Predicted effects of soil dry density and initial water content on performance of a heat exchanger buried in an unsaturated Loess Parent material

The influence of dry density and soil water content on the performance of a heat exchanger buried in a Loess Parent material was studied for heat rejection to the soil. A mathematical model was developed to predict heat exchanger performance based on partial differential equations for coupled heat and water flow. Soil properties in the analysis included thermal conductivity and matric potential, measured in the laboratory, and unsaturated hydraulic conductivity and water vapor diffusion coefficients, derived according to methods in the literature. In addition, the effect of thermal contact conductance between the heat exchanger and adjacent soil was considered. A lumped model for predicting reduction of thermal contact conductance at the exchanger-soil interface was incorporated into the model which was based on soil shrinkage and air-gap thermal contact conductance data obtained in the laboratory. Heat exchanger performance was predicted for three assumed heat and water flow cases; constant soil properties, thermally-induced water flow and thermally-induced water flow with thermal contact conductance. Results of the mathematical modeling efforts neglecting thermal contact conductance indicated that increasing dry density had a substantial impact on heat exchanger performance when thermally-induced liquid and vapor phase water was considered. For an initial water content of 0.16 Mg/Mg dry basis, increasing dry density from 1.40 to 1.60 Mg/m$\sp3$ increased heat exchanger performance by about 83 percent after 48 hours of operation. Increasing initial water content from 0.16 to 0.20 Mg/Mg at a dry density of 1.40 Mg/m$\sp3$ increased heat transfer by 29 percent after 48 hours. Adding thermal contact conductance effects to the model reduced heat exchanger performance by less than 11 percent for each water content-dry density combination. The results suggest that, for the manner in which thermal contact conductance was incorporated into the model, increasing dry density from 1.40 to 1.60 Mg/m$\sp3$ will more than double heat exchanger performance