New temperature response functions (G functions) for pile and borehole ground heat exchangers based on composite-medium line-source theory

This paper presents a new approach to modeling of heat transfer by ground heat exchangers, involving unsteady heat conduction in composite media together with complex geometry. Analytical solutions for continuous line and cylindrical-surface sources are developed based on Jaeger’s instantaneous line-source solution for composite media. New temperature response functions (G functions) are also presented for pile ground heat exchangers with spiral coils and for borehole ground heat exchangers with single or double U-shaped tubes. These temperature response functions can be used to analyze the impact of difference between properties of materials inside and outside boreholes or piles on the performance of ground heat exchangers. Theoretical results show that the difference in properties is an important factor affecting the temperature response of ground heat exchangers. Since the heat capacity of grout, inside boreholes, is fully considered by this line-source theory, the new G functions should be particularly suitable for predicting small-time dynamic behaviors of ground heat exchangers. Therefore, these G functions may be significant for energy analysis and in-situ thermal response tests of ground-coupled heat pump systems.