## 3 Results and Discussions
### Comparative Analysis of Water and Nanofluid Performance  
Temperature gradient values obtained from experimental and numerical analysis results were comparatively examined in Table 6. The slope values in this table represent  
Figure 11: Temperature comparison between the numerical and experimental analysis using nanofluid for Al TPMS at different flow rates. the temperature gradient (\({}^{\circ}\)C/mm) along the Al TPMS structure using distilled water, calculated as the rate of temperature change between the first (TC-1) and last (TC-7) thermocouple positions. In experimental studies, temperature gradient slopes were calculated as 0.019495 \({}^{\circ}\)C/mm, 0.021181 \({}^{\circ}\)C/mm, and 0.020157 \({}^{\circ}\)C/mm for flow rates of 23.56 cm\({}^{3}\)/s, 27.49 cm\({}^{3}\)/s, and 35.34 cm\({}^{3}\)/s, respectively. The gradient slope values obtained from numerical analyses were found to be 0.008391 \({}^{\circ}\)C/mm, 0.007946 \({}^{\circ}\)C/mm, and 0.009415 \({}^{\circ}\)C/mm for the same flow rates. Both experimental and numerical results for all cases were observed to be within the optimum performance range specified in the literature, below 0.03 \({}^{\circ}\)C/mm. The lower gradient values obtained from numerical results compared to experimental results can be attributed to the simulations reflecting ideal conditions without accounting for heat losses and experimental uncertainties present in the real system. Nevertheless, the values obtained from both analysis methods demonstrate that the TPMS structure provides effective temperature distribution. Temperature gradient values obtained using nanofluid in Al TPMS structure were analyzed in Table 7, where the slope values represent the temperature gradient along the flow direction. These slope measurements quantify the rate of temperature change (\({}^{\circ}\)C/mm) between TC-1 and TC-7 positions, serving as a critical indicator of thermal distribution uniformity. The experimental gradient slopes increased from 0.038796 \({}^{\circ}\)C/mm to 0.04119 \({}^{\circ}\)C/mm with increasing flow rates, demonstrating a direct correlation between flow velocity and thermal gradient. In numerical analyses, the calculated slope values varied within the narrower range of 0.008391-0.009415 \({}^{\circ}\)C/mm. Compared to pure water, the use of nanofluid resulted in approximately 90% increase in experimental gradient slope values. This significant enhancement in temperature gradient can be attributed to the improved heat transfer mechanism due to higher viscosity and thermal conductivity of the nanofluid. The lower gradient slope values in numerical results compared to experimental data are due to the limitations in modeling real system dynamics such as nanoparticle aggregation and sedimentation in simulations. Nevertheless, both experimental and numerical results demonstrate that nanofluid usage provides effective heat transfer in the TPMS structure, despite the steeper temperature gradients observed. \begin{table}
\begin{tabular}{c 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 & 29.1214 & 28.60074 & 28.59621 & 29.13505 & 29.48308 & 29.71951 & 29.61267 & 0.019495 \\ Num, 23.56 cm\({}^{3}\)/s & 28.46441 & 28.48721 & 28.5202 & 2  
Temperature distribution and gradient values obtained using pure water in Ag TPMS structure were analyzed in Table 8, where the slope values represent the temperature gradient along the heat exchanger length. These slope measurements quantify the thermal gradient (\({}^{\circ}\)C/mm) between the first and last thermocouple positions, providing insight into temperature uniformity across the structure. The experimental gradient slope values increased from 0.031575 \({}^{\circ}\)C/mm to 0.037759 \({}^{\circ}\)C/mm with increasing flow rates, indicating a direct relationship between flow velocity and thermal gradient steepness.