Abstract
A hybrid numerical/analytical one-dimensional model is proposed to predict the thermal behavior of borehole heat exchangers in the short period following a step change in operating conditions. Transient heat transfer in the borehole is solved numerically using an equivalent composite cylinder geometry, while ground heat transfer is evaluated analytically using the infinite cylindrical heat source solution. The proposed model is then used to generate -functions, which are based on a slightly different definition than the traditional g-functions. For short times, -functions depend on four nondimensional parameters: , (with equal to a new characteristic time), and and , nondimensional parameters related to the fluid and the ground, respectively. A set of universal -functions curves generated with the proposed model is presented. Then these curves are used in a borehole sizing problem. It is shown that the inclusion of borehole thermal capacity has a direct effect on the daily and monthly effective ground thermal resistances, which reduces the required borehole length by a few percent.
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