## 2 Materials and Methods
### TES Tank Design  
The TES tank design was modeled using computer-aided design (CAD) with Autodesk Fusion 360 software. The schematic representation and pictures of the bioinspired TES tank are shown in Figure 3. The tube portion of the TES tank mimics the structure of a biological fluid flow network, and it is contained inside a shell structure made of aluminum. It is designed as arteries and capillaries that carry blood throughout the human body, and like the phloem in leaves that transports nutrients from the plant root to its tip. The HTF inlet tube of the TES tank narrows until it reaches the first bifurcation point, at which it separates into branches, each of which continues to narrow down until it reaches the subsequent bifurcation point. The TES tank HTF tubes branch into seven new tubes at the end of each level in a symmetrical pattern. The two levels of branching are identically mirrored in the direction of HTF flow, generating a total of four levels. Table 1 summarizes the design of the bio-inspired TES tank with respect to the geometric dimensions. The TES tank shell side is designed to match the flow tubes of the HTF. The TES tank features a cylinder part in the middle, and the top and bottom sections of the shell converge to accommodate the HTF branching tubes. Consequently, during the charging and discharging cycles, the PCM may always be contained close to the HTF tube walls, and a homogeneous melting and solidification process can occur. Three liters of PCM can be held in the bio-inspired TES tank, and there is some space left over to accommodate the volumetric expansion that occurs during the phase transition. Due to the complex biomimetic design of the tank, additive manufacturing based on 3D printing was chosen as a methodology to produce the novel TES. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Dimensions** \\ \hline Outer diameter of the HTF tube at the inlet and outlet & 11 mm \\ Thickness of the HTF tube at the inlet and outlet & 0.648 mm \\ Diameter of the HTF at the bifurcation point of level 0 & 8 mm \\ Diameter of the HTF at the bifurcation point of level 1 & 6 mm \\ Angle between the level 0 branches and the axis of the TES tank & 59\({}^{\circ}\) \\ Angle between the level 1 branch and the axis of the TES tank & 59\({}^{\circ}\) \\ Volume of the bio-inspired TES tank (shell side) & 3 L \\ Heat transfer surface area & 66,248 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometric dimensions of the bio-inspired TES tank. Figure 3: \(Cont.\)By contrasting it with the conventional design (a shell-and-tube TES tank), the thermal performance of the bio-inspired TES tank design may be determined. Therefore, a baseline design resembling a conventional shell-and-tube TES tank with the HTF tubes arranged in a parallel configuration was developed. Table 2 summarizes the design of the conventional shell-and-tube TES tank with respect to the geometric dimensions. The shell-and-tube TES tank can hold 3 L of liquid PCM. A picture of the conventional shell-and-tube TES tank is shown in Figure 4.  
The thermocouples were strategically positioned in both the conventional shell-and-tube TES tank and the bio-inspired TES tank to measure the temperature of the PCM, which is located far away from the HTF tubes such that it has a higher \(\Delta\)T with the inlet HTF during charging and discharging cycles. The temperature sensor in a conventional shell-and-tube TES tank is positioned precisely in the middle of the gap between the HTF tubes at the rear part of the tank. In the bio-inspired TES tank, on the other hand, the temperature sensor was positioned between the tank wall and the outermost branch of the HTF tubes. This thermocouple placement guarantees that by the end of the cycle, each component of the PCM in the TES tank will have experienced a phase change. The position of the thermocouples in the TES tanks is represented with the symbol \"*\" in Figures 3a and 4.