Modeling of heat transfer of a vertical bore in ground-source heat pumps

The heat transfer of a vertical borehole is discussed for geothermal heat exchangers. An explicit analytical solution is given in terms of the one dimensional cylinder model. The solution of the simplified line source model is compared with that of the cylinder model, which demonstrates that the solution of line source model is fine to simulate the heat transfer of the vertical bore in larger Fourier number. But in small Fourier number, it has bigger error comparing with the cylinder model. In comparison with the semi infinite plate model, another approximate expression of the cylinder model has been obtained, which is simple and suited better to short times.