## 2 Experimental Measurements
### Temperature Distribution Analysis  
The thermal-hydraulic performance of TPMS-based heat exchangers has been examined using three-dimensional models of various surfaces with different volume ratios. [PERSON] et al. (2023) [18] conducted a comprehensive investigation on flow and heat transfer in various channels based on TPMS. Their findings reveal the significant impact of secondary flows, periodic flow acceleration/deceleration, and continuous flow direction changes on convective heat transfer. This research contributes to the design and implementation of TPMS-based heat exchangers [18]. Most studies have focused on the thermal performance of TPMS structures under laminar flow conditions. Nevertheless, recent research has begun to explore the effects of turbulent flow on their heat transfer characteristics. [PERSON] et al. examined the thermal conductivity of TPMS structures, finding that thermal conductivity decreases as porosity increases. Among the different TPMS topologies, the Gyroid structure demonstrated the highest thermal conductivity. The results suggested that TPMS structures could be effectively employed in thermal management systems, including heat exchangers. In the study, effective thermal conductivity values were measured for different TPMS topologies (Gyroid, Diamond, and Primitive), and the relationship between these values and the Re was investigated. At high Re (\(Re>2000\)), in the turbulent flow regime, it was observed that the heat transfer performance of TPMS structures significantly increased. For example, it was found that the Gyroid structure provided approximately 40% higher effective thermal conductivity in turbulent flow compared to laminar flow [22]. [PERSON] et al. (2019) [11] further contributed to this field by establishing critical criteria for evaluating temperature homogeneity in TPMS structures, providing valuable metrics for assessing thermal performance uniformity across different geometries and operating conditions. Three fundamental statistical parameters were utilized for the analysis of temperature distribution homogeneity: standard deviation, coefficient of variation, and temperature uniformity. Standard Deviation (\(\sigma\)), which indicates how much temperature measurements deviate from the mean value, is calculated using the following equation, where \(T_{i}\) is the temperature value at each thermocouple, \(T_{mean}\) represents the mean temperature of all thermocouples, and \(N\) is the number of thermocouples (\(N=7\)) [35]  
\[\sigma=\sqrt{\frac{1}{N}}\sum_{i=1}^{N}\Bigl{(}T_{i}-T_{mean}\Bigr{)}^{2} \tag{15}\]The coefficient of variation (\(CV\)), expressed as a percentage, represents the ratio of standard deviation to mean value, facilitating comparisons of distributions across different scale systems [35]  
\[CV=\left(\frac{\sigma}{T_{mean}}\right)\times 100\% \tag{16}\]  
The parameter, as proposed by [PERSON] et al. (2024), represents the temperature differential between the maximum (\(T_{max}\)) and minimum (\(T_{max}\)) temperatures observed within the system [30]:  
\[\Delta T_{max}=T_{max}-T_{min} \tag{17}\]  
These parameters provide a comprehensive approach to evaluate the temperature distribution homogeneity within the TPMS structure. Lower values of standard deviation and coefficient of variation indicate a more homogeneous temperature distribution [36], while a lower \(\Delta T_{\max}\) value demonstrates that the temperature gradient within the system has been minimized. The temperature gradient analysis was calculated as the ratio of the temperature difference between the first (TC1) and seventh (TC7) thermocouples to the distance between these two points. This ratio serves as a crucial parameter characterizing the rate of temperature change along the TPMS structure. Low gradient values indicate more uniform heat transfer and more effective cooling in the system, while high gradient values suggest potential inefficiencies in heat transfer and possible hot spot formation.