## 4 Results and Discussion
The highest speeds measured were 0.13 mm/s, 0.17 mm/s, and 0.19 mm/s at HTF speeds of 0.01 m/s, 0.1 m/s, and 1 m/s, respectively. This observation highlights the impact of HTF velocity on the dynamics of PCM movement in a system, where higher HTF velocities enable bigger magnitudes of velocity within a molten PCM region. Figure 7 represents how the amount of liquid in the phase change material (PCM) changed over time for different speeds of the heat transfer fluid (HTF). During the melting process, the amount of liquid steadily increased over time, and the melting rate rose proportionately to the heat transfer fluid's velocity. The overall duration required for complete melting varied, with recorded values of 1700, 1800, and 1900 s for HTF velocities of 1 m/s, 0.1 m/s, and 0.01 m/s, respectively. In contrast, at the 1000 s mark, the achieved liquid fractions were 0.81, 0.78, and 0.76 for the respective HTF velocities. These data highlight the significant impact of HTF velocity on the rate of phase change within the PCM domain. Higher velocities of the heat transfer fluid (HTF) are directly associated with faster melting rates. This leads to shorter overall melting durations and increased amounts of liquid at equivalent time intervals. These findings reveal the critical role that HTF velocity plays in controlling the efficiency and timing of phase change processes in thermal energy storage systems and heat exchangers that involve interactions between PCMs and HTFs. Figure 8 presents the temperature profile at a singular point at the center of the phase change material (PCM) domain. Initially, the PCM maintained a consistent temperature  
Figure 7: Liquid fraction for different velocities of the HTF. of 310 K, which persisted until 600 s into the heat exchange process. Subsequently, as heat was transferred to this point, the temperature significantly increased, primarily due to the convection process. Notably, the rate of temperature increase was observed to be faster with higher velocities of the heat transfer fluid (HTF). Specifically, at 900 s into the operation, temperatures of 326 K, 327.7 K, and 329.4 K were recorded for HTF velocities of 0.01 m/s, 0.1 m/s, and 1 m/s, respectively. This observed trend can be attributed to the enhanced heat transfer associated with higher HTF flow rates. Increased fluid velocity leads to more efficient convective heat transfer, resulting in a more rapid rise in temperature at the specified point within the PCM domain. Beyond 900 s, the heat exchange rate gradually diminished due to the decreasing temperature difference between the PCM and the HTF. Ultimately, at 1800 s, the temperature stabilized at 330 K and 333 K for the minimum and maximum HTF velocities, respectively. This comprehensive analysis underscores the significant influence of HTF velocity on temperature distribution and heat transfer dynamics within the PCM domain, highlighting the importance of fluid flow characteristics in optimizing thermal performance in phase change material systems. Finally, Figure 9 depicts an examination of the velocity of the molten phase change material (PCM) at the identical location studied in Figure 8. The movement of the PCM commenced at 600 s, aligning with the beginning of PCM liquefaction. Afterwards, the motion at this juncture experienced a sudden surge in speed due to the assimilation of convective heat, leading to a swift escalation in velocity until the 900 s mark. After this point, the movement gradually declined as the heat exchange rate lowered due to the decrease in temperature differences between the phase change material (PCM) and the heat transfer fluid (HTF). Ultimately, when the phase change material (PCM) temperature reached thermal equilibrium with the heat transfer fluid (HTF), the speed of the PCM lowered both at this specific spot and across the entire area. As the HTF velocity increased, the observed rise in PCM velocity could be attributed to the improved heat exchange facilitated by higher fluid velocities.