## 4 Results  
Figure 5 shows a comparison between the temporal variation of experimental temperatures inside the PCM, relative to the measuring points indicated in Section 2, and the corresponding numerical temperatures during the cooling energy charge. It can be seen that there is a good agreement between the numerical temperatures relative to the conduction-convection-based model and the experimental temperatures, while the temperature profiles resulting from the implementation of the conduction-based model fail to match the experimental ones during the first and last parts of the charging process. This is essentially because the conduction-based model does not permit to simulate the mixing of liquid PCM inside the aluminum container in the initial part of the cooling energy charge. Thus, the resulting temperature profiles present a slower decrease. Of course, this behavior at the initial part of the charge influences the entire charge process simulated by the conduction-based model. Indeed, in the last part of charge, the simulated temperature \(T_{A,cond}\) presents a sensible deviation from the corresponding experimental temperature. Figure 6 shows the comparison between the temporal variation of experimental and numerical temperatures inside the PCM relative to the cooling energy discharge. It can be seen that, in the initial part of discharge, the simulated temperatures relative to both the implemented models are are in good agreement with the experimental ones. This is because conduction heat transfer is the dominant heat transfer mechanism in the first part of discharge, when great part of the PCM is in the solid state, and the melted PCM is limited in a narrow layer close to the container internal wall. Heat transfer by free convection inside the PCM becomes higher as the melted layer thickness increases. Indeed, Figure 6 shows that, in the last part of discharge, the temperature profiles relative to the conduction-based model are very far from the experimental ones, differently from the ones relative to the conduction-convection-based model which present a better behavior in the last part of discharge. From the above, it can be stated that the conduction-based model is not suitable for the present application. For this reason, only the main results obtained with conduction-convection-based model are reported and discussed in the following. Figure 7a,b shows the temporal variation of the average liquid fraction of PCM volume during cooling energy charge and discharge, respectively, obtained by the conduction-convection-based model. Figure 7a clearly shows that the PCM solidification rate is relatively high in the first part of the charge, before it slows down as the thickness of the solid layer at the container wall increases. Indeed, from the beginning of step 1, PCM volume average liquid fraction reaches 0.5 after 23 hours, whereas the complete solidification of PCM is reached after about 63 hours. Conversely, Figure 7b shows that, during the cooling energy discharge, the melting rate is initially relatively low, before it becomes higher as the melted fraction increases, or, in other words, as heat transfer by free convection inside the PCM becomes higher. In Figure 7b, it can be noted that free convection becomes decisive from the seventh hour, and also that the PCM is not completely melted at the end of the discharge simulation. This last result is not in contrast with the experimental observations, since actually the PCM was not completely melted at the end of the experimental test. However, the real liquid fraction at the end of the experimental test was not measured, and probably it was higher than the simulated one obtained with the conduction-convection-based model, since the model underestimates the temperatures at the end of the discharge process, as it is be seen in Figure 6.  
Figure 5: Temporal variation of experimental and numerical temperatures during cooling energy charge. Figure 6: Temporal variation of experimental and numerical temperatures during cooling energy discharge.