Fractal analysis of effective thermal conductivity for three-phase (unsaturated) porous media

Abstract

A fractal analysis of effective thermal conductivity for unsaturated fractal porous media is presented based on the thermal-electrical analogy and statistical self-similarity of porous media. Here, we derive a dimensionless expression of effective thermal conductivity without any empirical constant. The effects of the parameters of fractal porous media on the dimensionless effective thermal conductivity are discussed. From this study, it is shown that, when the thermal conductivity of solid phase and wet phase are greater than that of the gas phase (viz., ks∕kg>1, kw∕kg>1), the dimensionless effective thermal conductivity of unsaturated fractal porous media decreases with decreasing degree of saturation (Sw) and increasing fractal dimension for pore area (Df), fractal dimension for tortuosity (Dt), and porosity (ϕ); when the thermal conductivities of solid phase and wet phase are lower than that of the gas phase (viz., ks∕kg<1, kw∕kg<1), the trends were just opposite. Our model was validated by comparing the model prediction with existing experimental data. Excellent agreement was found except for the cases at very low level of saturation.