## 4 Results and Discussion  
Figure 12 shows the temperature distributions of the two models when calculating the \(\lambda_{xx}\) (\(d_{fr}=1.2\) mm). The result shows a relatively uniform temperature distribution for two-unit cells. The temperature of \(T_{A=(0,0,0)}\) are both set to 0 K in UC1 and UC2. In order  
Figure 11: Meshed models of (**a**) UC1 and (**b**) UC2. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Diameter of the Fiber Rods**} & \multicolumn{2}{c}{**The Size of Unit Cell**} \\ \cline{2-3}  & **The Number of Elements** & **The Number of Elements** \\  & **of UC1** & **of UC2** \\ \hline
1.2 mm & 734,448 & 184,276 \\
1.4 mm & 841,896 & 211,464 \\
1.6 mm & 971,520 & 243,672 \\
1.8 mm & 1,112,496 & 273,240 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of elements of UC1 and UC2 with carbon fiber rods of different diameters. to compare the temperature distributions obtained by the two models, temperature on the lines \(X1=(x,w/2,h/2)\) and \(Y1=(l/2,y,h/2)\) for the two models are extracted. As can be seen in Figure 13, the values of temperature in lines \(X1\) and \(Y1\) of UC1 and UC2 are the almost equal. These results suggest that the temperature boundary conditions imposed on UC2 are accurate. Figure 14 shows the heat flux distributions used to calculate the \(\lambda_{xx}\) of UC1 and UC2 (\(d_{fr}=1.2\) mm), respectively. The results in Figure 14 can indicate that the heat flux in the matrix region is higher than other regions because the matrix has the higher thermal conductivities in the x direction. In addition, the heat flux distributions of UC1 and UC2 are extraordinarily similar. The measured thermal conductivities of the UC1 and UC2 are shown in Table 4 with the fiber rod diameter of 1.2 mm. The predicted values in transverse are 5.8 to 8.2% and longitudinal 6.2 to 6.8% both higher than the experimental values in [27]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Thermal Conductivity (W\(\cdot\)m\({}^{-1}\).k\({}^{-1}\))**} \\
**Direction** & & **Experimental Values in [27]** & **UC1** & **UC2** \\ \hline \multirow{2}{*}{Transverse} & X & & 79.82 & 80.13 \\  & Y & 75.2 & 81.10 & 81.89 \\ \multirow{2}{*}{Longitudinal} & Z & 58.73 & 63.01 & 62.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the FE results with the experimental results in [27]. Figure 12: Temperature distributions for the calculation of \(\lambda_{xx}\) in UC1 and UC2. Figure 13: Temperature on lines (**a**) X1; (**b**) Y1. The effect of carbon fiber rods with different diameters on the effective thermal conductivities of 4D C/C composites is shown in Figure 15. The transverse thermal conductivities (\(\lambda_{xx}\), \(\lambda_{yy}\)) predicted by UC1 are both higher than the results predicted by UC2 slightly. However, the longitudinal thermal conductivity (\(\lambda_{zz}\)) predicted by UC1 is always slightly smaller than that of UC2. In addition, it can be easily found that the longitudinal thermal conductivity of the 4D C/C composites increases as the diameter of the fiber rods increase, while the effective transverse thermal conductivities decrease. According to the discussions above, the heat flux and temperature distributions at the corresponding positions of the two-unit cells are both almost the same. The correctness of the temperature boundary conditions imposed on the UC2 derived from the boundary conditions of UC1 is verified. The UC2 can be used to predict the thermal conductivities of 4D C/C composites, which is constructed by two 180\({}^{\circ}\) rotational symmetry transformations of UC1. The smaller-size model can greatly save computing time and computing resources. In this work, the computational time (including the pre-processing, solving and post-processing) of UC2 is about only 32.9% of UC1. Figure 14: The distributions of heat flux for the calculation of \(\lambda_{xx}\) in UC1 and UC2. Figure 15: The effective thermal conductivities of UC1 and UC2 with carbon fiber rods of different diameters.