# Numerical Investigation of Latent Thermal Storage in a Compact Heat Exchanger Using Mini-Channels
## 3 Results and Discussion
The incorporation of fins results in a lower and higher outlet temperature in melting and solidification, respectively, as compared to the other configurations, and a modest reduction in the phase change time. In the  
the channel-2 case. For the rest of the process, the channel-2 case has a higher power. The rapid reduction in the power of channel-1 at the end of the processes is attributed to the completion of the phase change adjacent to the side walls and the relatively weaker heat transfer around the tips of channel-1. In the case of channel-2, the phase change is ongoing adjacent to the side walls throughout the entire process. The finned channel-2 case shows a higher rate of heat transfer in both melting and solidification processes than the bare channel-2, despite having a lower mass of PCM with about 1.8% lower packing factor. To be able to evaluate and compare the designs with a varying number of channels and packing factors, normalized mean power (represented by the mean UA-value) as an indicator of the thermal performance was used in the following. The mean UA-values are calculated based on 98% completion of the phase change. Figure 10 shows the dependency of UA values as a function of the PCM packing factor for the total range of the simulated air flow rate. The reduction in the packing factor indicates the increase in the number of channels as the vertical data points for a given packing factor designates the variation in the air flow rate. Figure 10 shows that as the PCM packing factor reduces, the mean UA value increases for all the simulated configurations in both melting and solidification processes. Figure 9: Transient power as a function of relative accumulated energy flow rates of 7 and 24 L/s: (**a**) melting-Tin = 30 \({}^{\circ}\)C, (**b**) solidification-Tin = 15 \({}^{\circ}\)C.  
For a constant air flow rate, the increase in the number of channels increases the mean power of phase change. As the number of channels is increased or fins are used (in the case of channel-2), the PCM packing factor reduces, resulting in a reduction in the latent storage capacity. Given a constant total flow rate of the HTF entering the cuboid, the increase in the number of channels reduces the flow rate per channel, resulting in a reduction in the heat transfer coefficient on the air side. However, the effect of the extended heat transfer surface as the number of channels increases is dominant over the reduction in the internal heat transfer coefficient, eventually increasing the total UA value and improving the thermal performance. Increasing the flow rate improves the normalized mean power for all the cases, particularly for the enhanced case of finned channel-2. For instance, for the configurations of channel-1 with PF = 82.4%, channel-2 with PF = 82% and finned channel-2 with PF = 80.2%, increasing the total flow rate of the HTF from 7 L/s to 24 L/s increases the mean UA values of melting by 30%, 35% and 44%, respectively. The interesting point is that adding fins to the cases of channel-2 instead of increasing the number of channels can result in higher mean UA values, attributed to the higher air flow per channel in the former case. As an example, given the flow rate range of 7-24 L/s, adding fins to the case with 72 channels (PF = 83%) increases the UA mean value of melting by 21-31%, as compared to the un-finned case with 72 channels (PF = 84.6%). Whereas increasing the number of un-finned channels from 72 (PF = 84.6%) to 84 (PF = 80.2%) enhances the mean UA value of melting by 13-24%. In total, the relative enhancements in the mean UA values of the finned channel-2 cases, as compared to the un-finned cases, lie within 15-31% for the entire range of simulated flow rates and packing factors. The difference in the air heat transfer coefficient of the two channels has an insignificant effect on their thermal performance within the phase change. Figure 11a shows the air heat transfer coefficients of channel-1 and bare channel-2 averaged over melting as functions of the total air flow rate.