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Heat Transfer Behaviours of Melting Process

Ice Thermal Storage (ITS) performance for cooling systems is greatly influenced by the poor thermal conductivity of Phase Change Material (PCM). The effect of natural convection on the melting process is significant for heat transfer enhancement. Thus, the melting performance of PCM in a Shell-and-Tube Latent Heat Storage (STLHS) unit is numerically studied by considering natural convection in terms of various heat source positions and configurations, i.e., central position, eccentric position, and flat-tube type. Temperature distribution, melting time, and the overall heat transfer coefficient during the process are investigated. The results show that the circulation vortex formed by natural convection is a dominant factor that affects melting front evolution and the overall heat transfer coefficient. When input heat flux is relatively weak, PCM below the heat source is liquefied first. In contrast, PCM in the upper part melts earlier when the heat flux is excellent.

July 14, 2023

The overall heat transfer coefficient decreases sharply with the increase in melting time in the early stage. Then, the heat transfer coefficient tends to be constant. PCM in an STLHS unit with a heat source in a lower position and a configuration of vertical flat-tube type has a desirable performance when compared with other cases, which could provide good support for ITS application…

Heat Source in Eccentric Postions

Figure 6 shows thermal characteristics of PCM in an STLHS unit based on a heat source in eccentric positions where up and down eccentric positions are illustrated. Figure 6a,b demonstrate the situation when considering different levels of heat flux, i.e., 500W.m^-2 and 03000W.m^-2, respectively. It reveals that the general development of the melting process 0 with a heat source in eccentric positions is almost similar to that of a heat source in a central position, i.e., heat convection direction with 500W.m^-2 goes towards the bottom of the STLHS unit, while the direction with 3000W.m^-2goes to the top. Accordingly, Figure 7 indicates the melting time of PCM based on a heat source in eccentric positions based on the different levels of heat flux in which 500 W.m^-2 and 3000 W.m^-2 are presented in Figure 7a,b, respectively. For a heat flux of 500W.m^-2, the total melting time of PCM in the upper heat source position of the STLTS unit is shorter than that of PCM with a central heat source position and that in a lower heat source position. This could be attributed to the fact that the convection direction goes to the lower part. Thus, the upper part of PCM is difficult to liquefy in the process. The larger the volume ratio of the upper area to the total area of the STLTS unit is, the longer the melting time of PCM becomes. The difference in melting time in different heat source positions is very small, and the increment or decrement of the melting time for PCM with a heat source in various positions is less than 1%. Considering the heat flux of 3000 W.m^-2, the total melting time of PCM with a heat source in the upper position is longer than that of PCM with a heat source in the central position and that with a heat source in the lower position. It could be observed that the shortest total melting time of PCM with a heat source in the lower position is 8248 s, which is about 14% and 25% smaller than that of PCM with a heat source in the central position and upper position, respectively. It is noted that the time saved by changing heat source position is quite distinct under the heat flux of 500W.m^-2 and 3000W.m^-2. The main reason is that the key effect of excellent heat transfer on latent thermal storage is the reduction in sensible heat when the total heat power input is fixed. In the case of weak heat flux, the average temperature of the melted PCM is low, and the proportion of sensible heat to total heat is relatively small. The benefit of reducing the sensible heat is negligible.

Figure 6. Thermal characteristics of PCM in the STLTH unit with eccentric heat source position in terms of heat flux of (a) 500 W.m-2; (b) 3000 Wm-2.

When the heat flux increases, the benefit brought by heat transfer enhancement becomes remarkable, and the time saved by changing the heat source position is significant. This proves that the lower position of heat source is more conducive to the melting process of PCM in an STLTS unit. To further compare and analyse this, Figure 8 indicates the heat transfer coefficient of PCM in the STLTS unit with a heat source in eccentric positions based on the different levels of heat flux in which 500W.m^-2 and 3000W.m^-2 are presented in Figure 8a,b, respectively. The heat transfer coefficients decrease sharply and are all similar at the beginning of the melting process due to the leading role of heat conduction. After that, the heat transfer coefficients slightly decrease. When heat flux is 500 W.m^-2, the heat transfer coefficient of PCM with a heat source in the upper position is higher than that of PCM with a heat source in the lower position and central position. For a heat flux of 3000W.m^-2, a reverse trend of PCM with a heat source in different positions could be found in the melting process.

Figure 7. Melting time of PCM in the STLTH unit with eccentric heat source position in terms of heat flux of (a) 500W.m-2;
(b) 3000 W.m-2.

Figure 8. Heat transfer coefficient of the STLTH unit with eccentric heat source position in terms of heat flux of (a)
500W.m-2; (b) 3000 W.m-2.

