## 2 Experimental Measurements
### Description of the Experiment  
Figure 1 presents the experimental setup and the test section. A pump with a controlled flow rate was used to force fluid through the test section. The flow rate was selected to maintain laminar flow. Any gas bubble formation was removed before starting the experiment. The heat was generated using a voltmeter and ammeter, and the heat flux was fixed at 30,800 W/m\({}^{2}\). A water bath was used to maintain a low temperature at the entrance of the test section. However, some variation occurred due to the difficulties of maintaining identical inlet temperatures. A heated block made of aluminum located below the test section was used in the experiment. The thermocouples were 1 mm below the interface between the heated block and the test section. In total, nine thermocouples were used: one at the inlet, seven below the interface, and one at the outlet. The test section had the dimensions of an Intel Core i7 computer processor. The base was square, of 37.5 mm long, and the height was 12.7 mm. The aluminum heated block and the TPMS structure had identical dimensions. A data acquisition system was used to collect data at different time steps. More details about the experiment can be found in ([PERSON] et al., 2017).  
Figure 2 presents the test section with the aluminum TPMS and silver TPMS. As shown, the flow enters from one side of the hexagonal and exits from the opposite side. Fluid circulates through the structure and absorbs heat conducted from the heated block. Thermo-pasts are added between the TPMS structure and the heated block. The test section is made of isolating material to stop heat leakage.  
A plastic sheet covered the top of the test section, and multiple screws were used to seal the top part of the test section.  
As indicated earlier, five different flow rates were applied during the experiment. These were 3.74 cm\({}^{3}\)/s, 7.86 cm\({}^{3}\)/s, 11.8 cm\({}^{3}\)/s, 15.73 cm\({}^{3}\)/s, and 19.85 cm\({}^{3}\)/s. The heat flux applied at the aluminum block remained constant at 30,800 W/m\({}^{2}\). The inlet temperature may vary slightly between runs, but the analysis measures and considers it. Figure 3 presents the timelapse for the case of the aluminum and silver structures. A nanofluid was used in this representation, and thermocouple number 4 was chosen for this presentation. Thermocouple number 4 was approximately 16.8 mm from where the flow starts entering the test section. The inlet temperature, as seen, varied in each run, but a steady state was achieved after approximately 45 min.  
Figure 1: Experimental setup [1].  
Figure 2: Test section with the TPMS structure. (**a**) Aluminum TMPS in the test section. (**b**) Silver TPMS in the test section.  
As seen in Figure 3, the temperatures, regardless of the flow rate and the inlet temperature, reached a steady state approximately after 45 min. Data collection may take up to two hours as the inlet temperature needs to drop to a reasonable level for the next run to begin. A slight fluctuation in the temperature is also shown. The investigation led us to believe that this fluctuation was due to some current instability leading to heat flux fluctuation. However, it is noticeable that it was adjusted after all, and the temperature rose to the correct value. Because silver thermal conductivity is almost double that of aluminum, more heat is extracted from silver than from aluminum. The inlet temperature for all cases fluctuated by one degree between runs. Even if an attempt was made to start the experiment at precisely the identical inlet temperature, this was impossible to reach. However, the inlet temperature was taken into consideration in the analysis.