## 3 Results and Discussion  
### Phase Transition Characteristics  
The change in the temperature of the PCM against time was logged during the charging and discharging cycles. The temperature range (15 \({}^{\circ}\)C to 45 \({}^{\circ}\)C) that was selected for logging was chosen specifically to encompass the phase transition regime of the PCM. Figures 5 and 6 show the comparison between the phase transition behavior of the PCM housed by a bio-inspired TES tank and by a conventional shell-and-tube TES tank during the charging and discharging cycles, respectively. To make comparisons easier, the HTF flow rate was kept constant at 3 kg/min in both scenarios. Figure 4: Picture of the shell-and-tube TES tank (”\({}^{\ast}\)\({}^{\ast}\)\({}^{\ast}\)\({}^{\ast}\)\({}^{\ast}\)\(  
From Figure 5, it is apparent that both the shell-and-tube and the bio-inspired TES tank took a similar amount of time (0.45 h and 0.49 h) to raise the temperature of the PCM from 15 \({}^{\circ}\)C to 29 \({}^{\circ}\)C. The temperature vs. time slopes of both cases were alike during the early stages of the charging cycle. Following the onset of the phase change process, there is only a small discrepancy in the charging rate between the conventional shell-and-tube and the bio-inspired TES tanks. Although the bio-inspired TES tank's charging performance was modest, it was nearly as good as that of the shell-and-tube tank. Each of the two types of TES tanks--conventional shell-and-tube and bio-inspired--had an entirely different geometry. The bio-inspired TES tank design resembles a near cylindrical container, with the HTF tubes that enter from the bottom, branch in the center, and emerge as a single tube at the end. TES tanks with the conventional shell-and-tube design are shaped like rectangular containers, with the HTF tube beginning at one end and extending to all parts of the tank in a serpentine manner until it emerges at the other end. During the pre-charging cycle, most of the heat is uniformly transferred to every area of the contained n-octadecane in the traditional shell-and-tube TES tank because the HTF enters the tank from one end and exits from the other. In contrast, the HTF enters the bio-inspired TES tank from the bottom, some of it divides through the branches, and some of it goes directly to the top. Therefore, the temperature of the n-octadecane rises first in the bottom, core area of the bio-inspired TES tank and in close proximity to the HTF tube walls, then spreads outward in a radial direction with respect to the HTF tubes at a rate determined by the n-octadecane's solid phase thermal conductivity. As the charging cycle progresses, natural convection occurs equally throughout all the cross sections of the traditional shell-and-tube TES tank. In contrast, in the bio-inspired TES tank, the n-octadecane located at the bottom of the tank, the core regions of the tank, and the area close to the tube walls initially turn liquid. Furthermore, the n-octadecane present throughout the tank's core must melt in order for natural convection to happen more rapidly in the bio-inspired TES tank. Therefore, when comparing the bio-inspired TES tank design to the traditional shell and tubes, the charging rate efficiency was not high. During the initial stages of the discharging cycle, the temperature vs. time profile was similar among the shell-and-tube and bio-inspired TES tanks. From Figure 6, it is evident that the onset of the phase change process (liquid phase to solid phase) happens in the same time frame in the TES tank type. However, following the onset of the phase change process, the discharging rate was substantially higher for the bio-inspired TES tank. Figure 6 also shows that the time required for the TES tank to discharge the heat stored in  
Figure 6: Comparison between shell-and-tube and bio-inspired TES tanks during the discharging cycle. the PCM was 1.4 h for the bio-inspired TES tank, 52% less than the shell-and-tube TES tank (2.8 h).