A Model of Finite-length Linear Heat-source for the Vertical Embedded Pipe of a Ground-source Heat Pump

Analyses and discussions were conducted of a non steady heat transfer model for the vertical embedded pipe of a geothermal heat exchanger. With the use of a virtual heat source and Green function method obtained is an analytical solution expression for the non steady temperature field generated by a finite length linear heat source in semi infinite large media. By way of comparison with a steady state temperature field solution discussed is the time required for the temperature field to attain a nominal "steady state". Meanwhile, an analysis is performed of the temperature field when it has reached a steady state. In this connection a mistake that appeared in current textbooks was indicated. Two representative steady state borehole wall temperatures, i.e., the temperature at the middle of the borehole and the integral mean temperature along the borehole, are defined. A comparison of the difference between these two temperatures has led to a simplified calculation formula, suitable for engineering applications. On the basis of the above analyses discussed further is the impact of the annual imbalance between heating and cooling loads of geothermal heat exchangers on their long term performance.