The effective thermal conductivity of porous media based on statistical self-similarity

Abstract

A fractal model is presented based on the thermal–electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity ( ϕ) and pore area fractal dimension ( D f ) when k s / k g > 1 . The opposite trends is observed when k s / k g < 1 . In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension ( D t ). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.