## 4 Analysis and Discussion of Results
### Interpretation of the Effects
#### 4.2.1 Global Thermal Resistance (\(G_{TR}\))  
The _effect of a factor_ is defined as the change in the response (\(G_{TR}\)_or \(h\)_) when it is moved from a lower level (\(-\)) to a higher level (\(+\)). Considering that the power supply (factor \(A\)) is the only statistically significant factor for the \(G_{TR}\) response (Table 6--entry 1, and Figure 7a), it is observed that the change from the level (\(-\)) to the level (\(+\)) of factor A (30 W to 65 W) increases the thermal resistance, on average, by 24.954 \(\times\) 10\({}^{-3}\)\(\circ\)C\(\cdot\)W\({}^{-1}\). The temperature effect is negative, indicating that increasing the temperature from a low of 22 \(\circ\)C to a high of 29 \(\circ\)C reduces thermal resistance, on average, by 11.643 \(\pm\) 0.9 \(\circ\)C\(\cdot\)W\({}^{-1}\). While this result aligns with the goal of decreasing thermal resistance, the \(t\)-test and Figure 7a show that the effect is not statistically significant at a 95% confidence level. This suggests that, although the temperature change may have a beneficial impact, it is not consistent enough to be considered reliable within the temperature range tested in the experiment. The flow rate is not statistically significant, and its effect is positive (12.356 \(\pm\) 9.3 \(\times\) 10\({}^{-3}\)\(\circ\)C\(\cdot\)W\({}^{-1}\)), indicating that increasing the flow rate from its low (2.5 L/min) to high level (5 L/min) increases the thermal resistance. Finally, none of the interactions (AB, AC, BC, or ABC) are statistically significant (Figure 7a and Table 4). This suggests that combinations of factors do not have a meaningful impact on thermal resistance within the levels tested. Figures 8 and 9 show the average increase in global thermal resistance at the dissipated power levels 30 W and 65 W as a function of the Reynolds number and the ambient temperature. Two of the three variables that were varied to assess the response of global thermal resistance were ambient temperature and volumetric flow rate. The Reynolds number increases with higher volumetric flow rates. It is also affected by ambient temperature due to the changes in water temperature that ambient temperature induces, which alters properties influencing the Reynolds number, such as viscosity and density. The analysis conducted within the range of variables in this experiment shows that only power significantly impacts the variations in thermal resistance. From the \(t-distribution\) analysis and Pareto chart (see Figure 7), changes in volumetric flow rate or temperature do not have a significant effect on thermal resistance. Hence, adjusting the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Level** &
\begin{tabular}{c} **Heat Transfer** \\ **Coefficient (h)** \\ \end{tabular} & **Statistically Relevant** \\ \hline Volumetric flow & High & Increase & No \\ \hline Ambient temperature & High & Increase & Yes \\ \hline Power supply & High & Increase & Yes \\ \hline
**Variables** & **Level** &
\begin{tabular}{c} **Global Thermal** \\ **Resistance (\(G_{TR}\))** \\ \end{tabular} & **Statistically Relevant** \\ \hline Volumetric flow & Low & Decrease & No \\ \hline Ambient temperature & High & Decrease & No \\ \hline Power supply & Low & Decrease & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Effects of the statistical evaluation. volumetric flow rate and ambient temperature within the specified range will not improve performance. Utilizing a lower-power pump may be a feasible option to reduce costs or energy spending on the equipment/to optimize the use of electrical energy in the system. Figure 8: Global thermal resistance and ambient temperature at the power level of 30 W.  
Figure 9: Global thermal resistance and ambient temperature at the power level of 65 W.  
As shown in Figure 9, higher Reynolds numbers correspond to improved thermal resistance. Nevertheless, the design of minichannels incorporating interrupted fin walls may result in the onset of an early transient regime.