## 3 Results and Discussion
### Temperature Test for Competitive Selection of Optimal Channel Scheme  
Firstly, the cooling channel in the all-movable rudder located downstream in the series arrangement was considered. Figure 17 illustrates the temperature distribution of the six different cooling schemes during the first round of testing, where the inlet flow rate was 2 g/s, and the inlet temperature was 400 K. The maximum outer-wall temperatures in the positive interval of the \(y\)-axis are all located at the tip of the leading-edge segment and are arranged in descending order as follows: 944.7 K (B2), 931.2 K (B1), 797.7 K (A1), 769.2 K (B1-M), 687.4 K (A2), and 665.7 K (B2-M). It is evident that B1 and B2 significantly surpass the evaluation threshold of 800 K. A1 barely meets the test requirements, but any decrease in the flow rate is expected to result in failure. B1-M also meets the standard, albeit with a narrow margin of only 30 K. Encouragingly, both A2 and B2-M demonstrate exceptional cooling performances by being 112.6 K and 134.3 K below the temperature limit, respectively. It is also important to note the differences in the outer-wall temperature distribution between the category A and category B cooling channels due to their distinct flow paths. For A1 and A2, the outer-wall temperature increases along the positive x-axis (flow direction), with a notable spike near the leading-edge segment. In contrast, for B1, B1-M, B2, and B2-M, the temperature sharply decreases along the negative x-axis (flow direction) in the leading-edge region, followed by slight undulations in the inclined segment, and stabilizes in the horizontal segment with outlet temperatures around 440 K. Figure 17 (right) shows the outer-wall temperatures along the negative y-axis. For B1, B1-M, B2, and B2-M, the temperature profiles are symmetrically distributed relative to the symmetry plane. In contrast, for A1 and A2, the outer-wall temperatures gradually decline along the negative x-axis (flow direction), reaching an outlet temperature of around 435 K.  
Figure 18 illustrates the temperature distribution along the outer wall of the cooling channels A1, A2, B1-M, and B2-M during the second-round tests. In this round, a reduced inlet velocity of 1 g/s was employed while maintaining an inlet temperature of 400 K. The impact of the decreased flow rate on the temperature distribution was immediately apparent: it resulted in a larger temperature difference between the inlet- and outlet-wall temperatures for both the category A and category B channels. Specifically, the outlet temperatures for A1 and A2 were approximately 467 K, whereas B1-M and B2-M exhibited outlet temperatures around 475 K. Moreover, the inclined segment in the category B channels displayed a more pronounced decrease in temperature. Finally, focusing on the critical performance assessment as anticipated, A1 and B1-M, which barely met the previous requirements, exceeded their respective maximum allowable temperatures with  
Figure 16: Contrast between calculated wall temperatures and experimental data [42] for a U-turn tube. values reaching 867.3 K and 822.2 K, respectively, during this round of testing. Conversely, both A2 and B2-M comfortably passed once again without exceeding any of the limits set forth by our study criteria. Notably, even under further reduced flow conditions, channel B2-M demonstrated a peak temperature as low as 720 K, which is significantly below our predetermined threshold, suggesting its potential to meet all the requirements. Figure 18 presents the outer-wall temperature distributions for the cooling channels A1, A2, B1-M, and B2-M during the second-round tests, where the inlet velocity was reduced to 1 g/s while the inlet temperature remained at 400 K. The impact of the reduced flow rate on the temperature distribution was immediately evident: the lower flow rate resulted in a greater temperature differential between the inlet- and outlet-wall temperatures for both the category A and category B channels.