## 5 Conclusions  
A numerical study of the anisotropic thermal conductivities, especially the thermal conductivity in the thickness direction, of the 2.5-D braided CMC material was carried out. Two prediction models, an RVE model with a periodicity hypothesis and a full-size model with actual thickness, were established. An experimental test of the thermal conductivity in the thickness direction was also used to validate these two prediction models. The influence of the thickness on the ATC and the critical thickness that was suitable for the RVE model were further investigated under different operating conditions of the thermal properties of the fibers. The main observations can be summarized as follows:  
1. The temperature field and the heat flux field inside the 2.5-D braided CMC material were clearly heterogeneous, and these fields were affected by the difference between the thermal conductivities of the fiber bundles and matrix. For example, in the full-size model, the relative fluctuation of the temperature field and the relative fluctuation of the heat flux field in the middle section reached 6.39% and 280.40%, respectively.
2. In the thermal analysis of a thin-walled structure, such as a turbine vane, the RVE model would lead to a large deviation in the estimation of the effective thermal conductivity so that the periodic hypothesis could not be satisfied. The relative variation of the thermal conductivity based on the RVE model compared with the experimental data was 15.62%, while the relative variation was only 3.53% when the full-size model was applied.
3. When the thickness increased, the effective thermal conductivities based on the RVE model and the full-size model were close to each other. For the ATC of the sample used in this study, when the thickness was bigger than the critical thickness of 18.4 mm, the RVE model was suitable for the prediction of the ATC.
4. When the absolute value ratio and the level of anisotropy of the thermal conductivities of the fiber bundle were changed, the influence of the thickness on the thermal conductivity was different and the critical thickness for the RVE model changed. When the absolute value ratio increased,  
Figure 13: The variations of the critical thickness with different ATCs.  
the critical thickness firstly decreased and then increased, and the critical thickness decreased almost monotonously with increasing the level of anisotropy.  
Conceptualization, [PERSON] and J.M.; methodology, Z.T.; software, Z.T., X.X.; validation, Z.H. and X.H.; formal analysis, Z.T.; investigation, Z.T.; resources, Z.T.; data curation, Z.T.; writing--original draft preparation, Z.T.; writing--review and editing, X.H.; visualization, [PERSON]; supervision, J.M.; project administration, J.M.; funding acquisition, Z.T., Z.H. and X.H.  
This research was funded by the China Postdoctoral Science Foundation, grant number 2018M642248, the National Natural Science Foundation of China, grant number 51806103 and the Jiangsu Provincial Natural Science Foundation of China, grant number BK20160794.  
[PERSON] acknowledges the support of the Jiangsu Specially-Appointed Professor Program.  
The authors declare no conflict of interest.