Heat Source with Various Configurations

Figure 9 shows thermal characteristics of PCM in an STLHS unit with a heat source with flat-tube configuration in terms of different heat source configurations, i.e., horizontal and vertical flat-tube type. The heat flux values of 500 W.m^-2 and 3000 W.m^-2 are presented in Figure 9a,b, respectively. From Figure 9a, it is noted that the temperature distribution of PCM with the configurations of round heat source or flat-tube heat source are almost the same at the beginning of the melting process since, during this period, heat transfer is dominated by heat conduction. Then, for the melting process, it is dominated by heat convection, and PCM with the configuration of a vertical flat-tube heat source has a better performance than that of heat source in a central position and a horizontal flat-tube heat source when the heat flux is 500W.m^-2. This is mainly because the heat source may cause flow resistance during the melting process. The structure of the vertical flat-tube fits with the streamline of natural convection that is better than the circle tube and horizontal flat-tube, leading to a weaker flow resistance and better heat transfer performance. This situation is also found when heat flux is 3000W.m^-2, as shown in Figure 9b. The larger the ratio between L and D is, the more obvious the situation becomes. Figure 10 demonstrates the total melting time of PCM in an STLHS unit with various heat source configurations. With the increase in the melting time, the melting process of PCM with five different configurations of heat source is compared in terms of heat flux values of 500W.m^-2 and 3000 W.m^-2. It was observed that the total melting time of PCM with vertical flat-tube heat source is much shorter than that of a heat source in the central position and horizontal flat-tube type due to the above reasons for heat convection processes. Similar to the total melting time of PCM in different configurations of heat source, the performance is very close when heat flux is 500 W.m^-2, as shown in Figure 10a. Comparably, in Figure 10b, the total melting time of PCM with various heat source configurations has a larger difference under a heat flux of 3000W.m^-2. The longest melting time of PCM is 6994 s when a heat source is adopted as a horizontal flat-tube with an L:D ratio of 2. It reveals that the shortest melting time of PCM could be obtained by the configuration with a vertical flat-tube heat source with an L:D ratio of 2, which is up to 6.3% smaller than that of PCM with a heat source in a central position and the configuration of horizontal flat-tube heat source. Accordingly, Figure 11 shows the heat transfer coefficients of PCM in an STLHS unit with a heat source in a central position and the configuration of various flat-tube types, which aims to further analyse and understand the thermal characteristics of the melting process. Figure 11a,b present the performance of PCM with heat flux values of 500 W.m^-2 and 3000 W.m^-2, respectively. Heat transfer coefficients of PCM with various heat source configurations are almost similar in the heat conduction process. For a heat flux of 500 W.m^-2, the heat transfer coefficient of PCM shows the highest value of 213 W.m^-2K with the configuration of vertical flat-tube heat source which has an L:D ratio of 2 at 15,200 s during the convectiondominating period. During the melting process, which is dominated by heat convection, the heat transfer coefficient with the configuration of the vertical flat-tube heat source is around 1.5% higher than that with the heat source in a central position and the configuration of horizontal flat-tube heat source. This is mainly due to the improved natural convection. Moreover, considering a heat flux of 3000 W.m^-2, the overall trend of the heat transfer coefficient is almost the same as that with a heat flux of 500 W.m^-2. The heat coefficient of PCM with the configuration of the vertical flat-tube heat source is around 241W.m^-2K, which is higher than that of PCM with a heat flux of 500 W.m^-2. This is mainly due to the more significant natural convection caused by the larger temperature difference. Based on the above analysis of different heat source positions and configurations, it can be concluded that PCM in an STLHS unit with a heat source in the lower position and configuration of the vertical flat-tube type could reveal a superior performance when compared with other cases. The above results could be a good basis for the design of ice storage.

Figure 9. Thermal characteristics of PCM in an STLTH unit based on a heat source with flat-tube configuration in terms of
heat flux of (a) 500 W.m-2; (b) 3000 W.m-2.

Figure 10. Melting time of PCM in an STLTH unit based on heat source with flat-tube configuration in terms of heat flux of
(a) 500 W.m-2; (b) 3000 W.m-2.

Figure 11. Heat transfer coefficient of PCM in an STLTH unit based on heat source with flat-tube configuration in terms of
heat flux of (a) 500 W.m-2; (b) 3000 W.m-2.

Conclusions

Different heat source positions and configurations were adopted to investigate the effect of natural convection on the melting process of PCM in an STLTH unit. Melting evolution, the melting time, and the overall heat transfer coefficient during the melting process were analysed and compared. The conclusions are as follows. This study demonstrates that natural convection is gradually dominant in the melting process with circulation vortices and would further promote the heat exchange process. The direction of flow toward upper and lower parts of the STLHS unit are determined by different heat flux values ranging from 500W.m^-2 to 3000W.m^-2. The critical point for heat convection of PCM in the STLTH unit ranges between 1000 W.m^-2 and 2000 W.m^-2. Moreover, a higher heat flux leads to a larger liquefaction rate. The melting time of PCM with a heat flux of 500 W.m^-2 is more than five times longer than that of PCM with a heat flux of 3000 W.m^-2. The melting process with a heat source in eccentric positions has a similar trend with that of a heat source in a central position. Due to the different natural convection directions, the larger the volume ratio of upper area to total area of an STLTS unit is, the longer the melting time of PCM becomes. Different heat source configurations, i.e., horizontal and vertical flat-tube type have different effects on the melting processes. Under a heat flux of 3000W.m^-2, the shortest melting time of PCM is obtained by a heat source that has a vertical flat-tube with an L:D ratio of 2. For a heat flux of 500W.m^-2, the heat transfer coefficient of PCM shows the highest value of 213W.m^-2K with a vertical flat-tube heat source and an L:D ratio of 2 at 15,200 s during the convection-dominating period. To conclude, PCM in an STLTH unit with a heat source in the lower position as well as configuration of vertical flat-tube type could achieve a superior melting performance when compared with other cases in this work. For practical application, air conditioning in buildings would be the main target for ITS. The research finding of this work could be a basis for the design of storage units. Thus, a high overall thermal performance would be achieved in terms of system compactness and energy storage efficiency.

…concluded

Chunwei Zhang and Dongdong Chai belong to Beijing Institute of Aerospace Testing Technology, Beijing 100074, China. Yubin Fan, Wenyun Zhang and Long Jiang belong to Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China. Meng Yu belongs to Special Equipment Safety Supervision Inspection Institute of Jiangsu Province, Nanjing 210036, China. Zhenwu Wang belongs to The School of Architecture and Civil Engineering, Jinggangshan University, Jinggangshan 343009, China.

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