## 4 Analysis and Discussion of Results
### Interpretation of the Effects
#### 4.2.2 Heat Transfer Coefficient (_lh_)  
The response variable heat transfer coefficient (_lh_) indicates better performance at higher values. The analysis of the factorial effects reveals that temperature (_B_) has the largest positive effect (Table 6 and Figure 7b), indicating that increasing the temperature from its low (22 \({}^{\circ}\)C) to high level (29 \({}^{\circ}\)C) significantly increases \(h\) by 33.462 \(\pm\) 9.8 W\(\cdot\)m\({}^{-2.\circ}\)C\({}^{-1}\), on average. This effect is statistically significant (Figure 7b), making temperature the most influential factor for improving \(h\).  
The power supply is statistically significant (Table 6 and Figure 7b), confirming its importance for enhancing performance. This factor also shows a positive effect, suggesting that using 65 W improves \(h\) by 28.050 \(\pm\) 9.8 W\(\cdot\)m\({}^{-2.\circ}\)C\({}^{-1}\), on average. Otherwise, the flow rate has a smaller positive effect in the _lh_, as shown (16.189 \(\pm\) 9.8 W\(\cdot\)m\({}^{-2.\circ}\)C\({}^{-1}\)) and is also not statistically significant. None of the interaction terms are statistically significant, indicating that the combined effects of factors do not meaningfully affect _lh_ in this experimental setup.  
Therefore, to maximize _lh_, all factors should be adjusted to their highest levels, including a high-power supply, high temperature, and high flow rate. This combination leverages the positive main effects of all factors, particularly the significant contributions of temperature and power supply.  
Based on the preference for minimizing thermal resistance as the operational and commercial criterion for evaluating heat dissipation performance, the recommended levels of the factors would prioritize configurations that achieve the lowest \(G_{\mathrm{TR}}\). From the earlier analysis, the optimal levels for minimizing thermal resistance were Power Supply (Low, 30 W), Temperature (High, 29 \({}^{\circ}\)C), and Flow Rate (Low, 2.50 L\(\cdot\)min\({}^{-1}\)). This combination reduces the thermal resistance, ensuring that the heat sink is more effective at transferring heat away from the electronic component, which is critical for practical applications such as heat sink design and selection.  
Figures 10 and 11 display the average increase in the heat transfer coefficient (_lh_) as the dissipated power levels of 30 W and 65 W and the ambient temperature (range of 22 \({}^{\circ}\)C to 29 \({}^{\circ}\)C) with the Reynolds number. It is important to note that the volumetric flow rate does not significantly affect the changes in _lh_ within this range. The Reynolds number is included because it rises with an increase in the volumetric flow rate, and the ambient temperature also has an effect due to its relationship with variations in water temperature, as well as changes in density and viscosity, which are used in the Reynolds number calculation.  
Figure 11 supports the explanation given in Figure 9 regarding the improvement in global thermal resistance at a heat dissipation level of 65 W and at high Reynolds numbers. This enhancement in heat transfer coefficient, accompanied by a decrease in thermal resistance, may be attributed to an earlier transition from laminar to turbulent flow regimes. The results showed that the heat transfer coefficient increased with higher dissipated power, consistent with the findings of [PERSON] ([PERSON], 2016), who investigated the influence of nanofluids on heat transfer in a natural convection system.