关键词: effective thermal conductivity, asymmetric tree-like branched networks, geometric parameters

Abstract: Asymmetric tree-like branched networks are explored by geometric algorithms. Based on the network, an analysis of the thermal conductivity is presented. The relationship between effective thermal conductivity and geometric  structures is obtained by using the thermal-electrical analogy technique. In all studied cases, a clear behaviour is observed, where angle ($\delta ,\theta )$ among parent branching extended lines, branches and parameter of  the geometric structures have stronger effects on the effective thermal conductivity. When the angle $\delta $ is fixed, the optical diameter ratio $\beta^\ast$ is dependent on angle $\theta $. Moreover, $\gamma $ and $m$ are  not related to $\beta ^\ast $. The longer the branch is, the smaller the effective thermal conductivity will be. It is also found that when the angle $\theta < \delta / 2$, the higher the iteration $m$ is, the lower the  thermal conductivity will be and it tends to zero, otherwise, it is bigger than zero. When the diameter ratio $\beta _1 < 0.707$ and angle $\delta $ is bigger, the optimal $k $ of the perfect ratio increases with the increase  of the angle $\delta $; when $\beta _1 > 0.707$, the optimal $k$ decreases. In addition, the effective thermal conductivity is always less than that of single channel material. The present results also show that the effective  thermal conductivity of the asymmetric tree-like branched networks does not obey  Murray's law. 

Key words: effective thermal conductivity, asymmetric tree-like branched networks, geometric parameters