On Thermally Interacting Multiple Boreholes with Variable Heating Strength: Comparison between Analytical and Numerical Approaches

The temperature response in the soil surrounding multiple boreholes is evaluated analytically and numerically. The assumption of constant heat flux along the borehole wall is examined by coupling the problem to the heat transfer problem inside the borehole and presenting a model with variable heat flux along the borehole length. In the analytical approach, a line source of heat with a finite length is used to model the conduction of heat in the soil surrounding the boreholes. In the numerical method, a finite volume method in a three dimensional meshed domain is used. In order to determine the heat flux boundary condition, the analytical quasi-three-dimensional solution to the heat transfer problem of the U-tube configuration inside the borehole is used. This solution takes into account the variation in heating strength along the borehole length due to the temperature variation of the fluid running in the U-tube. Thus, critical depths at which thermal interaction occurs can be determined. Finally, in order to examine the validity of the numerical method, a comparison is made with the results of line source method.