# A Novel Liquid-Solid Fluidized Bed of Large-Scale Phase-Changing Sphere for Thermal Energy Storage
## 4 Results and Discussion
### Rationalizing the Enhanced Heat Transfer  
It can be seen from Section 4.2 that the heat-absorbing and -releasing rate can be greatly enhanced by the fluidization movement. Both the reduced convection resistance outside the spheres and the enhanced phase changing heat transfer inside the spheres can be responsible for this. Taking 20 min as an average phase-changing duration (this can be justified from Figures 8 and 9), the overall heat-transfer coefficient from inside the PCM to outside the fluid can be estimated to be 62.5 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) (the total heat transferred  
Figure 9: Variation of brightness along with PCM melting or solidifying for a fluidized bed. being the latent heat of the PCM and the temperature difference being 7 K). Meanwhile, using the correlation \(Nu=2+0.27\)\(Re^{0.62}Pr^{1/3}\)[34], which was developed to predict the heat-transfer coefficient for fluid flowing around a ball, the external convection coefficients between the outted surface of the PCM sphere and fluid are estimated to vary between 890 and 1360 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) within the flow rates covered. Considering this huge difference in the order of magnitude, it can be confidently confirmed that the main thermal resistance lies in the interior of the PCM sphere. This order of magnitude analysis also acts as an explanation for why the increasing flow rates shown in Figures 8 and 9 merely manifest influence on phase-changing duration. With the above analysis, it can be concluded that it is the enhanced phase-changing heat transfer inside the spheres that mostly contributes to the accelerated heat-absorbing or -releasing rate, during which the fluidization plays an important role. To explore the underlying mechanisms for the increased heat transfer inside spheres, high speed videography of 240 fps was adopted with 1080 pixels width and 1920 pixels height covering a physical width of 90 mm and height of 160 mm. Figure 10 shows three modes of movement of the PCM spheres caused by the fluidization. Figure 10a,b were drawn by extracting one particular sphere in multiple successive frames (with time interval 0.05 s) and overlapping them in one image. Figure 10c was obtained by extracting two spheres that are about to collide and arranging them in the sequence (with time interval 0.05 s) indicated by the arrow. As shown in Figure 10a where the sphere is accelerating when moving upwards and changing velocity direction, the shifting movement features variation of velocity in both magnitude and direction. The rotating movement features rotating with possible translational movement, as shown in Figure 10b. Through scrutinizing the high-speed video, it is found that the rotating could be caused by collision with other spheres or the wall of the bed. Colliding movement can occur between spheres and between the sphere and the wall, and two colliding spheres are demonstrated in Figure 10c. Countless occurrences of all these three modes constitute the fluidization of the PCM spheres. It can be observed from Figure 10 that the relative motion of the un-melted PCM with the sphere wall, or the so-called motion of the solid-liquid interface, could be stimulated by the shifting, rotating and colliding of spheres. The motion of the solid-liquid interface is due to differences in solid and liquid properties, including but not limited to density. Meanwhile, the vacant space left to tolerate the possible volume change in PCM forms a liquid-gas interface, which is also found to oscillate when the three movement modes occur. Both relative motions of the solid-liquid interface and the liquid  
Figure 10: Three basic movements caused by fluidization contributing to heat-transfer enhancement. gas interface play roles in stirring the internal flow field and thus enhance the convection heat transfer inside.