Fractal approach to calculate the thermal conductivity of moist soil

Abstract

The ground heat exchanger (GHE) is a key component in the design of a GSHP system and the effective thermal conductivity is one of the most important parameters that determine the heat transfer underground. In this paper, the effect of particle sizes and distributions on the sand thermal conductivity were studied both experimentally and analytically. Fractal method was considered for simulating the thermal conductivity of both dry and moist, unsaturated sand. Seven types of dry sand samples and six types of moist, unsaturated sand were selected in the experiments and results showed that both porosity, fractal dimension and particle size ratio affect the sand thermal conductivity. Based on the fractal theory, the fractal models were applied to predict the sand thermal conductivity under both dry and wet conditions. By comparing to the experimental findings, the proposed model was able to predict the variation on the sand thermal conductivity. However, the contact thermal resistance and water distribution pattern are two key impacts on the soil behaviors and need to be further studied.