## 4 Conclusions  
In this study, the active cooling of all-movable rudders under severe thermal loads was investigated using supercritical n-decane as the coolant. Two cooling schemes with different flow paths and structural configurations were proposed, and six cooling channel designs were developed by altering the leading-edge details. The cooling performance was evaluated under actual flight conditions (30 km altitude, Mach 8), focusing on temperature control and reducing the coolant flow rates. Both series and parallel configurations of the cooling circuits were considered, with appropriate settings for the inlet flow rates and temperatures. A comprehensive analysis was conducted to evaluate the temperatures, flow fields, and thermal-mechanical characteristics of the different cooling channels. The following conclusions are drawn:  
(1) In both the series and parallel arrangements of the two rudders, Schemes B1 and B2 exhibited inadequate cooling, with temperatures exceeding the 800 K threshold, indicating poor performances under the tested conditions. Schemes A1 and B1-M showed moderate performances but risked failure at lower flow rates. In contrast, Schemes A2 and B2-M displayed superior cooling efficiencies, maintaining temperatures well below the threshold and performing effectively under reduced flow conditions;  
(2) Flow field analyses revealed that Schemes B1 and B2, due to their larger cavity geometries, exhibited primarily laminar flow and developed stagnation regions, leading to low cooling efficiencies. Schemes A1 and B1-M outperformed them due to their higher flow velocities near the leading-edge wall. The superior performances of A2 and B2-M are attributed not only to convective heat transfer but also to the mixing of high-temperature and low-temperature fluids facilitated by the recirculation zones near the leading-edge wall and the turbulence generated at the bends;  
(3) Structural assessments showed that Schemes A1 and B2-M not only improved cooling but also maintained the structural integrity. Category A and category B exhibited  
Figure 30: The reduction in the stress concentration resulting from increasing R4. (**a**) R4 = 0.5 mm; (**b**) R4 = 0.75 mm. distinct deformation patterns, which were dictated by their respective structural configurations. Notably, category B experienced significantly higher Mises stresses compared to category A, with stress peaks consistently occurring at the junction of the inclined channel and core channel, which can be mitigated by increasing the geometric radius R4. As the aircraft performance continues to improve, the application of active cooling on the control surfaces of hypersonic vehicles will become realistic. The cooling channel design and performance evaluation methods proposed in this study offer an effective way to address the thermal protection issues of hypersonic vehicle control surfaces. Additionally, this work lays the groundwork for optimizing the overall thermal management systems of hypersonic vehicles. Conceptualization, T.W. and T.L. ; methodology, T.W. and T.L. ; software, T.W. and S.L. ; validation, T.W. and S.L. ; writing--original draft preparation, T.W. ; writing--review and editing, T.W. ; supervision, J.S. and T.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Science Foundation for Post-Doctoral Scientists of China, grant number 325042, and the High-Level Innovation Research Institute Program of Guangdong Province (No. 2020B0909010003). The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors would like to thank [PERSON] from the Institute of Mechanics, Chinese Academy of Sciences, for his valuable suggestions on the conceptual and methodological aspects of this paper, as well as the reviewers for their insightful comments on this study. The authors declare no conflicts of interest.