## 4 Results and Discussion
### Comparison between Experimental Measurements and Numerical Data
#### 4.1.1 Water as the Cooling Fluid  
Using the COMSOL software, the model was solved using the finite element methods. Some boundary conditions were adopted from the experimental measurement, such as the inlet temperature, flow rate, and applied heat flux. With those boundary conditions, the model was solved for different numerical conditions, and results were compared with the experimental data. Using the numerical data, the experimental temperature measurement and the numerical calculated value were compared, as shown in Figure 9, for water as the circulating fluid. As shown, a good agreement between the two measurement sets was achieved. The slight variation in the experimental measurement was trivial and expected. The difference between the two datasets could be due to heat flux fluctuation, heat losses, or inlet flow fluctuation. The difference between the experimental and numerical datasets was less than 2 \({}^{\circ}\)C. Figure 10 compares water as a cooling fluid using the silver TPMS. Figure 9: Comparison of the temperature between the numerical and experimental measurements (aluminum TPMS and water) (**a**) Flow rate 3.74 cm\({}^{3}\)/s and 19.85 cm\({}^{3}\)/s (**b**) flow rate 7.86 cm\({}^{3}\)/s and 11.8 cm\({}^{3}\)/s, (**c**) flow rate 15.73 cm\({}^{3}\)/s. A similar comparison agreement was observed for the case of the aluminum TPMS but at lower temperatures. Figures 9 and 10 show that the numerical modelling results differ slightly from the experimental results. This is due to some heat losses in the experiment, even with perfect insulation; thus, slightly lower experimental results were achieved. The differences between the experimental and numerical results are shown in Table 2. The difference between experimental and numerical results is reasonable and well justified. The Nusselt number explained in Equation (10) represents the best heat removal indicator. Figure 11a illustrates the comparison when the TPMS structure is aluminum, and Figure 11b shows an identical case when the TPMS structure is silver. There is a good agreement between the two sets of Nusselt numbers. It is essential to note that, for the case of the aluminum structure, the numerical data show a slightly higher value than the experimental data at high flow rates. This may be due to heat losses occurring during the experiment. Figure 10: Comparison of the temperature between the numerical and experimental measurements (silver TPMS and water). (**a**) Flow rate 3.74 cm\({}^{3}\)/s and 19.85 cm\({}^{3}\)/s (**b**) flow rate 7.86 cm\({}^{3}\)/s and 11.8 cm\({}^{3}\)/s, (**c**) flow rate 15.73 cm\({}^{3}\)/s. On the other hand, the results for the silver TPMS structure show that the higher value of the experiment may be due to a fluctuation in the heat flux. Even a one-degree change in the temperature can lead to a more significant change in the Nusselt number. However, the agreement is generally good, with an increase in the Nusselt number as the flow rates increase accordingly. An important parameter that combines the thermal and hydraulic effects is the performance evaluation criterion, obtained using Equation (12). In the experimental side, no measurement was taken for the pressure drop; so, one can rely only on the numerical PEC, as shown in Figure 12.  
By closely examining Figure 12, one can immediately identify the silver TPMS structure as the best structure for heat removal in engineering applications. The pressure dropped for both cases, or the friction factor was the same since the structure design was identical and for a similar flow rate. However, the performance evaluation criterion was higher in magnitude since the silver structure had a higher Nusselt number. In addition, as the flow rates increased, the performance evaluation criterion also increased.