Unsaturated cell model of effective thermal conductivity of soils

Abstract

In this study, a cell model based on new physical conceptualizations is developed to calculate the effective thermal conductivity of unsaturated soils. The evolution of water phase saturation is treated using a cell model consisting of solid particle being enveloped by a mixture of water and air phases. The thermal conductivity of the mixed fluid phase is determined by the volume-weighted average of water and air thermal conductivities. The temperature distribution in the cell of soil and fluid mixture is solved along with boundary condition of linearly varying temperature field. The heat transfer through the cell is calculated by integration of the temperature gradient along with thermal conductivities of soil and fluid. The effective thermal conductivity of the unsaturated soils is determined by conceptualizing the soils as having the same heat transfer as the cell of solid particle and fluid mixture. The new model is compared with 268 data entries of unsaturated soil effective thermal conductivity measurements from the literature. The developed effective thermal conductivity model compares favorably with the experimental data. When the porosity is small, the increase in the effective thermal conductivity with water phase saturation is more significant and non-linear. When the porosity increases, the increases of effective thermal conductivity with water phase saturation approaches a linear relationship.