Development of an analytical framework for thermal design of energy walls

Energy walls are conventional retaining structures integrated with heat exchangers to harness near-surface geothermal energy for space heating and cooling. Despite their growing application, limited research has focused on developing analytical formulations that streamline the thermal design of energy walls. This study presents an analytical framework that combines the infinite plane source and shape factor methods, designed to accurately predict the temperature changes within energy walls. Three novel method modifications are introduced: an equivalent length for the infinite plane source method, a new shape factor formulation, and optimising the reference surface selection. The proposed formulations are validated through two-dimensional finite element numerical models and subsequently tested using monitored data from a full-scale Cutter Soil Mix (CSM) energy wall test. The results show the predicted outlet temperature from the heat exchanger pipes differs by only 5.7% from the measured data under near steady-state conditions. These findings demonstrate the reliability and accuracy of the new analytical formulations, providing an improved fast run-time tool for advancing the thermal design of energy walls.