A generalized model for the effective thermal conductivity of unsaturated porous media based on self-similarity

A new generalized model for the effective thermal conductivities of unsaturated porous media is developed by extending both Ma et al.'s (2004) and Feng et al.'s (2004) works. The proposed model takes account of the pore fractal dimension changing with porosity. The Sierpinski carpets of side length L = 13 with different cutouts are constructed to model the unsaturated porous media and to derive the effective thermal conductivity of unsaturated porous media based on the thermal-electrical analogy technique. The recursive expression for the thermal conductivity is obtained. The model predictions are compared with the available experimental data, and good agreement is found between the model predictions and experimental data in the porosity range 0.14 similar to 0.60.