## 3 Results and Discussion
### Flow Characteristics  
A quantitative analysis of the outer-wall temperature in the cooling channel is provided above. However, it is crucial to gain a profound understanding of the underlying mechanisms governing the distinct heat transfer observed in all the considered configurations. Here, we present an in-depth discussion of the flow and temperature fields in the leading-edge segment within each channel configuration. We first analyze the flow characteristics to explain the poor performance of the B1 and B2 channels during the initial tests in both the series and parallel arrangements. Figure 22 shows the wall temperature distribution and streamline patterns on the streamwise-spanwise (x-y) plane for Scheme B1. When the flow rate is 2 g/s and the inlet temperature is 400 K, multiple recirculation zones appear. These zones are located near the inner wall, bends, and heated surfaces, as highlighted by the red dashed box. While recirculation zones generate localized turbulence, as seen in Figure 23, which could enhance heat transfer, they also cause stagnation. In these stagnation regions, the flow velocity approaches zero due to the large cavity size. This reduces the cooling efficiency, leading to poor heat removal. At a reduced flow rate of 1 g/s and an inlet temperature of 300 K, the flow remains mostly laminar. This is consistent with the low turbulent kinetic energy (TKE) shown in Figure 23. In this condition, the fluid near the outer wall moves slowly. This limits heat transfer, causing high wall temperatures. A small recirculation zone forms near the inner-wall bend, but it has a minimal impact on the outer-wall cooling. Figure 21: Overall performances of six cooling channels in the tests conducted for both series and parallel arrangements. Figure 24 presents the temperature distribution and flow streamlines for the B2 channel. At a flow rate of 2 g/s and an inlet temperature of 400 K, the B2 channel exhibits more complex recirculation or stagnation zones due to its larger cavity compared to B1. While these chaotic flow structures generate higher turbulence intensity, as shown in Figure 25, the turbulence occurs in the center of the cavity, far from the walls, and thus fails to enhance heat transfer. Under reduced flow rate conditions, B2 develops additional recirculation zones compared to B1. These regions of nearly stagnant fluid offer no improvement in heat transfer. Figure 23: TKE distribution on streamwise-spanwise plane (x-y plane) for Scheme B1. Figure 22: The wall temperature distribution and streamline patterns on the streamwise–spanwise plane (x-y plane) for Scheme B1 (the red dashed box represents the recirculation zone). The performances of the more effective cooling channels were analyzed under the conditions of the second-round test with an inlet flow rate of 0.5 g/s and an inlet temperature of 300 K. Figure 26 illustrates the temperature distribution and streamline characteristics for channels A1, A2, B1-M, and B2-M. It is evident that A1 and B1-M predominantly exhibited laminar flow features, which aligns with the low TKE shown in Figure 27. In contrast, A2 developed extensive recirculation zones at the leading-edge segment. These recirculation zones were closely adjacent to the leading-edge wall, continuously increasing the mixing of fluid near the wall and thereby enhancing the thermal energy exchange between the coolant and the channel walls. Additionally, B1-M formed small recirculation zones, which are also observed in the temperature distribution, are also observed in the temperature distribution. Figure 24: The wall temperature distribution and streamline patterns on the streamwise–spanwise plane (x-y plane) for Scheme B2 (the red dashed box represents the recirculation zone). Figure 25: TKE distribution on streamwise–spanwise plane (x-y plane) for Scheme B2. zones near the wall, which led to increased turbulence and significantly improved the heat transfer performance.