Theoretical Prediction of the Soil Thermal Conductivity at Moderately High Temperatures

The theoretical model of the present paper assumes the unit cell of the porous medium as composed of a cubic space with a cubic solid particle at the center. The thermal conductivity is evaluated by solving the heat conduction equation with the assumption of parallel isotherms within the cubic space. The liquid water in the porous medium is distributed around the solid particle according to the phenomena of adsorption and capillarity. The thermal conductivity of the gas present within the pores takes into account the thermal conductivity of the water vapor and dry air, without enhanced vapor diffusion. The model simplifies the variation of the relative humidity, from dryness to the field capacity, with a linear increase. The predicted results, compared to experimental data, show the agreement is very good at the temperatures in the range (30–50°C) and acceptable at 70°C. At high temperature (90°C) the predictions are higher than the experiments and a better agreement could be obtained by decreasing the thermal conductivity of the gas phase. Besides, the trend of the theoretical predictions is in good agreement with the experiments also at high temperatures.