A Novel Model For Effective Thermal Conductivity Of Tree-Like Branching Network With Fractal Roughened Surfaces

The tree-like branching network shows prominent advantages in heat and mass transfer, which has been studied for a long time. In this paper, a novel model for the effective thermal conductivity is proposed for the tree-like branching network with fractal roughened surfaces. The proposed model is a function of structure parameters of the tree-like branching network with fractal roughened surfaces, including the relative roughness (𠜀), the length ratio (α), the diameter ratio (β), the total number of branching levels (m) and the branching number (n). The influence of structure parameters on the effective thermal conductivity is discussed individually based on the systematic data analysis. It is found that the relative roughness has a clear effect on the thermal conductivity. Furthermore, the effective thermal conductivity decreases with an increase in the relative roughness. It is also seen that the effective thermal conductivity decreases with an increase in the length ratio. In addition, there is an interesting phenomenon that the effective thermal conductivity increases initially and decreases afterwards with an increase in the diameter ratio. The determined dimensionless effective thermal conductivity of the whole tree-like branching network with roughened surfaces is in good agreement with existing model reported in the literature. The proposed model does not include any empirical constant and every parameter has physical meaning, which can better reveal the mechanism of heat transfer in the tree-like branching network.