## 4 Result and Discussion  
The graphs below show the experimental results obtained during the melting (Figure 4) and solidification (Figure 5) of the PCM in the spherical capsule. Each graph shows the temperatures of the four thermocouples inside the flask and of the thermocouple used to monitor the water bath temperature (T\({}_{\mathrm{w}}\)). According to the findings that a specific single melting temperature was not found for the PCM, there is no plateau in the temperature profile, but a more or less continuous trend (either increasing or decreasing) is observed. As might be expected, the curves corresponding to the inner thermocouples (T2 and T3) always show a delayed response with respect to those closer to the external surface in contact with the tank water. Figure 3: Representation of the temperature-monitoring points (thermocouples T1 to T4). During melting, as the temperature of the bath increases, the time required to reach thermal equilibrium is significantly reduced. Thermal equilibrium occurs when the temperature of the whole paraffin sphere equals the wall temperature (that is the temperature of the water in the thermostatic bath) and therefore the PCM is no longer able to absorb energy. By increasing the wall temperature from 56 to 71 \({}^{\circ}\)C, the time to complete the charge (i.e., to reach thermal equilibrium) decreases by approximately 70% (more than 1.5 h). In addition to the observation about the inner temperature profiles mentioned above, in the case of the melting phase, as far as the extreme temperatures are concerned, it can be seen that, after some time, the temperature at T1 becomes higher than at T4, probably due to the convective motions inside the increasing liquid mass within the sphere. During solidification (Figure 5), the measured temperatures initially drops almost simultaneously inside the paraffin mass, until a temperature of approximately 49 \({}^{\circ}\)C is  
Figure 4: Temperature trend inside the spherical capsule during the PCM melting phase for (a) \(\mathrm{T_{wall}}=56\)\({}^{\circ}\)C and (b) \(\mathrm{T_{wall}}=71\)\({}^{\circ}\)C.  
Figure 5: Temperature trend inside the spherical capsule during the solidification of the PCM for \(\mathrm{T_{wall}}=22.5\)\({}^{\circ}\)C and: (a) \(\mathrm{T_{i}}=56\)\({}^{\circ}\)C; (b) \(\mathrm{T_{i}}=71\)\({}^{\circ}\)C.  
Figure 8: Comparison between simulated and measured temperature during the test with T\({}_{\rm wall}\) = 71 \({}^{\circ}\)C and T\({}_{\rm inial}\) = 22.4 \({}^{\circ}\)C at the thermocouple: (**a**) T1; (**b**) T2; (**c**) T3; (**d**) T4. Figure 6 shows the comparison between the simulated and the experimental temperatures in the correspondence of the four thermocouples, in the case of solidification with a wall temperature equal of 22.5 \({}^{\circ}\)C and an initial paraffin temperature of 71 \({}^{\circ}\)C. The agreement between the values is rather good, with the model accurately predicting the temperature trend until the solidification start temperature is reached; for values lower than 49 \({}^{\circ}\)C a faster cooling is calculated with respect to the experimental trend. This will reflect in a calculated shorter time to reach equilibrium: the time predicted by the model is approximately 2.3 h, while experimentally a time of 2.8 h was measured. In any case, overall, the model is capable of reproducing rather well the experimental data during solidification at the four thermocouples, with the exception of thermocouple T1, where a greater discrepancy between the experimental and simulated temperature trends is observed: the simulation predicts a prolonged flattening of the curve in the correspondence of the melting temperature of the PCM. Probably, this discrepancy is partly also due to the presence of the flask neck which modifies the symmetry of the system; however, given the position of the thermocouples, its effect is expected to be small, compared to the whole system.