FRACTAL ANALYSIS FOR THERMAL CONDUCTIVITY OF DUAL POROUS MEDIA EMBEDDED WITH ASYMMETRIC TREE-LIKE BIFURCATION NETWORKS

Abstract

Heat transport in tree-like bifurcation networks has been widely studied in various fields. In this work, we investigate heat conduction in the dual porous media embedded with asymmetric tree-like bifurcation networks. In addition, considering the effects of nonuniform tube shape, we assume that the bifurcated tube shows sinusoidal fluctuations. Based on the fractal distribution of pore size and bifurcation structure, we established a dimensionless effective thermal conductivity (ETC) model of the dual porous media. The dimensionless ETC ([Formula: see text] obtained is related to the porosity ([Formula: see text], the fluid–solid thermal conductivity ratio ([Formula: see text], the pore area fractal dimension [Formula: see text] and the structural parameters of the bifurcation network (bifurcation level [Formula: see text], length ratio [Formula: see text], radius ratio [Formula: see text], fluctuation amplitude factor [Formula: see text], bifurcation angle [Formula: see text]. To verify the validity of this model, a comparison of the present dimensionless ETC model with available experimental data was carried out and the results were in good agreement. We have discussed the effects of each parameter on the dimensionless thermal conductivity in detail and constructed parametric planes to evaluate the structural parameters more directly. The model has positive implications for revealing the heat transport mechanism in asymmetric tree-like bifurcation dual porous media.