## 5 Conclusions  
This work used numerical techniques to examine how water velocity affects phase change material (PCM) melting in a vertical cylindrical container. A quantitative investigation was carried out to clarify the connection between enthalpy and porosity using the ANSYS/FLUENT 16 program. Rubitherm RT42, a paraffin wax-based substance exhibiting phase transitions, was used in this experiment. With a constant temperature of 333 K, the study investigated the effects of different water velocities, specifically at speeds of 0.01 m/s, 0.1 m/s, and 1 m/s. This work sought to understand the dynamics of the melting process, which has consequences for comprehending the thermal behavior of PCM systems under various flow circumstances. The main conclusions of this work are as follows:  
1. The melting process initiates near the domain boundaries, with the solid PCM gradually transitioning to liquid state over time regardless of the heat transfer fluid (HTF) velocity.
2. Higher HTF velocities result in a more rapid increase in the liquid phase size and a corresponding decrease in the solid phase, indicating a faster melting process.
3. The upward movement of liquid PCM within the domain is primarily influenced by convective currents, buoyancy forces, and thermal gradients, rather than solely by density differences.
4. The density variations caused by melting solid PCM lead to natural convection, where less dense liquid rises due to increased temperature and denser, cooler liquid sinks.
5. Enhanced HTF velocities lead to faster melting rates and a decrease in the remaining solid phase, underscoring the importance of fluid dynamics in affecting phase change kinetics.
6. The velocity of molten PCM within the domain directly correlates with HTF speed, highlighting the significant impact of HTF velocity on PCM movement and the overall efficiency of phase change processes.  
Future studies could examine how container geometries affect phase change material melting, how temperatures affect water velocity and PCM behavior, and how numerical simulations can be experimentally validated to improve accuracy and reliability. Further research could also optimize thermal energy storage system design parameters using PCM-HTF interactions, including material properties, flow dynamics, and heat transfer processes.  
Conceptualization, A.F.K., F.L.R., S.A.L., A.A. and H.I.M.; Methodology, A.F.K., F.L.R., S.A.L., A.A. and H.I.M.; Software, A.F.K., F.L.R., S.A.L. and H.I.M.; Formal analysis, A.F.K., F.L.R., S.A.L., A.A. and H.I.M.; Investigation, A.F.K., F.L.R., S.A.L. and H.I.M.; Resources, A.A.;  
Figure 9: The velocity of the PCM for different velocities of the HTF.  
Data curation, A.F.K., F.L.R., S.A.L., A.A. and H.I.M.; Writing--original draft preparation, A.F.K., F.L.R., S.A.L. and H.I.M.; Writing--review and editing, A.F.K., F.L.R. and A.A.; Visualization, A.F.K., F.L.R., S.A.L., A.A. and H.I.M.; Project administration, F.L.R. and A.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available in article.  
The authors declare no conflicts of interest.