PREDICTING EFFECTIVE THERMAL CONDUCTIVITY OF UNSATURATED FRACTAL POROUS MEDIA WITH ROUGH SURFACES USING FRACTAL-MONTE CARLO SIMULATIONS

The effective thermal conductivity (ETC) plays a critical role in studying heat transfer processes in unsaturated porous media. In this work, a probability model for the dimensionless ETC of unsaturated fractal porous media with rough surfaces is proposed by combining fractal geometry theory with Monte Carlo simulations. The proposed model of the dimensionless ETC is expressed in terms of porosity, the relative roughness, the saturation, the fractal dimension of pore size distribution, the tortuosity fractal dimension, thermal conductivities of gas (non-wetting phase), water (wetting phase) and solid phase, the straight capillary length of the representative elementary volume (REV), and the random pore size. The effects of structural parameters on the dimensionless ETC are discussed in detail. The dimensionless ETC predictions using Fractal-Monte Carlo (FMC) simulations are compared with available experimental data, showing good agreement to validate the proposed model. The results indicate that the dimensionless ETC decreases with increasing relative roughness and tortuosity fractal dimension. Specifically, the proposed FMC simulations may have advantages in predicting heat transport properties in porous media.