## 5 Results  
In general, by loading fins to the PCM, heat transfer within the PCM can be enhanced to maximize the objective function. The objective function is different for various applications. In electronic cooling applications, the objective function is defined as enlarging SOT. For this purpose, given the problem constraints (constant volume of the heat sink), the optimal number of horizontal fins within PCM will be examined. The presence of horizontal fins is expected to improve heat distribution within the PCM. For this purpose, the variations of SOT in the PCM filled heat sink equipped with horizontal fins was compared with the corresponding value in the PCM filled heat sink (without horizontal fins). The variations of SOT are shown in Figure 4.  
As can be seen in Figure 4, by adding horizontal fins, the contact surface between PCM and fins intensified which consequently increased the objective function (SOT) in each aspect ratio (\(AR=\frac{W}{H}\)). The results presented in Figure 4 are for a heat sink equipped with three horizontal fins (\(n=3\)) at length ratio of \(LR=0.3\). As can be seen in Figure 4, as the horizontal fins were incorporated to the PCM, the contact surface area intensified which consequently improved the conductive heat transfer, hence SOT is improved. Therefore, it is desirable to add horizontal fins. To evaluate the effects of the number as well as the length of horizontal fins on heat sink performance, a heat sink at a constant height of (\(H=10\) mm) is selected. Some horizontal fins at length ratios of \(LR=0.3\), \(0.5\), \(0.7\) and \(0.9\) were loaded at \(5000\frac{W}{m^{2}}\) applied from the bottom surface. For the heat sink with three horizontal fins (\(n=3\)), the effects of length ratio on SOT are shown in Figure 5.  
Figure 3: Comparison between the current study and the experimental data [20]. Figure 4: The variations in SOT owing to the incorporation of horizontal fins into the PCM filled heat sink. Figure 5: The effect of increase in length ratio (LR) on SOT (\(H=10\) mm, three horizontal fins (\(n=3\)), \(AR=1\)). As shown in Figure 5, with the rise in the length ratio (equivalent with the fins length growth), SOT increases. In Figure 6, the streamlines are illustrated for both \(LR=0.3\) and \(LR=0.9\). As shown in Figure 6, as the horizontal fin length rises, the contact area, as well as the convection intensity increased, which consequently SOT improves. Now, the number of horizontal fins efficacy is examined. By increasing the horizontal fins from 3 to 13, the SOT was recorded and shown in Figure 7. However, for a convenient understanding of the effect of the number of horizontal fins (\(n\)), the results were summarized for \(n=3\), 5, 11 and 13 as illustrated in Figure 7.  
When the number of horizontal fins is five (\(n=5\)), increasing the fin length from the \(LR=0.3\) to \(LR=0.7\) improves the SOT, but more increase in LR, diminishes SOT. The incorporation of horizontal fins has a positive effect (thermal conductivity enhancement) as well as a negative effect (latent heat reduction). As shown in Figure 7, the optimal number of horizontal fins is five. As the number of fins rises up to five, the incremental effect of thermal conductivity improvement (positive effect) was superior to the decremental effect of the latent heat reduction (negative effect), hence the objective function (SOT) improved. However, with a further increase in the number of fins upon five, the negative effect prevailed over the positive effect and therefore the safe operation time diminished. In a study conducted by [PERSON] and [PERSON] [12], using constructal theory, it was shown that under the best conditions, the number of horizontal fins is equal to four. In [12], the heat flux input to the heat sink was considered to be constant. Of course, with increasing the aspect ratio, the input energy also increases. In this study, the input energy for all heat sinks was considered constant.