**ABSTRACT**

In order to provide a more comprehensive depiction of the actual heat transfer process in energy piles, this research paper presents an approximate solution for a finite line heat source model operating under variable heat flow conditions. This solution is established by integrating the finite line heat source model and the superposition principle. Furthermore, the W-tube heat exchanger is divided into many segments, and a segmented superposition approach is used based on the thermal response. Consequently, a heat transfer model for a single-pile heat source is formulated, taking into consideration the heat exchange between the circulating water and the energy pile. Notably, the soil temperature predicted by this proposed model closely aligns with the results obtained from the FLUENT numerical model, thereby substantiating the accuracy of the proposed approach. Simultaneously, the heat transfer model is employed to analyze variations in temperature and heat flux density within the heat exchanger and to investigate the influence of parameters such as mass flow rate, pile-soil heat transfer coefficient, pile-soil density, and pile-soil specific heat capacity on the heat transfer characteristics of energy piles. This model enables the determination of time-varying heat flux and precise outlet temperature, thereby facilitating a rapid assessment of the heat transfer efficiency of energy piles.

**KEYWORDS**

PAPER SUBMITTED: 2023-06-03

PAPER REVISED: 2023-07-10

PAPER ACCEPTED: 2023-07-18

PUBLISHED ONLINE: 2023-09-02

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