## 4 Conclusions  
Due to the nonuniform distribution of the radial fuel temperature, the overall heat transfer coefficient cannot be calculated by a cross-sectional average parameter. To solve this problem, a modified calculation method of the overall heat transfer coefficient was proposed in this study. To provide turbulence parameters for the modified overall heat transfer coefficient method, we used the flow and heat transfer cases of n-decane when the outlet fuel temperature was in the supercritical temperature region. The results of the modified overall heat transfer coefficient method were compared with the unmodified method. The conclusions are as follows. 1. Considering the stratification of the velocity and temperature in a fluid, a formula for calculating the overall heat transfer coefficient based on the flow state was established. 2. During the change in the fuel temperature from the subcritical to supercritical region, the overall heat transfer coefficient was mainly determined by the effective thermal conductivity and the surface convective heat transfer coefficient. Similar to the trend of the constant-pressure specific heat capacity, the peak point of the overall heat transfer coefficient also appeared in the pseudo-critical temperature region. 3. Compared with the unmodified overall heat transfer coefficient, the modified overall heat transfer coefficient was smaller in general, which implies that the existing method might overestimate the overall heat transfer coefficient. The modified method not only considered the influence of the temperature based on the thermophysical property of fuel but also considered the influence of the flow state caused by the fuel heat convection, which indicates that the modified overall heat transfer coefficient may be closer to reality. 4. The modified method is adaptive in a three-dimensional case. For the convenience of heat transfer enhancement design in a cooling channel, a quasi-one-dimensional case will be considered in our next stage of search. Conceptualization, H.L. and G.L. ; methodology, H.L. ; software, X.F. ; validation, Q.X., X.F. and S.X. ; formal analysis, G.L. ; investigation, X.F. ; resources, Q.X. ; data curation, G.L. ; writing--original draft preparation, G.L. ; writing--review and editing, H.L. ; visualization, S.X. ; supervision, Q.X. ; project administration, H.L. ; funding acquisition, Q.X. All authors have read and agreed to the published version of the manuscript. This study was funded by the Fund of Characteristic innovation projects of ordinary colleges and universities in Guangdong Province (2019 KTSCX058), the Program for Scientific Research Start-up Funds of Guangdong Ocean University (R20073), the Zhanjiang Marine Youth Talent Innovation Project (21083014542867), and the Postgraduate Education Innovation Project of Guangdong Ocean University (202257). Not applicable. This study was funded by the Fund of Characteristic innovation projects of ordinary colleges and universities in Guangdong Province (2019 KTSCX058), the Program for Scientific Research Start-up Funds of Guangdong Ocean University (R20073), the Zhanjiang Marine Youth Talent Innovation Project (21083014542867), and the Postgraduate Education Innovation Project of Guangdong Ocean University (202257). Not applicable. This study was funded by the Fund of Characteristic innovation projects of ordinary colleges and universities in Guangdong Province (2019 KTSCX058), the Program for Scientific Research Start-up Funds of Guangdong Ocean University (R20073), the Zhanjiang Marine Youth Talent Innovation Project (21083014542867), and the Postgraduate Education Innovation Project of Guangdong Ocean University (202257). **Nomenclature**