Fractal-like tree networks reducing the thermal conductivity

The effective thermal conductivity of composites with embedded self-similar H-shaped fractal-like tree networks is studied. It is found that the effective thermal conductivity of the composites with these networks is related to the structures of the networks and the ratio of the component thermal conductivities: the longer the branches, the lower the thermal conductivity; the smaller the ratio (beta) of successive branch diameters, the lower the thermal conductivity; the denser the network, the lower the thermal conductivity. It is also found that the thermal conductivity of the H-shaped fractal-like tree networks does not obey Murray's law. The present results show that a network embedded in a composite plays an important role, and the thermal conductivity of the network itself may be less than that of the original material by several orders of magnitude. Fractal-like tree networks can significantly reduce the thermal conductivity compared to an equivalent single cylinder.