# Comparison of Heat Transfer Enhancement Techniques in Latent Heat Storage
## 4 Discussion
### KPI Comparison  
Considering the many already available KPI for LHES systems, Table 5 compiles some of the most relevant KPIs concerning heat transfer performance and compactness degree, as well as the  
Figure 6: NHITPC vs. \(\Phi_{PCM}\) for all units in each category in logarithmic scale.  
pair presented in this study for three systems at different experimental conditions. Even though the considered KPIs are not intended to represent the same phenomena or were conceived with the same objectives, it is still interesting to see how they vary with experimental conditions and how they compare among each other.  
Similarly to the robustness testing section, Units 2, 3, and 4 are used as representative systems, with varying inlet temperature, mass flow rate, and overall size, with the intent to analyze how the KPIs change accordingly.  
As shown in the table, ED is intrinsically dependent not only on material properties and dimensions, but also on the sensible contributions and thus temperature levels imposed on the unit, as seen in the results for Unit 2 at two temperature levels. With a similar point of view, \(\Phi_{PCM}\) shows a similar trend between the Units, but focusing only on the share of main energy storage material. Although it does not provide the exact same information, it can be useful in representing  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**KPI** & **Unit 2** & **Unit 2** & **Unit 3 (_in_, **Unit 3 (_in_, **Unit 4 (_in_, **Unit 4 (_in_, **15 \({}^{\circ}\)C**) & **(_Tin_, 40 \({}^{\circ}\)C**) & **2088 kg/h)** & **6984 kg/h)** & **Unit 4 (_in_, **24 kg/h)** & **Unit 4 (_in_, **62.4 kg/h)** \\ \hline Energy Stored [kWh] & 2.10 & 1.70 & 18.77 & 18.77 & 0.23 & 0.24 \\ \hline Energy Density [kW/m\({}^{3}\cdot\)K] & 105.16 & 85.23 & 47.93 & 47.93 & 26.19 & 27.23 \\ \hline NHTTC [kW/m\({}^{3}\cdot\)K] & 31.39 & 31.81 & 1.60 & 1.56 & 4.22 & 4.36 \\ \hline \(\Phi_{PCM}\) & 0.83 & 0.83 & 0.66 & 0.66 & 0.33 & 0.33 \\ \hline \(t_{Disch}\) [h] & 0.15 & 0.28 & 1.75 & 1.20 & 0.28 & 0.22 \\ \hline \(\mathcal{Q}_{avg}\) [kW] & 9.37 & 4.96 & 7.90 & 11.52 & 0.63 & 0.80 \\ \hline
5 min-Peak Power [kW] & 16.37 & 8.67 & 23.25 & 35.69 & 0.86 & 1.51 \\ \hline
5m-P.Power-Energy sto.[1/h] & 7.78 & 5.09 & 1.24 & 1.90 & 3.80 & 6.40 \\ \hline \(\gamma\) [1/h] & 4.46 & 2.91 & 0.42 & 0.61 & 2.79 & 3.40 \\ \hline \(\varepsilon_{avg}\) & 0.77 & 0.78 & 0.41 & 0.13 & 0.73 & 0.58 \\ \hline \(h_{v}\) [kW/m\({}^{3}\cdot\)K] & 16.85 & 20.70 & 3.68 & 16.48 & 9.17 & 14.54 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of different KPIs for LHES.  
both the compactness degree of the design, and the potential for energy density of the unit without considering the current experimental temperature differences.  
On the heat transfer performance side, specific charging rate \(\gamma\) as proposed by [PERSON] et al. [39], and 5 min peak power-energy stored ratio by [PERSON] et al. [38] seem to agree with the overall trend shown by NHITPC across the units. They provide indications of the average heat transfer behavior with respect to the total energy, but remain dependent on both temperature and HTF mass flow rate differences. In contrast, NHITPC remains almost constant for a given system across different experimental conditions.  
Although they all provide very useful information on particular aspects, slightly more drastic variations can be seen with the volumetric heat transfer coefficient \(h_{v}\) and average temperature effectiveness \(\varepsilon_{avg}\) presented by [PERSON] et al. [40] as well as \(t_{Disch}\), \(Q_{avg}\) and 5 min. Peak Power.