| Fractal theory has been widely employed by scholars to investigate the heat transfer mechanism of dendritic tree-like branching networks,due to their self-similar fractal properties.This special structure has been given considerable attention in both the natural and engineering realms.However,because of the complexity of the thermal transport process of the tree-like branching network,there is still a gap in the study of the thermal transport characteristics of the tree-like branching networks.Due to the current research on thermal transport in tree-like bifurcation networks either neglecting their asymmetric structure or not considering thermal convection during the thermal transpor.Based on fractal geometry theory and basic thermodynamic theory,this paper focuses on exploring the problems of heat conduction and heat convection in porous media embedded with damaged tree-like branching networks,constructs a fractal theoretical model of effective thermal conductivity,and studies the detailed mechanism of the influence of microstructure parameters of porous media on heat transport.The specific research contents are as follows:(1)Construction of thermal conductivity model of porous media of embedded single damaged tree-like bifurcation network with rough surface: Based on the fractal geometry theory,the thermal conductivity model of porous media of embedded damaged tree-like bifurcation network with rough surface is constructed by analyzing the self-similarity characteristics of the damaged tree like bifurcation network structure.Then,based on Fourier’s law and Newton’s law of cooling,the heat conduction and convection processes in the damaged tree bifurcation network are studied.The expression for the effective thermal conductivity of an embedded single damaged tree-like branching network porous medium with a rough surface was derived,and the influence of the microstructure parameters of the thermal conductivity model on the effective thermal conductivity coefficient of the porous medium was studied.The research results indicate that the effective thermal conductivity coefficient of this thermal conductivity model is related to structural parameters such as the length to diameter ratio of damaged tree branches,and the number of damaged pipes.(2)Construction of porous media thermal conductivity model of damaged tree-like bifurcation network with randomly distributed main diameter: based on the fractal selfsimilarity theory,the expression of effective thermal conductivity of randomly distributed damaged tree-like bifurcation network porous media is derived by analyzing the thermal conduction and thermal convection process of porous media,based on Fourier’s law and Newton’s law of cooling.The influence of microstructure parameters of the thermal conductivity model on the effective thermal conductivity of porous media was studied.The research results indicate that the dimensionless effective thermal conductivity coefficient of the thermal conductivity model is related to structural parameters such as porosity,number of branches,and number of branching layers.When the fractal dimension increases,the heat conduction of the damaged branch network plays a leading role in the heat transfer of porous media.At the same time,comparing the existing experimental data with the thermal conductivity model,it was found that the thermal conductivity model has good consistency with the existing experimental data.This study can enrich and develop the thermal transport mechanism of porous media embedded with damaged tree-like bifurcation network,and provide certain theoretical guidance for related applications in the engineering field. |
