A finite line‐source model for boreholes in geothermal heat exchangers

Abstract An analytical solution of the transient temperature response in a semi‐infinite medium with a line source of finite length has been derived, which is a more appropriate model for boreholes in geothermal heat exchangers, especially for their long‐duration operation. The steady‐state temperature distribution has also been obtained as a limit of this solution. An erratic approach to this problem that appears in some handbooks and textbooks is indicated. Two representative steady‐state borehole wall temperatures, the middle point temperature and the integral mean temperature, are defined. Differences between them are compared, and concise expressions for both are presented for engineering applications. On this basis the influence of the annual imbalance between heating and cooling loads of the geothermal heat exchangers is discussed regarding their long‐term performance. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 558–567, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10057