The Study On The Effective Thermal Conductivity Of Asymmetric Fractal Tree-like Networks

It has drawn great attention to the study on the transport characteristic of the fractal tree-like branched networks. The scholars of all the world have carried through extensively studies on the physical properties of the fractal tree-like branched networks. However, the relationship between the thermal properties and its geometrical features is not well understood, especially for the asymmetric fractal tree-like branched networks.Thus, in this thesis we have studied the heat conduction in asymmetric fractal tree-like branched networks and derived the expression for the effective thermal conductivity(ETC) of the networks. It is found that the ETC of the networks is related significantly to the geometrical structure of the networks. The present results show that the ETC decrease with the increase of the length of the branches, the dense of the networks and the number of the branches. It is also found that when the area factorξ= 1, which is corresponding to the area conservation, the ETC obtains the maximum value. In addition, the value of the diameter fractal dimension Dd , which is corresponding to the maximum ETC, is determined by the asymmetric factorα. It is also found that the asymmetric fractal tree-like branched networks has the optimal state if we adjust the geometric parameter rationally, which is very instructive for the engineering application.