## 3 Results and Discussions
### Comparative Analysis of Water and Nanofluid Performance
In numerical analyses, gradient slope values remained within the consistent range of 0.008391-0.009415 \({}^{\circ}\)C/mm. Compared to Al TPMS structure, Ag TPMS exhibited lower temperature values and more uniform temperature distribution as evidenced by the slope measurements. This improvement is attributed to the higher thermal conductivity of Ag, which facilitates more efficient heat spreading throughout the structure. The difference between experimental and numerical slope results stem from heat losses and measurement uncertainties in the experimental system. However, both analysis methods demonstrate that Ag TPMS structure provides approximately 20% lower temperature gradient slope values compared to Al TPMS. These slope comparison results confirm that Ag TPMS structure delivers more effective heat transfer performance through enhanced thermal conductivity. Temperature distribution and gradient values obtained using nanofluid in Ag TPMS structure are presented in Table 9, where the slope values characterize the temperature gradient along the heat exchanger. These slope measurements quantify the thermal gradient (\({}^{\circ}\)C/mm) between TC-1 and TC-7 positions, offering valuable insights into heat transfer efficiency and temperature uniformity. In experimental studies, while the gradient slope value was observed as 0.046672 \({}^{\circ}\)C/mm at the lowest flow rate (23.56 cm\({}^{3}\)/s), this slope value decreased to 0.028964 \({}^{\circ}\)C/mm as flow rate increased. This reduction in slope steepness indicates improved heat transfer performance of the nanofluid with increasing flow rate, as the temperature distribution becomes more uniform. In numerical analyses, gradient slope values varied within the consistent range of 0.008391-0.009415 \({}^{\circ}\)C/mm. Compared to pure water usage, nanofluid application resulted in higher gradient slope values at the lowest flow rate; however, this difference diminished with increasing flow rates. This slope variation phenomenon may be attributed to nanoparticles' sedimentation tendency at low flow rates, which affects thermal conductivity distribution. Nevertheless, overall temperature values were found to be approximately 15-20% lower compared to pure water. These slope analysis results demonstrate that the combination of Ag TPMS structure and nanofluid provides effective cooling performance, particularly at higher flow rates where more uniform temperature distribution is achieved. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Position (mm)** & **4.2** & **8.4** & **12.6** & **16.8** & **21** & **25.2** & **29.4** & **Slope** \\ \hline Exp, 23.56 cm\({}^{3}\)/s & 26.28672 & 26.2418 & 26.09287 & 26.66219 & 26.78533 & 27.0631 & 27.0824 & 0.031575 \\ Num, 23.56 cm\({}^{3}\)/s & 24.96441 & 24.98721 & 25.0202 & 25.06192 & 25.10496 & 25.14355 & 25.17587 & 0.008391 \\ Exp, 27.49 cm\({}^{3}\)/s & 25.18159 & 25.07145 & 25.04203 & 25.61619 & 25.78724 & 26.07998 & 26.08699 & 0.035928 \\ Num, 27.49 cm\({}^{3}\)/s & 23.99838 & 24.0391 & 24.07434 & 24.11083 & 24.14588 & 24.17542 & 24.19862 & 0.007946 \\ Exp, 35.34 cm\({}^{3}\)/s & 24.07447 & 24.20875 & 24.04555 & 24.24421 & 24.82284 & 25.14791 & 25.02599 & 0.037759 \\ Num, 35.34 cm\({}^{3}\)/s & 22.10791 & 22.17198 & 22.2165 & 22.25724 & 22.29334 & 22.32253 & 22.34517 & 0.009415 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Temperature gradient analysis for Ag TPMS structure using distilled water at different flow rates. Table 10 presents the percentage temperature differences and their percentage averages between the experimental and numerical results, based on the data obtained from the 7 temperature sensors located in the test block. The average temperature differences between the results range from 4.65% to 7.02%, which is within acceptable limits. \(Nu\), given in Equation (10), is an important dimensionless parameter commonly used to evaluate heat removal performance. \(Nu\) represents the ratio of heat transfer by convection to heat transfer by conduction and is a measure of heat transfer performance.