For the melting process, the heat transfer rate (q) to the phase change material (PCM) is depicted over time in Figure (7), providing a comparison of heat transfer rates among the three models. In all three models, the heat transfer rate initiates an upward trend as the adjusting layer of PCM begins to melt and contacts the fin surfaces. This trend continues until it reaches the peak heat transfer rate. At this point, the width of the melted PCM layer expands, leading to a reduction in conduction heat transfer. Consequently, the heat transfer rate experiences a rapid decline from its peak. It eventually reaches a stage where four distinct regions of natural convection, as discussed in the previous section, become apparent. In this stage, the increase in natural convection counters the decrease in conduction, resulting in the heat transfer rate becoming nearly constant over time. As stage three commences, marked by the restriction of natural convection and the reduction of the front line of melting due to the merging of upper regions of melted PCM, the heat transfer rate gradually decreases until full melting is achieved.
The optimal heat transfer performance is associated with a higher heat transfer rate over time across all stages. The highest peak in heat transfer rate is observed in the A-1 model, characterized by equal fin lengths. This peak is attributed to the uniform melting process at the fin surfaces. In contrast, the A-2 and A-3 models exhibit lower peaks due to the varying melting rates among the fins. Fins 1, 2, and 3 melt more rapidly than fins 4 and 5, with the faster-melting fins reaching stage one before the longer fins reach full melting. However, it’s worth noting that the peak value doesn’t significantly impact the overall heat performance. During stages 1 and 2, the heat transfer rate remains nearly constant for all models due to the consistent surface area of the fins, leading to an equal melting front line for all. Stage 2 is relatively shorter in duration for these models, primarily because the upper melted PCM region merges earlier, as depicted in Figure (4). In stage 3, the longer bottom fins (4 and 5) enhance heat transfer to the PCM in the form of latent or sensible heat. This heated or melted PCM rises to the top until the upper half reaches the temperature of the heat transfer fluid. At this point, heat transfer to the melted PCM at the bottom occurs through conduction, highlighting the significance of fin length at the solid bottom. Therefore, the heat transfer rate for both A-2 and A-3 models in stage 3 is approximately equal, as they possess similar bottom fin lengths. The A-2 model exhibits the best heat transfer performance, although it is only marginally higher than that of the A-3 model, as indicated by the heat transfer rate graph.