## 2 Experimental Measurements
### Experimental Procedure
The data from 7 temperature sensors located under the TPMS heat exchanger were recorded for each second. The plate thickness at the point where the channel contacts the heated block is 0.3 cm. During the experiment, three different flow rates were applied. These flow velocities are 30 cm/s, 35 cm/s, and 45 cm/s, and data were recorded for flow rates of 23.42 cm\({}^{3}\)/s, 27.29 cm\({}^{3}\)/s, and 35.41 cm\({}^{3}\)/s, respectively. The heat flux applied to the Al and Ag blocks was kept constant at 30.8 kW/m\({}^{2}\) throughout all experiments. Slight variations in inlet temperature were observed for each experiment, and measurements were performed considering this situation during the analysis phase. The friction factor was not taken into account in all evaluated scenarios. The nanofluid, which is circulated through the block channels by forced circulation, is a mixture of 0.6% Al\({}_{2}\)O\({}_{3}\) and 99.4% distilled water, synthesized by a manufacturer. A nanoparticle size of 50 nm was used to ensure the suspension and homogeneous distribution of the nanoparticles. This liquid was then diluted with distilled water to the targeted volume concentration. To suspend the nanofluid in distilled water, homogenization was achieved by using a magnetic stirrer for 40 min. Distilled water was used as the cooling liquid in the experimental setup. The physical properties of the pure water and nanofluid \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Surface Thermocouples** & **TC-1** & **TC-2** & **TC-3** & **TC-4** & **TC-5** & **TC-6** & **TC-7** \\ \hline Location of thermocouples from inlet (mm) & 4.2 & 8.4 & 12.6 & 16.8 & 21 & 25.2 & 29.4 \\ \hline TPMS block dimensions (L \(\times\) H) (mm) & & & & 37.5 \(\times\) 12.7 & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Properties of the materials. used in the experimental setup are presented in Table 2. The thermal conductivity, density, and heat capacity of the nanofluid are higher than those of pure water, and the increase in the viscosity coefficient also increases the pressure loss. The nanofluid demonstrates superior thermal conductivity, density, and heat capacity relative to pure water. In addition, the rise in viscosity coefficient leads to an increase in pressure loss. An uncertainty analysis was conducted on the components of the apparatus utilized for experimental data collection. The flowmeter and T-type thermocouples were identified as the main sources of error propagation within the device. Through comprehensive calibration procedures, the flowmeter's associated error was quantified at 0.44%. Calibration procedures established the uncertainty of the T-type thermocouples at 0.75% (\({}^{\circ}\)C). Additionally, fluctuations in the uncertainties of non-dimensional parameters, including \(Nu\) and temperature, were noted as a result of changes in temperature and flow rate. To elucidate this relationship, \(Nu\) and \(Re\) are expressed mathematically as follows [30]: \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Materials**} & \(\rho\) & \(\mu\times 10^{-4}\) & \(\mathbf{C_{p}}\) & \(\mathbf{k}\) & EC \\  & **(kg/m\({}^{3}\))** & **(kg/m.s)** & **(J/kg.K)** & **(W/m.K)** & **(\(\mu\)S/cm)** \\ \hline Water (Distilled) & 998.2 & 10.01 & 4128 & 0.613 & 0.055 \\ Nanofluid (0.6\% Al\({}_{2}\)O\({}_{3}\) + distilled water) & 1013.811 & 10.4 & 4109.198 & 0.6242 & - \\ \hline \end{tabular}
\end{table} 
Table 2: Thermophysical properties [24]. Figure 2: Test unit of TPMS structure: (a) Al, (b) Ag. \[Nu=\frac{h_{x}\cdot D}{k_{f}} \tag{1}\]  
\[Re=\frac{u_{in}\cdot D}{\
u} \tag{2}\]  
The Reynolds number is determined based on the hydraulic diameter of the inlet side of the Gyroid or Schwarz-P lattice structure, where the hydraulic diameter \(D_{h}\) is calculated as:  
\[Re_{D_{h}=\frac{\mu UD_{h}}{\
u}} \tag{3}\]  
\[D_{h}=\frac{4A}{P} \tag{4}\]  
The area \(A\) and wetted perimeter \(P\) of the inlet cross-section are used in this calculation.