A unified model and analytical solution for borehole and pile ground heat exchangers

Abstract

This paper presents a new cylindrical source heat transfer model for simulating the influence of the thermal properties difference between the borehole and pile ground heat exchangers and the surrounding soil directly. Based on the energy conservation law, the model proposes a heat transfer equation that heat transfers from the heat source to both sides, and the analytic solution in Cartesian coordinate system is obtained via Laplace transform and inverse transformation. Because special cases of the analytical solution can be deduced to the classical models, the proposed model can be considered a unified model of the classical ones. The heat transfer analysis using this model shows that the thermal properties of the materials inside and outside the heat source have a greater impact on the initial period of heat transfer. Furthermore, the proposed model enables more accurate energy consumption analysis and energy pile design. Base on the model, to improve the heat transfer efficiency, the following measures can be adopted for the materials inside and outside the heat source. The moisture content of the soil outside the heat source can be increased, optimally keeping the soil saturated. Inside the heat source, on the premise of satisfying the requirements of mechanical properties, the thermal conductivity can be increased, whereas the volumetric heat capacity and diameter can be decreased.