## 4 Results and Discussions
### Comparison between the RVE Model and the Full-Size Model
#### 4.1.4 Validation of the RVE Model and the Full-Size Model  
To validate the accuracies of the RVE model and the full-size model, the thermal conductivity of the z-axis k\({}_{\rm Z}\) for the sample shown in Figure 1a was tested. A NETZSCH LFA 457 Micro-Flash instrument was used to measure the thermal diffusion coefficient, and the specific heat capacity was measured with a DSC 200 F3. The geometrical sizes of the samples were 10 mm \(\times\) 10 mm \(\times\) 2.8 mm (length \(\times\) width \(\times\) height), which satisfied the demands of the test equipment. Finally, the thermal conductivity was calculated using the density, the thermal diffusivity, and the specific heat capacity. In the experiment, the k\({}_{\rm Z}\) values at four different positions of the sample were tested.  
According to the experimental results, the density of the sample was 1.711 \(\times\) 10\({}^{3}\) kg/m3 and the specific heat capacity was 0.688 \(\times\) 10\({}^{3}\) J/(kg\(\cdot\)K). Table 2 shows the experimental data of the thermal diffusivity and the corresponding thermal conductivity on the Z axis. The thermal conductivities at four different positions on the sample were tested. The results show that the four different thermal conductivities were close to each other. The average k\({}_{\rm Z}\) value was 4.053 W/(m\(\cdot\)K).  
The numerical results in Section 4.1.3 are also given in Table 2. The numerical results of the k\({}_{\rm Z}\) values based on the RVE model and the full-size model are 3.42 W/(m\(\cdot\)K) and 3.91 W/(m\(\cdot\)K), respectively, and the relative differences compared to the experimental data are 15.62% and 3.53%, respectively. The numerical result based on the full-size model is closer to the experimental data. In the thermal analysis of thin-walled structures such as a turbine vane, the RVE model would lead to a large  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Experimental Data**} & \multicolumn{4}{c}{**Numerical Data**} \\ \hline \multicolumn{1}{c}{\multirow{2}{*}{**Thermal Diffusivity/m\({}^{2}\)/s**}} & \multicolumn{2}{c}{**Thermal Conductivity**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Standard**} & \multicolumn{1}{c}{**RVE**} & \multicolumn{1}{c}{**Full-Size**} \\  & & \multicolumn{2}{c}{**k\({}_{\rm Z}\)/W(m\(\cdot\)K)**} & \multicolumn{2}{c}{**Value/W(m\(\cdot\)K)**} & \multicolumn{2}{c}{**Deviation/W(m\(\cdot\)K)**} & \multicolumn{2}{c}{**Model/W(m\(\cdot\)K)**} & \multicolumn{2}{c}{**Model/W(m\(\cdot\)K)**} \\ \hline
3.427 & 3.460 & 3.444 & 3.443 & 4.036 & 4.072 & 4.053 & 4.052 & 4.053 & 0.015 & 3.42 & 3.91 \\ \hline \hline \end{tabular}
\end{table}
Table 2: A comparison of the experimental and numerical data.  
Figure 9: The effective thermal conductivities based on the two models.  
deviation in the estimation of the effective thermal conductivity. The reason for this is that the main difference between the RVE model and the full-size model is the boundary part shown in Figure 10. The periodic hypothesis of the RVE model could not be satisfied in the CMC's boundary parts, and the volume fractions of the fibers and the braided structure are also different, which would lead to the variation of the heat transfer in these parts. In the RVE model and the full-size model, the volume fractions of the fibers \(F_{f}\) were 54.34% and 39.61%, respectively. Therefore, the full-size model could truly reflect the internal structure of a CMC thin-wall structure.