## 2 Experimental Measurements
### Boundary Conditions
Various parameters were considered to measure the heat removal capacity of the TPMS. Among the parameters considered, the heat transfer coefficient (\(h\)) was primarily evaluated and defined by Equation (9). The local \(Nu\), which is a critical parameter in heat transfer analysis, is defined by Equation (10) as follows [34]:  
\[h=\frac{q^{\prime\prime}}{(T-T_{in})} \tag{11}\]  
\[Nu=\frac{hD}{k_{f}} \tag{12}\]  
The design of cooling systems significantly relies on pressure drop. This phenomenon is characterized by the friction factor (\(f\)), which is expressed in the following Equation (11) as follows [18; 30; 34]:  
\[f=\frac{0.5\Delta pD}{\rho Lu_{in}^{2}} \tag{13}\]  
_PEC_ is an important criterion used to evaluate the efficiency of heat exchangers and other thermal systems, and it is given in Equation (12). _PEC_ quantitatively expresses the overall system effectiveness by evaluating the heat transfer performance and hydraulic performance of a system together. The factors included in _PEC_ are generally the increase in heat transfer and friction factor, and constant pumping power. The increase in heat transfer indicates how much more heat the developed system transfers compared to a standard system. The increase in friction factor indicates how much more pressure drop the developed system causes compared to the standard system. In constant pumping power comparisons, it is generally assumed that the power is kept constant. _PEC_ combines these factors to reveal how much extra energy (for pumping) a system spends while increasing heat transfer. Obtaining a high _PEC_ value indicates that the increase in heat transfer of the system is more advantageous compared to the increased pumping costs. Therefore, it \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Boundary** & **Condition Type** &
\begin{tabular}{c} **Mathematical** \\ **Representation** \\ \end{tabular} & **Description** \\ \hline Inlet & Velocity inlet & \(u=u_{in}\) & Uniform velocity in x-direction \\ \hline \hline  & Temperature & \(T=T_{in}\) & Constant inlet temperature \\ \hline Outlet & Pressure outlet & \(\partial p/\partial n=0\) & Zero pressure gradient (open boundary) \\ \hline  & Outflow & - & Fully developed flow condition \\ \hline Bottom surface & Heat flux & \(q^{\prime\prime}=30.8\) kW/m\({}^{2}\) & Constant heat flux applied \\ \hline All external surfaces & Thermal & \(\partial T_{Surface}/\partial n=0\) & Adiabatic condition (no heat transfer) \\ \hline All solid–fluid interfaces & Velocity & \(u=v=w=0\) & No-slip boundary condition \\ \hline  & Thermal & \(T_{fluid}=T_{solid}\) & Thermal equilibrium at interfaces \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Boundary conditions applied in the TPMS model simulation. shows that system performance is improved. This criterion, where \(Nu_{\text{local}}\) represents the local \(Nu\), is defined by the following formula [18; 28; 29; 30; 34]:  
\[PEC=\frac{Nu_{local}}{f^{\frac{1}{3}}} \tag{14}\]  
A mesh sensitivity analysis was conducted to assess the numerical model's accuracy and reliability. This process ensures that the results obtained are dependable and consistent across different mesh configurations. This analysis involves systematic evaluation of different mesh sizes. The optimization of the mesh structure was guided by \(Nu\). A mesh structure was deemed optimal when the difference in \(Nu\) between two consecutive meshes was less than 1%. This approach aims to provide the most suitable balance between computational accuracy and computation time. As a result of the analysis, a medium-density mesh structure consisting of 133,8201 elements was determined for the optimal solution. This mesh structure includes a combination of tetrahedral and boundary elements. The selected mesh structure ensures that the numerical model produces accurate and reliable results while also offering a reasonable computation time.