## 3 Results
From Figure 7, \(P_{r}=6\), \(B_{r}=0.375\), \(a=90^{\circ}\), and \(Re=5000\) should be selected for maximum \(\eta\). The parameter \(B_{r}\) has the dominant influence on the performance. The performance \(\eta\) decreases sharply with an increase in the baffle blockage ratio \(B_{r}\). This proves that when \(B_{r}\) increases, the increase in the Nusselt number cannot compensate for the increase in the pressure loss penalty (see Figures 5 and 6). In addition, the prediction of the Taguchi method shows that \(\eta\) decreases with increasing Reynolds number. This phenomenon can be explained by the fact that at a large Reynolds number (\(Re>10\),000), the friction factor of the smooth duct decreases with increasing \(Re\), but that of the baffled duct is nearly constant. There are many parameters related to inclined baffles. With an optimization procedure, the number of independent parameters can be diminished, and the maximum thermohydraulic performance can be reached. To confirm the optimal results from the Taguchi method and further examine the effect of the parameters on heat and fluid flow inside the baffled duct, four more numerical test cases are tested at the optimal geometry parameters (i.e., \(P_{r}=6\), \(B_{r}=0.375\), and \(a=90^{\circ}\)) and different Reynolds numbers. Figure 8 displays the Nusselt number and friction factor for these cases. The Nusselt number and friction factor of the smooth duct predicted from the Gnielinski and Petukhov equations are also plotted for comparison. The Nusselt number of the baffled duct increases sharply with increasing Reynolds number, as predicted by the Taguchi method (Figure 5). The Nusselt number of the baffled duct is 2.3 times higher than that of the smooth duct. The friction factor of the duct with baffles is extremely large compared to that of the smooth duct due to the reduction in the flow cross-sectional area and vortex formation of the baffles. For the baffled duct, the friction factor decreases as Re increases from 5000 to 15,000. However, for a larger Re, the friction factor becomes constant with variation in Re. Figure 9 shows the thermohydraulic performance parameter with Re at optimal geometrical parameters. It can be clearly seen that at a certain Reynolds number, the optimized geometrical parameters attain much higher performance than the test cases initiated in Table 1. This confirms the prediction of the Taguchi optimization method and numerical methodology in this study. The maximum performance of 1.01 is obtained at a Reynolds number of 5000. A mean value of 0.92 can be found in the Reynolds number range of 10,000-20,000. [PERSON] et al. [15] studied baffles mounted on the back plate of a solar air heater duct. The baffles are perpendicular to the back plate with an inclined upper part as shown in Figure 9. They examined the effect of a very high blockage ratio from 0.7 to 0.979 on the thermohydraulic mechanism of the duct. Their investigation implied that the thermohydraulic performance reduced when increasing the blockage ratio from 0.7 to 0.979 on the thermohydraulic mechanism of the duct. The results of the simulation study are shown in Figure 9.  
ratio. The performance with the smallest blockage ratio and the same baffle pitch ratio was plotted in Figure 9. It could be concluded that the present baffle configuration with optimal parameters of this research points to better results. To compare the thermohydraulic characteristics of the baffled duct studied, the results of the effects of the geometry parameters extracted from the 16 cases in Table 1 and 4 additional cases are shown in Figures 10-12. Figure 10 shows the effect of the parameter \(B_{r}\) on the temperature and flow distribution in the baffled duct while the remaining three parameters are fixed.