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.
Received: 24 February 2008
Revised: 23 September 2008
Accepted manuscript online:
Fund: Project supported by the State Key
Development Program for Basic Research of China (Grant No
2006CB708612), the National Natural Science Foundation of China
(Grant No 10572130), and the Natural Science Foundation of Zhejiang
Province, China (Grant No Y607
Cite this article:
Kou Jian-Long(寇建龙), Lu Hang-Jun(陆杭军), Wu Feng-Min(吴锋民), and Xu You-Sheng(许友生) Analysis of thermal conductivity in tree-like branched networks 2009 Chin. Phys. B 18 1553
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
