## 4 Results and Discussion
### Comparison between Experimental Measurements and Numerical Data
#### 4.1.2 Nanofluid as the Cooling Fluid  
Previous work by the authors of this paper used a nanofluid to study channel heat enhancement [18]. In the current paper, the nanofluid was mixed using a sonic mixture before being used in the experiment. Also, it is essential to indicate that, after each experiment, the system was flushed with distilled water to remove all the metallic particles from the piping system. The TPMS porous structure was also carefully cleaned to avoid solidifying the nanoparticles in the channel of the structure. Figures 7 and 8 experimentally present the temperature distribution measured by the thermocouple for the same flow rate as the previous case in the presence of the aluminum and silver TPMS structures. The first observation worth mentioning and confirmed earlier with fluid circulation is that the silver TPMS structure helps in heat removal better than the aluminum structure. As shown in Figures 7a and 8a, a lower temperature is detected in the presence of the silver structure. Furthermore, by examining Figures 7c and 8c against Figures 5c and 6c, one may notice that, by eliminating the inlet and outlet temperature from the data, the nanofluid provided better cooling than the distilled water case. It is essential to indicate that the inlet nanofluid varied between each run; thus, studying the variable \(\theta\) is the right approach. In addition, nanofluid maintains temperature uniformity, proving to us that the structure design led to this uniformity. Figure 13 compares the measured experimental data and the calculated numerical temperature. One notices a good agreement between the two datasets, and the differences presented in Table 2 for water as the circulating fluid are very close to the differences in Figure 13 when the nanofluid is the circulating fluid. However, it will be interesting to investigate the nanoparticles' agglomeration and path inside the structure. This could be conducted numerically and will be the subject of future investigation. The authors believe this is the first case of a nanofluid experimentally conducted inside a TPMS structure. Figure 13d-f shows that the difference between the computed and measured data is significant compared to all other cases. The main reason for these discrepancies, based on experience, may be an error in the flow rate measurement. It is noticeable that, sometimes, the nanoparticles create a false reading for the flow rate due to some accumulation in the pump. The second reason is that the fluctuation of electric current may provide a lower heat flux, leading to lower temperatures. This issue will be addressed in a different article. The variation trend is reasonable between the two sets of data. Figure 12: Performance evaluation criterion for the two cases: (a) aluminum TPMS structure and (b) silver TPMS structure. The uniformity of the temperature distribution is worth mentioning. The temperature slope was evaluated numerically and experimentally. Figure 14 shows the changes in the slope for the two cases for all flow rates. It is noticeable that the silver structure exhibits a lower slope when compared to the aluminum structure. In addition, the slope value is very low for both cases, which is a good indicator of the uniformity of the cooling process. Figure 13: Temperature comparison between the experimental measurement and numerical calculation using the nanofluid. (**a**) Temperature distribution along the aluminum-heated block. (**b**) Temperature difference with the aluminum structure. (**c**) Non-dimensional temperature with the aluminum structure. (**d**) Temperature distribution along the silver-heated block. (**e**) Temperature difference with the silver structure. (**f**) Non-dimensional temperature with the silver structure. The performance evaluation criteria for the nanofluid case were calculated.