma\) continuously increases, indicating a steady state has not yet been reached. As the same trend of \(\delta\) = 1 mm, When \(\delta\) is 0.5 mm, \(T_{\rm max}\) rises to \(T_{m}\) and is maintained around \(T_{m}\) temporarily. In addition, the time when \(T_{\rm max}\) can be maintained around \(T_{\rm m}\) is prolonged. After that, with the continuous increase in \(\gamma\), \(T_{\rm max}\) begins to rise, and the chip temperature cannot be kept within the allowed range. Figure 8: The variations in \(T_{\rm max}\) under heat pulses without PCM. Based on the above discussion on \(T_{\rm max}\) and \(\gamma\), it can be seen that \(T_{\rm max}\) can be maintained around \(T_{m}\) if the metallic PCM can completely return to the solid state (\(\gamma\) = 0) before the next heat pulse. If the PCM cannot fully recover to the solid state (\(\gamma\) > 0) during the heat pulse interval, the metallic PCM adjacent to the heating surface will lose heat storage capability due to phase change. As the thermal conductivity of metallic PCM (33.2 W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\) for solid, 10.6 W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\) for liquid) is far less than aluminum (238 W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\)), the heat cannot conduct away efficiently through the PCM within a short period. Therefore, the bottom temperature of the heat sink will start to rise when the next pulse comes. According to the calculation results of \(\delta\) at 1 mm and 0.5 mm, we can see that \(T_{\rm max}\) can be maintained within a certain range for a longer time after reaching \(T_{m}\) with the decrease in \(\delta\). The results of \(T_{\rm max}\) and \(\gamma\) when \(\delta\) are 0.1 mm and 0.05 mm are shown in Figure 10. It can be seen from the figure that \(T_{\rm max}\) and \(\gamma\) vary periodically when the thicknesses are 0.1 mm and 0.05 mm. The metallic PCM can be fully recovered to the solid state during heat pulse intervals, and \(T_{\rm max}\) and \(\gamma\) have been stabilized within a short period. \(T_{\rm max}\) can be maintained around \(T_{m}\), and the maximum temperature is reduced from 66.9 \({}^{\circ}\)C to 61.8 \({}^{\circ}\)C when \(\delta\) = 0.1 mm and 61.5 \({}^{\circ}\)C when \(\delta\) = 0.05 mm. \(T_{\rm max}\) changes little with the decrease in \(\delta\) from 0.1 mm to 0.05 mm, but the maximum \(\gamma\) is increased from 6.7% to 11.4%, indicating a more effective utilization of PCM. Figure 11 shows the phase change process of the metallic PCM after reaching the periodic state when \(\delta\) = 0.05 mm (corresponding to 44 ms\(-\)46.2 ms in Figure 10). The liquid fraction \(\theta\) is 0 before the arrival of the heat pulse. During the heating period, the liquid fraction \(\theta\) and phase change region increase rapidly, and then gradually decrease to 0 after the pulse. At the end of the heating period (45 ms), the phase change reaches its maximum, with a liquid fraction \(\theta\) greater than 0.9 at the bottom and the thickness is about 0.005 mm. In the perpendicular direction, the phase change extends to 1/2 of the thickness, and the liquid fraction \(\theta\) decreased with increasing thickness.