## 3 Results
### Mode 2: Discharging  
#### 3.2.1 Temperature Profiles during the Discharging of the PCM  
Regarding Mode 2, the influence of both HTF inlet temperature and flow rate was evaluated with the PCM initially at \(-4\)\({}^{\circ}\)C. Figure 11 shows the PCM and HTF temperature profiles in Mode 2 for HTF inlet temperature at \(9\)\({}^{\circ}\)C, \(12\)\({}^{\circ}\)C, and \(15\)\({}^{\circ}\)C, and at constant HTF flow rate of \(100\) L\(\cdot\)h\({}^{-1}\). It was observed that the PCM discharging time is shortest for the highest inlet temperature, because of the higher temperature difference between the PCM and the HTF that increases the heat transfer rate. Figure 11: PCM temperature profile during discharging at \(100\) L\(\cdot\)h\({}^{-1}\) with HTF inlet temperature at (**a**) \(9\)\({}^{\circ}\)C, (**b**) \(12\)\({}^{\circ}\)C, and (**c**) \(15\)\({}^{\circ}\)C and (**d**) position of the sensors. Dotted lines denote PCM temperature at top level, dashed lines at middle level, and solid lines at the bottom. Figure 10: Influence of compressor power on total cold energy stored in the PCM. A temperature gradient was observed inside the PCM in the direction parallel to the HTF flow (see the curves of the same colour presenting temperature profiles) since the HTF is cooling down as it flows through the RPW-HEX by releasing heat to the PCM, which causes the phase change front to progressively move in the direction from the HTF inlet towards the outlet. However, a temperature gradient is also observed from the top to the bottom of the PCM tank, being the PCM temperature at the top part of the RPW-HEX higher than at the bottom (see the curves of the same type). This means that the HTF stratifies inside the tank, which causes an asymmetric PCM melting that starts earlier at the top part. During PCM phase change, the temperature difference between the top and the bottom of the tank is around 3 \({}^{\circ}\)C at all locations and for all HTF inlet temperatures tested. Figure 12 shows the PCM and HTF temperature profiles in Mode 2 for HTF inlet temperature of 12 \({}^{\circ}\)C and flow rates of 50 L-h-1, 100 L-h-1, and 150 L-h-1, respectively. Hereby, the duration of the discharging process decreases by increasing the HTF flow rate. At the lowest flow rate value, the melting front requires around 15 min to move from one edge of the tank to the opposite one, while for the highest flow rate value it requires around 4 min. Both the stratification of the HTF inside the RPW-HEX, as well as the temperature gradient inside the PCM in the direction of HTF flow, are slightly reduced by increasing the HTF flow rate. 2.2 Instantaneous Cold Energy in PCM, Average PCM Discharge Rate and Time Required to Discharge the PCM  
Figure 13 shows the influence of HTF inlet temperature on the PCM instantaneous cold energy at constant HTF flow rate of 100 L-h-1. In the previous section it was observed that PCM can be completely discharged by HTF inlet temperature at either 12 \({}^{\circ}\)C or 15 \({}^{\circ}\)C, while it is only partially discharged at 9 \({}^{\circ}\)C. Considering that the PCM is completely discharged when the final temperature of 12 \({}^{\circ}\)C is achieved, the cold energy stored in the PCM can even take negative values when the HTF  
Figure 12: PCM temperature profile during discharging with HTF inlet temperature at 12 \({}^{\circ}\)C and at a flow rate of (**a**) 50 L-h-1, (**b**) 100 L-h-1, (**c**) 150 L-h-1 and (**d**) position of the sensors. Dotted lines denote PCM temperature at top level, dashed lines at middle level, and solid lines at the bottom. temperature inlet is at 15 \({}^{\circ}\)C. Since the RPW-HEX was considered completely discharged at 12 \({}^{\circ}\)C, the negative values mean that it is over discharged beyond the limit. Figure 14 shows the influence of HTF inlet temperature on the average PCM discharge rate and time taken during the discharging mode at constant HTF flow rate of 100 L-h\({}^{-1}\).