## 3 Results and Discussion
### Effect of Tube Diameter  
One of the main geometrical parameters in this work is the impact of the tube diameter of the TCHC throughout the charging and discharging processes. Three tube diameters are investigated.  
Figure 7 shows the relative percentage of energy gained during charging against charging time for a range of tube sizes (9.52 mm, 12.70 mm, and 15.88 mm). For short pitches (P = 30 mm), the figure shows that the trend of the percentage of energy conserved is similar across all tested diameters. The liquid layer thickness becomes thicker with time during the charging process, and a smaller amount of heat is transferred by the conduction dominant mode. Therefore, the melting is considered constrained. Further, there is a convection mode driven by heat flux from the coil wall and this convection induces thermal instability. Due to the presence of this thermal instability, the melting is considered constrained. Increases in coil tube diameter result in a higher percentage of energy stored and a quicker charging time. In addition, the trends for the second two pitches (P = 40 mm and P = 50 mm) are consistent across all coil tube diameters investigated. Linear patterns may be seen in the first half of the charging period. For all tube diameters at both examined pitches, the curve flattens out after charging is complete, demonstrating that the rate at which energy is stored grows linearly. In addition, the coil tube diameter has a negligible impact on the coil pitch; therefore, the overall charging time is decreased when the coil tube diameter is increased. As a result, it is advised that the chiller be turned off as soon as possible to save energy consumption when the coil tube diameter and pitch are both high.  
Figure 7: Effect of tube diameters on the energy stored percentage versus time using three pitches during the charging process.  
Figure 8 depicts the percentage of energy recovered during discharging as a function of operation time for a range of tube diameters. The graphic demonstrates that across all tested pitches, there is a consistent upward trend in the proportion of acquired energy over all three diameters. For modest coil pitches (P = 30 mm), the discharging process speeds up as the coil tube diameter grows, reducing the time needed for 100% energy obtained. For larger diameter coil tubes and smaller pitches, the trend seems linear, suggesting that the rate at which energy is recovered increases linearly until full discharge occurs. Due to the shorter discharge period, the chiller should be shut off as soon as possible to prevent wasteful energy use.  
Figure 9 displays the effect of the coil tube diameter on the average charging rate versus time for the three investigated coil pitches. For the largest coil tube diameter, it has been shown that the average charging rate decreases rapidly with time, particularly for the smallest pitch. All coil tube diameters exhibit essentially the same behavior. Further, when coil tube diameter increases, charging time decreases. This is because a larger diameter coil tube provides a larger surface area for transferring heat and, hence, a greater effect. Figure 10 shows the effect of coil tube diameter on the average discharging rate against time. For all coil tube diameters examined, the average discharging rate drops sharply after the first 60% of the discharging process. After then, the typical rate of discharge remains almost the same. The time needed to discharge also decreases as the coil tube diameter increases. This is because an increase in coil tube diameter increases the surface area for heat transmission.  
Figure 8: Effect of tube diameters on the energy regained percentage versus time using three pitches during the discharging process.  
Figure 10: Average discharging rate versus time using various tube diameters with different pitches during the discharging process.  
Figure 9: Average charging rate versus time using various tube diameters with different pitches during the charging process.