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.

In this paper, a fractal model is proposed for gas diffusion in dry and wet fibrous media with tortuous converging–diverging capillary bundle on the basis of the fractal theory. The proposed theoretical model for the normalized gas diffusivity (NGD) can be expressed as an explicit functional relation of porosity, [Formula: see text], fluid saturation, [Formula: see text], fractal dimensions, [Formula: see text] and [Formula: see text], the minimum average radius, [Formula: see text], the maximum average radius, [Formula: see text], the straight capillary length of a unit cell [Formula: see text] as well as fluctuation amplitude [Formula: see text]. The predictions of the proposed model have been compared with the existing experimental data and the available model predictions, and a good agreement can be observed. The effect of various parameters on the NGD is studied alone. It is observed that the NGD decreases with an increase in the fluctuation amplitude. Also, it is seen that the NGD decreases with an increase in the tortuosity fractal dimension. Moreover, it is found that the NGD in wet fibrous media decreases with an increase in the fluid saturation. The present model has no empirical constant and each parameter contains clear physical meaning. These may better reveal the physical mechanisms of gas diffusion in fibrous media.