Heat Transfer Control Mechanism in a Vertical Ground Heat Exchanger: A Novel Approach

In order to maximize maximise the temperature of the ground heat exchanger (GHE), this chapter presents a mathematical model of the behavior of heat transfer between the liquid inside vertical underground geothermal pipes and the surrounding ground. The GHE is a crucial component of the GHPS and plays a key role in utilizing the earth’s heat energy by exchanging heat with the ground due to its actual contact. Most benefits from the earth’s thermal energy can be attained when the GHE is well-designed, including in terms of configuration, installation location, borehole heat exchanger capacity, and performance factors, which ensure that the GHE’s output temperature reaches the ground temperature.

The heat transfer mechanism between the circulating water inside the vertical U-tube pipe and the surrounding grounds is as follows: through conduction, the heat transfers from the grout to the outer pipe wall and from the outer to the inner pipe wall, and by convection from the inner pipe wall to the circulating water. The model was implemented in MATLAB using an ordinary differential equation (ODE) solver. The results reveal that the acceptable range of the water velocity for Oakland University’s GHE was between 0.35 and , which ensured that the heat pump system delivered the proper temperature to provide the Human Health Building (HHB) with a comfortable temperature regardless of the season. The suggested water velocity ranges in vertical single U-tube pipes with diameters of De , De , and De are between 0.33 and to , and 0.38 to , respectively. In the future, the study anticipates controlling this nonlinear system at several operational points, controlling each point separately, and switching between these controllers using the single controller block to control it more effectively along its trajectory.