Analytical solutions for two pile foundation heat exchanger models in a double-layered ground

In the energy pile technology, pipes of the heat exchanger are installed in the concrete pile. When the pipes are configured in the form of spiral coils, they can usually be described by the solid cylindrical heat source model or the ring-coil heat source model. This paper investigates the temperature responses of these two heat source models in a double-layered ground, and the corresponding analytical solutions are established using the Green's function method. The Green's function, which delineates the temperature response induced by an instantaneous ring source in a double-layered ground, is obtained by the separation of variables technique, and in order to solve the nonlinear equations of the eigenvalues, a constrained Newton method is also developed. The analytical solutions are verified by two means. After that, computational examples are presented. The difference between the temperature response in a layered ground and that in a homogenous ground is discussed, and the computational error of using the homogeneous model to describe the temperature response of a layered ground is also studied.