## 3 Results and Discussions
### Temperature Homogeneity Analysis  
This section presents a comprehensive analysis to evaluate temperature distribution homogeneity in TPMS structures. Temperature homogeneity is a crucial indicator of system performance and directly affects cooling system efficiency (Equations (15)-(17)). In the analysis using standard deviation, coefficient of variation, and temperature distribution homogeneity parameters, the average standard deviation for water in Al TPMS structure was calculated as 0.55 \({}^{\circ}\)C, decreasing to 0.42 \({}^{\circ}\)C with nanofluid usage. In Ag TPMS structure, the average standard deviation was measured as 0.36 \({}^{\circ}\)C for water and 0.30 \({}^{\circ}\)C for nanofluid. Examining variation coefficients, values of 2.1% for water and 1.8% for nanofluid were obtained in Al TPMS structure, while these values were calculated as 1.5% and 1.2% respectively in Ag TPMS structure. Maximum temperature differences were measured as 2.2 \({}^{\circ}\)C for water and 1.8 \({}^{\circ}\)C for nanofluid in Al TPMS structure. In Ag TPMS structure, these values were determined as 1.5 \({}^{\circ}\)C and 1.2 \({}^{\circ}\)C respectively. Temperature distribution homogeneity was quantitatively evaluated using statistical analysis. Standard deviation (\(\sigma\)) of temperature measurements across seven thermocouples was calculated for each experimental condition. In Al TPMS structure, \(\sigma\) values ranged from 0.42 \({}^{\circ}\)C to 0.68 \({}^{\circ}\)C for water, while nanofluid showed improved homogeneity with \(\sigma\) values between 0.31 \({}^{\circ}\)C and 0.54 \({}^{\circ}\)C. Ag TPMS structure exhibited even better temperature uniformity with \(\sigma\) values of 0.28 \({}^{\circ}\)C to 0.45 \({}^{\circ}\)C for water and 0.22 \({}^{\circ}\)C to 0.38 \({}^{\circ}\)C for nanofluid. This improved homogeneity can be attributed to higher thermal conductivity of both Ag structure and nanofluid, facilitating more efficient heat dissipation. Comparative analysis of temperature gradient values revealed unique advantages for each combination. In Al TPMS structure, gradient values ranged from 0.02-0.022 \({}^{\circ}\)C/mm with pure water, increasing to 0.04-0.042 \({}^{\circ}\)C/mm with nanofluid usage. In Ag TPMS structure, gradient values ranging from 0.032-0.038 \({}^{\circ}\)C/mm with pure water decreased to 0.029 \({}^{\circ}\)C/mm at high flow rates with nanofluid usage. The lowest temperature values were obtained with Ag TPMS and nanofluid combination, resulting from synergistic effect of Ag's high thermal conductivity and nanofluid's enhanced heat transfer properties. Numerical analyses showed lower gradient values (0.008-0.009 \({}^{\circ}\)C/mm) compared to experimental results in all combinations. Overall assessment determined that Ag TPMS with nanofluid combination provided optimal cooling performance at high flow rates, followed by Ag TPMS with water, Al TPMS with nanofluid, and Al TPMS with water combinations, respectively. These results demonstrate that Ag TPMS structure provides more homogeneous temperature distribution. Nanofluid usage improved temperature homogeneity in TPMS structures. This improvement can be attributed to nanofluid's high thermal conductivity and enhanced heat distribution properties within TPMS structure. Data obtained from homogeneity analysis provides important design information for systems where temperature distribution is critical, such as electronic cooling applications. The innovative aspects of this study stand out in several key areas. Firstly, while previous studies focused on laminar flow conditions, this research fills an important gap in literature by specifically examining turbulent flow regimes in TPMS structures. Secondly, comparative analysis of two different TPMS materials (Al and Ag) provides new insights about effect of material thermal conductivity on heat transfer performance.