## 1 Introduction  
Solar energy is strongly tied to human everyday life and substantially influences modern civilization's development, which depends on several critical industries. Most people know that specific energy sources ultimately run out and others have negative environmental repercussions. As a consequence, researchers across the globe are working to develop substitute renewable energy sources. The fact that renewable energy is long-term, affordable, and ecologically reasonable is only one of its many advantages. It has the potential to be utilized everywhere, but the lack of regular access to sources like wind and sunshine is its major constraint [1; 2; 3]. One method to deal with this is by storing thermal energy. PCMs are the primary materials used in thermal energy storage [4; 5; 6]. Many experiments have been conducted on various forms composed of phase changing materials and the impact that shape has on a material's thermal energy storage capacity. Studies on methods to enhance heat transmission show that copper rods are the most successful. Many studies have demonstrated the benefit of using numerical projections in experiments [7; 8; 9; 10]. The melting of PCMs is sped up with every degree that the temperature of the air being introduced increases, and the energy charge for both sensible and latent PCM heat increases considerably [11; 12; 13]. The PCM melting process in a rectangular container was numerically and experimentally analyzed by [PERSON] et al. [14]. According to the study's findings, the melting process accelerated with every increase in heat flow. A computational investigation on the possibility of PCM-filled cylindrical cells acting as thermal energy storage devices was conducted by [PERSON] et al. [15]. Because of the PCMs' very high temperature in the center of the PCM cylinder, the cylinders in the first cell of the column melted more quickly than those in the cells that followed it in the column. Experimental research presented by [PERSON] et al. [16] focused on the PCM melting process in a spherical cell. According to the study, the melting process decreased as cell lead width increased. An experimental examination of shell and tube latent heat storage for solar dryers conducted by [PERSON] and [PERSON] [17] used paraffin wax as the heat storage medium. According to the research, the impact of natural convection was less significant in the bottom half of the region spectrum than in the top region. Natural convection is the primary mechanism for heat transmission, and melting occurs more quickly near the top owing to the buoyant effect [18]. The PCM's multi-tube melting process was analyzed by [PERSON] et al. [19]. According to the research, melting progress sped up as temperature and tube count rose. [PERSON] et al. [20] conducted research on how PCMs melt in a shell and tube configuration. The research demonstrated that the melting process had distinct effects on heat tubes. Increasing the inner HTF tubes caused an acceleration in the melting process, and enhanced heat transport with the addition of the nanoparticle was experimentally tested. Several studies have demonstrated that adding nanoparticles to PCM improves heat transport, shortening the time for the melting process to complete [21; 22]. Other studies conducted experiments in which nanofluids were added to PCMs as a new phase to investigate their effect on a material's capacity for thermal energy storage [23; 24]. The studies' findings indicated that the addition of nanofluid to PCM improved thermal conductivity, leading to a decrease in the time needed for the melting process. This study explores the effects of water velocity on the melting of PCM in vertical cylindrical containers for thermal energy storage systems. The investigation was conducted using advanced numerical models. The study examines the behavior of a phase transition paraffin wax-based material, Rubitherm RT42, under different flow conditions, providing new insights into the underlying processes that govern PCM behavior.