New Analytical and Numerical Solutions for the Short-term Analysis of Vertical Ground Heat Exchangers

Journal article, 2011

This paper presents the background, development and the validation of new analytical and numerical solutions for the modeling of short-term response of borehole heat exchangers. The new analytical solution studies the borehole's heat transfer and the related boundary conditions in the Laplace domain. A set of equations for the Laplace transforms for the boundary temperatures and heat-fluxes is obtained. These equations are represented by a thermal network. The use of the thermal network enables swift and precise evaluation of any thermal or physical setting of the borehole. Finally, very concise formulas of the inversion integrals are developed to obtain the time-dependent solutions. The new analytical solution considers the thermal capacities, the thermal resistances and the thermal properties of all the borehole elements and provides a complete solution to the radial heat transfer problem in vertical boreholes. The numerical solution uses a special coordinate transformation. The new solutions can either be used as autonomous models or easily be incorporated in any building energy simulation software.