18 May 2017
Mean integral solutions to the equations of the moving finite line- source (MFLS) and the moving spiral source (MFSS) models for ground heat exchangers with groundwater flow are presented. The solutions for the average temperature in the MFLS and MFSS models are expressed, respectively, as single and double integrals averaging the exact solutions over both depth and circumference. Depth to diameter ratio of vertical heat source defines the intermediate time interval, where thermal capacities of energy pile/borehole and flowing groundwater influence significantly on temperature response. Approximate expressions for the average temperature are derived analytically from the MFLS model within the intermediate time scale.