A generalized thermal conductivity model for unsaturated porous media with fractal geometry. (May 2020) - Shen, Yuqing; Xu, Peng; Qiu, Shuxia; Rao, Binqi; Yu, Boming
Highlights: Fractal model for conductive heat transfer in unsaturated porous media is developed. Analytical expression for effective thermal conductivity is presented. Pore fractal dimension is calculated based on nitrogen adsorption experiment. Abstract: Evaluation of effective thermal conductivity (ETC) of unsaturated porous media is significant for many engineering applications and thus has received growing attention in multi-disciplinary fields. However, the existing models for ETC cannot realistically account for the complex pore structures and generally contain empirical parameters. In this study, fractal dimensions for pore size distribution and capillary tortuosity are introduced to characterize the pore-scale structure. A generalized model for ETC of unsaturated porous media is developed based on thermal-electrical analogy. The proposed fractal model has been validated by comparing with available experimental data. The results show that ETC of unsaturated porous media increases with the increase of liquid saturation as the thermal conductivity of solid and liquid phases are larger than that of gas phase. However, ETC is inversely proportional to liquid saturation as the thermal conductivity of solid and liquid phases are smaller than that of gas phase. The pore structures indicate significant effect on ETC of unsaturated porous media. ETC gradually decreases with the increment of porosity and pore fractal dimension as well as tortuosity fractal dimension. All the parameters in the proposed ETC model have specific physical meanings, and it may capture the microstructure characteristics and help understanding the heat transfer mechanisms of unsaturated porous media.