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.