4214 -- Development of an Equivalent Diameter Expression for Vertical U-Tubes Used in Ground-Coupled Heat Pumps

An expression for the equivalent diameter was developed for the heat transfer of a vertical U-tube heat exchanger used in applications of ground-coupled heat pumps. The expression was derived using the assumptions of steady-state heat transfer and concentricity of one leg and the borehole. Potential errors in applying the results to a transient start-up problem are also quantified and discussed in this paper, using transient cylindrical heat source solutions available in the literature. A conformal mapping technique was used to develop a solution to examine the errors in evaluating the external thermal resistance with a concentricity assumption. The principle of superposition of multiple heat sources was applied in the present work. The results show that the equivalent diameter depends on the tube diameter and the leg spacing. The ratio of the calculated equivalent diameter to the tube diameter can be two or greater.

Units: SI