## 4 Results
### Experiments Without Thermal Spreader
The temperature profiles of the upper (\(T_{U1}\)-\(T_{U4}\)) and lower (\(T_{L1}\)-\(T_{L5}\)) surface of PCM package B are shown in Figure 5b. It is observed that the shape of the temperature profiles does not differ a lot from the experiment where PCM package A was used. A maximum heater temperature of 115 \({}^{\circ}\)C was reached after 60 min. The maximum temperature of the cover surface at the center (\(T_{C1}\)) of the setup was 58.5 \({}^{\circ}\)C after 60 min of charging. \(T_{C6}\), which is located at the greatest distance to the center, only increases by 1.6 \({}^{\circ}\)C, showing a similar absence of heat spreading with the added package. \(T_{L3}\), which is the temperature of the lower surface of the PCM package at a radial distance to the center of 25 mm, reached the melting temperature after 48.5 min. \(T_{U3}\), which is the equivalent temperature located on the upper side, reached the melting temperature after 63 min. The temperatures with a further radial distance than 25 mm did not increase above the melting temperature. Accordingly, the melting front did not  
Figure 4: **(a)** Temperature profile of the heater (\(T_{H}\)) and cover surface (\(T_{C}\)); **(b)** Temperature profiles of the upper (\(T_{U1}\)–\(T_{U4}\)) and lower (\(T_{L1}\)–\(T_{L5}\)) surface of the PCM package A (\(n\)-eicosane) for the experiment with a constant power input of 5 W for 60 min. reach the position of \(T_{U4}\) and \(T_{L4}\). Comparing the temperature profiles measured on the package surface for package A and B, a smaller amount of PCM melted in package B (dodecanoic acid with the highest melting temperature) since the spread of temperatures reaching the melting temperature of the PCMs as measured on the surface does not extend as far. This is logical based on the highest melting temperature of the PCM. In order to compare the influence of adding the PCM packages to the thermal performance of the setup, the experiment was also performed without the addition of any PCM package. Figure 6 illustrates the temperature profiles of the heater, \(T_{H}\), and the cover surface, \(T_{C1}\), for all three experiments. Only these temperature curves are illustrated since most of the heat was transferred in the axial direction along the center of the setup. Hence, these temperatures represent the maximum temperatures of the heater and the cover surface. As visible in Figure 6, both the heater and the cover temperatures were higher during the entire charging and discharging process when no PCM package was used compared to the cases with PCM packages. More specifically, the maximum heater temperature after 60 min of charging was 15 \({}^{\circ}\)C lower for PCM package A and 17 \({}^{\circ}\)C lower for PCM package B compared to the experiment without the PCM package. The peak temperature of the cover was reduced by 14 \({}^{\circ}\)C for both PCM packages. There are mainly two different effects that cause the reduction of the peak temperatures of both the heater and the cover when a PCM package was used. First, the thermal conductivity of the air in the cavity (0.024 W/m-K) is lower than the thermal conductivity of both PCM packages (0.46 W/m-K for the solid PCM in package B). The lower thermal conductivity of air created a higher resistance for the heat to dissipate from the heater. Since the heat input for all three experiments was the same, the increased resistance led to a greater increase of the heater temperature when no PCM package was used. Moreover, the low thermal conductivity of air minimizes the thermal spreading of heat in the radial direction.