## 3 Results and Discussions
### Comparative Analysis of Water and Nanofluid Performance
The higher \(Nu\), the more effective the heat transfer by convection, resulting in improved heat transfer performance. Low \(Nu\) indicates that heat transfer occurs more through conduction and that convection is less effective. Therefore, low thermal resistance and high \(Nu\) indicate more effective heat removal performance. Materials with high thermal conductivity, such as Al or Ag, reduce the thermal resistance of the system by allowing heat to spread more quickly and efficiently within the material. High \(Nu\) is typically a result of factors such as turbulent flow, high flow velocities, or enhanced heat transfer surfaces. Performance analysis of TPMS structures with different coolants has been experimentally and numerically investigated. Figure 12 shows comparative \(Nu\) analysis for both water and nanofluid at different flow rates in Al and Ag TPMS structures. Figure 12a presents experimental results while Figure 12b displays numerical results comparatively. Results reveal that nanofluids exhibit higher Nu values at low flow rates (23.56 cm\({}^{3}\)/s), showing approximately 4.6% increase in Al TPMS and 5.4% increase in Ag TPMS compared to water. In experimental results, the highest \(Nu\) value of 82.18 was obtained with nanofluid usage in Ag TPMS structure at 27.49 cm\({}^{3}\)/s flow rate. This value represents approximately 33% improvement compared to Al TPMS-water combination under the same conditions. Numerical analyses showed a similar trend, with Ag TPMS-nanofluid combination reaching a \(Nu\) value of 85.42 at 27.49 cm\({}^{3}\)/s flow rate. At the highest flow rate of 35.34 cm\({}^{3}\)/s, both experimental and numerical results showed a significant decrease in \(Nu\) values, particularly for Ag TPMS-nanofluid combination. This decrease was caused by increased turbulence intensity at high flow rates within the complex geometry of TPMS structure, especially \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Diff. (\%)** & **TC-1** & **TC-2** & **TC-3** & **TC-4** & **TC-5** & **TC-6** & **TC-7** & **Average** \\ \hline Al, 23.56 cm\({}^{3}\)/s & 5.35 & 3.54 & 3.41 & 5.06 & 6.03 & 6.65 & 6.20 & 5.18 \\ Al, 27.49 cm\({}^{3}\)/s & 6.54 & 4.98 & 4.79 & 6.39 & 7.34 & 7.86 & 7.55 & 6.49 \\ Al, 35.34 cm\({}^{3}\)/s & 7.33 & 5.34 & 5.18 & 6.81 & 7.85 & 8.50 & 8.13 & 7.02 \\ Ag, 23.56 cm\({}^{3}\)/s & 5.03 & 5.54 & 5.26 & 3.38 & 3.66 & 3.77 & 5.93 & 4.65 \\ Ag, 27.49 cm\({}^{3}\)/s & 4.70 & 3.32 & 4.66 & 6.66 & 4.43 & 5.39 & 5.32 & 4.92 \\ Ag, 35.34 cm\({}^{3}\)/s & 8.17 & 5.93 & 6.36 & 5.31 & 4.15 & 5.67 & 5.52 & 5.87 \\ \hline \end{tabular}
\end{table} 
Table 10: Comparison of surface thermocouple temperature differences between experimental measurements and numerical calculations for distilled water. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Position (mm)** & **4.2** & **8.4** & **12.6** & **16.8** & **21** & **25.2** & **29.4** & **Slope** \\ \hline Exp, 23.56 cm\({}^{3}\)/s & 22.26588 & 22.2714 & 22.42568 & 22.51726 & 22.61818 & 23.52345 & 23.44203 & 0.046672 \\ Num, 23.56 cm\({}^{3}\)/s & 24.06441 & 24.08721 & 24.1202 & 24.16192 & 24.20496 & 24.24355 & 24.27587 & 0.008391 \\ Exp, 27.49 cm\({}^{3}\)/s & 21.58988 & 21.60485 & 21.66426 & 21.74852 & 21.64094 & 22.41727 & 22.34347 & 0.029904 \\ Num, 27.49 cm\({}^{3}\)/s & 24.39838 & 24.4391 & 24.47434 & 24.51083 & 24.54588 & 24.57542 & 24.59862 & 0.007946 \\ Exp, 35.34 cm\({}^{3}\)/s & 20.41504 & 20.40304 & 20.42589 & 20.56916 & 20.44391 & 21.27838 & 21.14493 & 0.028964 \\ Num, 35.34 cm\({}^{3}\)/s & 22.00791 & 22.07198 & 22.1165 & 22.15724 & 22.19334 & 22.22253 & 22.24517 & 0.009415 \\ \hline \end{tabular}
\end{table} 
Table 9: Temperature gradient analysis for Ag TPMS structure using nanofluid at different flow rates. affecting the heat transfer mechanism in Ag TPMS, resulting in reduced convective heat transfer performance. The _PEC_ analysis presented in Figure 13 demonstrates a critical performance parameter that integrates thermal and hydraulic effects.