## 2 Experimental Measurements
### Experimental Procedure  
The experimental setup was designed to investigate the thermal and hydraulic characteristics of the system under controlled turbulent flow conditions. A variable-flow pump was employed to regulate working fluid circulation, ensuring the desired turbulence levels. Figure 1 provides a detailed illustration of the experimental apparatus and methodology. Prior to commencing the experiment, trapped air bubbles were meticulously removed to ensure accurate results. A voltage and current-controlled power source supplied a constant heat flux of 30.8 kW/m\({}^{2}\). To ensure a steady low temperature at the inlet of the test unit, a water bath was utilized. Nevertheless, slight fluctuations were noted due to the inherent difficulties in achieving uniform inlet temperatures. The test section was firmly attached to an Al heating block, with thermocouples placed 0.1 cm below the interface. An inlet thermocouple was placed at the entrance of the system, while another was installed at the outlet, and seven additional thermocouples were arranged along the interface. The test unit was constructed to match the dimensions of an Intel Core i7 processor. Both the Al heating block and the TPMS structure were precisely manufactured to these specifications, allowing for a valid comparison of their thermal performance and flow characteristics. Table 1 presents the dimensions of the TPMS and the distances of the surface thermocouples. A data acquisition system continuously recorded temperature data at specified time intervals throughout the experiment. Figure 1: Overview of the system: (**a**) experimental setup, (**b**) schematic diagram. All temperature measurements in this study are associated with a calibrated uncertainty of \(\pm\)0.75% (\({}^{\circ}\)C), which is attributed to the T-type thermocouples utilized in the experimental setup. This measurement uncertainty is found to be significantly lower than the observed thermal performance differences between materials (15% enhancement with Ag versus Al TPMS) and cooling fluids (12% improvement with nanofluids versus water). The maximum uncertainty in calculated Nusselt numbers (\(Nu\)) is determined to be 2.6%, which remains substantially below the performance variations documented across experimental configurations. These uncertainty values confirm the statistical significance of the reported results and validate the reliability of the comparative thermal performance evaluations conducted in this investigation. To address potential heat losses in the experimental setup, comprehensive thermal insulation measures were implemented. The test section was fabricated utilizing low thermal conductivity materials, and all external surfaces, except for the measurement interfaces, were insulated with polyurethane foam. Thermal paste was applied at the interface between the TPMS structure and test block to minimize contact resistance. Heat loss quantification tests were conducted prior to experiments, validating that less than 3% of the input power was dissipated to the surroundings under steady-state conditions. This minimal heat loss was quantified and incorporated into all thermal calculations, ensuring the accuracy of the reported heat transfer coefficients. The uncertainty analysis confirms that the experimental methodology yields reliable results, with the influence of these quantified heat losses remaining within the stated measurement uncertainty bounds. As depicted in Figure 2, the test block incorporates Al and Ag TPMS, with the fluid flowing through the hexagonal structure from inlet to outlet. The liquid flows through the TPMS structure, effectively absorbing heat from the heated block. To reduce heat loss, the test section was made from insulating material, and thermal paste was used at the interface between TPMS structure and test block. The upper part of the experimental setup is covered with a transparent polyethylene sheet. It is fixed using multiple screws to ensure the sealing and circulation of the nanofluid in the system.