# Comparison of Heat Transfer Enhancement Techniques in Latent Heat Storage
## 3 Results and Discussion
### Fimed Tube Bundles  
Finned Tube Bundle (FTB) geometries are the most widely studied Heat Exchanger (HEX) configuration for LHES applications. They consist of fixed-fin geometries, of different topologies and configurations, generally protruding from the tubes used to carry the HTF, into the PCM mass. Highly conductive metals such as copper and aluminum are the most commonly used. The disposition of the fins, packing fraction, thickness, and amount determine the performance of a finned tube bundle. The selection of analyzed studies which addressed the addition of fins to a tube bundle (TB) heat exchanger geometry to enhance the heat transfer rates of a LHES unit is summarized in Table 1. It includes reference numbers, notation, some descriptive information, and a representative picture or scheme of the discussed units. All additional data required for the calculation of NHITPC are presented in Table 1. The outer volumes of the units V\({}_{TOT}\), including the container tank surrounding the TB or FTB (and additional manifolds if required) without considering any insulation, were for the most part explicitly reported along with container material and properties. In the cases were information  
Figure 1: Sensitivity analysis. Calculated NHITPC vs. \(\Phi_{PCM}\) at different temperature levels and HTF mass flow rates in logarithmic scale. The most commonly found arrangements pertain fixed fins embedded in the PCM bulk, oriented perpendicularly (A.2, B.1, D, G, H) or longitudinally (C, E, F, I, J) to the HTF flow inside the tubes. Some interesting alternative variations see longitudinal fins used such as in triplex heat exchanger configurations by [PERSON] et al. [9] (C), complex geometries to fit specific applications by [PERSON] et al. [10] (E) or even fixed on the side of the flowing HTF, as presented by [PERSON] et al. [12] (J). Regarding performance, the study carried out by [PERSON] et al. [7] provided data for a rinsed copper tube bundle (A.2) and additional in-house data from the same study was used for the analog plain tube bundle (A.1). The addition of aluminum fins traded an additional 3% of PCM volume fraction for a \begin{table}
\begin{tabular}{c c c c c c} \hline
**Type** & \(\mathbf{T_{PC}}\)[\({}^{\circ}\)C] & \(\mathbf{V_{TOT}}\) & \(\hat{m}_{HITF}\) & \(\boldsymbol{c_{p,HTF}}\) & **Geometry** & **Ref.** \\  & & [m\({}^{3}\)] & [kg h\({}^{-1}\)] & [kJ/(kg K)] & \\ \hline FTB (G) & 125 & \(3.9\times 10^{-1}\) & \(1.5\times 10^{3}\) & 2.03 & [47] \\ \hline FTB (H) & 53 & \(8.7\times 10^{-3}\) & \(2.4\times 10^{1}\) & 4.18 & [13] \\ \hline FTB (I) & 42 & \(6.1\times 10^{-2}\) & \(1.8\times 10^{2}\) & 4.18 & [49] \\ \hline FTB (J) & 169 & \(6.5\times 10^{-3}\) & \(3.5\times 10^{2}\) & 3.10 & [12] \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: Calculated NHTTC vs. \(\Phi_{PCM}\) for the references concerning tube bundles (TB) and finned tube bundles (FTB) in LHES unit configurations in logarithmic scale. significant discharge time reduction of around 50% and a total threefold improvement in the calculated NHTPC. However, it is necessary to highlight the performance of the tube bundle structure (A.1) as it exceeds most of the FTB designs. Taking the unit used by [PERSON] et al. [49] (I) as comparison point, the sheer difference in heat transfer surface could explain this behavior. Even though A.1 presents no fins, the heat transfer surface to volume ratio of unit A.1 is over two times higher (63 m\({}^{2}\)/m\({}^{3}\)) than that of unit I (27 m\({}^{2}\)/m\({}^{3}\)). In a similar comparison approach, [PERSON] et al. [48] (B.2) achieved a sevenfold increase (when compared to B.1) in heat transfer performance by trading an approximate 7% of PCM volume to accommodate circular radial fins. The FTB unit presented by [PERSON] et al. [14] (D.1) attained the higher performance in this case with an additional 4% of the total volume dedicated to the analog copper finned tubes than the FTB unit investigated by [PERSON] et al. [7].