## 4 Results and Discussion
At the 1200 s mark, the average temperature of the PCM hit 328 K. The highest regions of the domain recorded temperatures as high as 332 K, while the bottom sections remained at 310.18 K. An observable pattern arose where the rate of temperature increase intensified as the velocities of the heat transfer fluid (HTF)  
Figure 4: Predicted evolution of the melting process at various velocities: (**a**) 0.01 m/s, (**b**) 0.1 m/s, and (**c**) 1 m/s. increased due to enhanced heat exchange between the phase change material (PCM) and the HTF. Furthermore, after 1200 s, a noticeable increase in the average PCM temperature was observed as the HTF velocities increased, with temperatures reaching 329 K and 331 K at HTF velocities of 0.1 m/s and 1 m/s, respectively. These data emphasize the significant impact of HTF velocity on the dynamics of temperature distribution within a system. They illustrate the crucial role of heat transfer mechanisms in forming thermal profiles and emphasize the consequential effect on phase change kinetics within the PCM domain. Figure 6 presents a detailed representation of velocity distributions within the phase change material (PCM) domains at different velocities: (a) 0.01 m/s, (b) 0.1 m/s, and (c) 1 m/s. The molten phase change material (PCM) speed was closely connected to the speed of the system's heat transfer fluid (HTF). This relationship is emphasized by the improvement of  
Figure 5: Temperature distributions of the PCM domains at various velocities: (**a**) 0.01 m/s, (b) 0.1 m/s, and (c) 1 m/s. convective heat transfer at higher HTF speeds, which affected the heat transfer rate during the melting process. Furthermore, the HTF velocity significantly impacted the development of boundary layers on the PCM surface. This led to increased mixing and agitation inside the PCM and changes in its effective thermal conductivity. All of these factors directly affected the velocity profiles of the PCM. The design and geometry of a system also influence the relationship between the velocities of a heat transfer fluid (HTF) and phase change material (PCM). These include factors such as flow constraints or turbulence caused by small passages or intricate shapes, which affect the shape of the velocity profiles. The linkages between fluid mechanics and heat transfer principles are of utmost importance in enhancing the performance of thermal energy storage systems and heat exchangers that involve interactions between phase change materials (PCMs) and heat transfer fluids (HTFs). A captivating interaction between heat transmission and fluid dynamics characterizes PCM melting. At first, heat transfers from the source via the solid phase change material  
Figure 6: Velocity distributions in the PCM domains at various velocities: (**a**) 0.01 m/s, (**b**) 0.1 m/s, and (**c**) 1 m/s. (PCM), causing a thin layer near the hot surface to melt. Melting causes density variations that lead to natural convection. Less dense liquid PCM rises due to increased temperature, while denser, cooler liquid sinks, resulting in intricate flow patterns inside the domain. The melting front, the interface between solid and liquid states, changes continuously due to the combined effects of heat transmission and flow dynamics. A \"mushy zone\" with a combination of solid and liquid components adds complexity to the flow characteristics. The flow patterns are greatly influenced by the shape and orientation of the container, as well as by any present fins or heat transfer enhancers. Comprehending the complex relationship between thermal and fluidic processes is essential for enhancing PCM performance in various applications. The flow of the molten PCM began in a narrow region next to the wall, progressively spreading in size and speed throughout the process. Significantly, velocities were considerably higher in regions close to the solid phase, where the most efficient heat transfer occurred. As mentioned before, the speed of the molten PCM was directly related to the speed of the HTF.