## 3 Results  
Table 1 shows the 16 test runs, in which 4 factors are generated by the Taguchi method in Minitab software (Minitab Inc.). Each factor has four levels corresponding to the L\({}_{16}\) (4\({}^{4}\)) orthogonal array. The Reynolds number varies from 5000 to 20,000. This range is wide enough to clarify the flow mechanism in an inserted solar air heater duct, as pointed out by [PERSON] and [PERSON] (2018). Note that by using the Taguchi method, the number of simulations is significantly reduced, from 4\({}^{4}\) = 256 to 16 cases. This is a great advantage of the Taguchi DOE. The objective functions (responses) of this study are the Nusselt number (_Nu_), friction factor (_f_), and thermohydraulic performance parameter (_η_), which are drawn from the above mathematical model. To examine the effects of the factors on the responses, Figures 5-7 present the mean values of the responses and the importance of the independent parameters. The behavior of the Nusselt number with the geometrical parameters of the baffle and the Reynolds number can be seen in Figure 5. Within the investigated range, the average Nusselt number of a baffled duct is approximately 125. The prediction of the Taguchi method shows that with increasing Reynolds number, the Nusselt number increases sharply, as expected. Among the geometric parameters of the baffle, the baffle blockage ratio (\(B_{r}\)) has the most influence on the heat transfer because when \(B_{r}\) increases, the air flow in the duct is strongly accelerated. Conversely, with increasing baffle pitch ratio (\(P_{r}\)), Nu decreases due to the longer distance between the baffles, leading to a reduction in the air velocity and swirling intensity. A baffle angle of 30\({}^{\circ}\) yields the smallest Nu because the baffle length is the longest together with the smallest slope, resulting in air acceleration lower than that at other angles. A baffle angle between 60\({}^{\circ}\) and 90\({}^{\circ}\) yields the highest Nusselt number. At these angles, the air flow is reversed perpendicular to the absorber  
Figure 6: Taguchi analysis based on the friction factor. Figure 7: Taguchi analysis based on the thermohydraulic performance parameter (\(\eta\)). plate, causing impingement heat transfer zones. The baffle angle of 120\({}^{\circ}\) yields a moderate Nusselt number because the primary vortex downstream of the baffle is not as large as those of the baffles with angles of 60\({}^{\circ}\)-90\({}^{\circ}\). The friction factor with the geometrical parameters of the baffle and the Reynolds number can be observed in Figure 6. The average friction factor is approximately 3, which is very large compared to that of a smooth duct of the same duct dimensions and air flow according to the study of [PERSON] et al. [15]. Due to the flow resistance of the baffles, the friction factor is considerably large. The effect of \(B_{r}\) on the pressure loss is the strongest. The Taguchi method predicts the effect of \(P_{r}\) on the friction factor well, i.e., the friction factor decreases with increasing \(P_{r}\). When \(Re\) increases from 5000 to 10,000, the friction factor decreases, which is a common trend for the friction factor with \(Re\). However, when \(Re\) is greater than 10,000, the friction factor fluctuates with the Reynolds number. This is because the complete turbulence flow in the roughened duct makes the friction factor less dependent on the Reynolds number. This regime leads to increasing and decreasing trends of the friction factor. The baffle angle of 90\({}^{\circ}\) results in the highest friction factor due to the presence of secondary vortices upstream and downstream of the baffle and the strong reversal of the air flow. Figure 7 shows the influence of the geometrical parameters and Reynolds number on the thermohydraulic performance parameter (\(\eta\)) obtained from the Taguchi method. The average performance is approximately 0.88. This is also the maximum required parameter in this study.