Analysis of thermal conductivity in tree-like branched networks |
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| Authors: | Kou Jian-Long Lu Hang-Jun Wu Feng-Min and Xu You-Sheng |
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| Affiliation: | Institute of Condensed Matter Physics, Zhejiang Normal
University, Jinhua 321004, China |
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| 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. |
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| Keywords: | effective thermal conductivity asymmetric tree-like branched networks geometric
parameters |
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