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 (λ+) obtained is related to the porosity (ϕ), the fluid–solid thermal conductivity ratio (λf/λs), the pore area fractal dimension Df and the structural parameters of the bifurcation network (bifurcation level i, length ratio γ, radius ratio η, fluctuation amplitude factor ξ, bifurcation angle 𝜃). 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.
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