## 5 Results
However, in this study, as can be seen in Figure 7, the number of optimal horizontal fins is equal to five, which is very close to the corresponding value in [12]. Figure 6: Comparison of the convection strength between \(LR=0.3\) and \(LR=0.9\) (\(n=3\), \(H=10\) mm, \(AR=1\)). In Figure 8 the streamlines for the three \(LR\) values (0.3, 0.7 and 0.9) are depicted. As can be seen, at length ratio of \(LR\) = 0.7, the convection is formed in two places (between the horizontal fins and the distance between the horizontal fin tip and the line of symmetry). But at \(LR\) = 0.5 and \(LR\) = 0.9 the convection is formed only in one place. The presence of streamlines in each zone indicates that there is a liquid phase motion which implies the possibility of the natural convection heat transfer. Figure 8: Convection strength at \(LR\) = 0.5, 0.7 and 0.9 (\(n\) = 5, \(H\) = 10 mm). Figure 7: Effects of length ratio (LR) on SOT at different horizontal fins number (\(H\) = 10 mm). It seems that the liquid phase movement at \(LR\) = 0.7 is much better than the other two cases (\(LR\) = 0.5 and 0.9). Because the streamlines are well distributed throughout the heat sink, hence that the possibility of the liquid phase movement is higher at \(LR\) = 0.7. At \(LR\) = 0.5, the liquid phase does not move well in the space between the horizontal fins. In the third case (\(LR\) = 0.9), due to the long length of the horizontal fins, it is difficult to establish a connection between the space of each fin. In other words, the liquid phase movement is blocked due to the long length of the horizontal fins. Therefore, it seems that the convection strength for \(LR\) = 0.7 is superior to \(LR\) = 0.7 and \(LR\) = 0.7, which consequently leads to higher objective function. As can be seen in Figure 9, for heat sink with 13 horizontal fins, adding larger fins disrupt the convection. As shown in Figure 9, the liquid PCM movement is disturbed owing to an increase in fins length, hence the convection intensity reduces. For this reason, SOT reduces with increasing fins length for heat sink with 13 horizontal fins as shown in Figure 5.0  
Considering the constant heat sink height, as the heat sink width grows, the aspect ratio \(\left(AR=\frac{W}{H}\right)\) increases. The effects of increasing AR on \(SOT\) are shown in Figure 5.1 According to Figure 10, the increase in AR does not affect the number of optimum fins. That is, for \(H\) = 10 mm from \(AR\) = 1 to \(AR\) = 5, the optimal fin number is 5 (i.e., \(n_{opt}\) = 5). As mentioned, adding fin has a positive effect (thermal conductivity enhancement) as well as a negative effect (latent heat reduction). As the number of fins rises up to five, it seems that the incremental effect of thermal conductivity improvement (positive effect) is superior to the decremental effect of the latent heat reduction (negative effect), hence the objective function improved. However, by increasing the number of fins from 5 to 13, the negative effect prevails over the positive effect and therefore the objective function will diminish. As the aspect ratio grows \(\left(AR\uparrow\right)\), the horizontal distance between the vertical walls increases, hence the conduction heat transfer diminished. In this case, convection heat transfer has a larger role in SOT. In other words, as AR grows, the role of convection heat transfer in the objective function becomes more important and therefore the optimal length ratio should be reduced. As shown in Figure 10, the optimal length ratio \(LR\) decreases with increasing \(AR\). Figure 5.2 Comparison of strength convection between \(LR\) = 0.3 and \(LR\) = 0.9 (\(n\) = 13, \(H\) = 10 mm). Following Figure 10 (\(AR=5\)), the objective function (SOT) diminishes as the length ratio (LR) grows. Because at high aspect ratio (\(AR\)), convection heat transfer plays a key role, and the shorter the fin length, the greater convection intensity there will be (Figure 11). Figure 5.3 Optimum fins number at different AR.