Thermal resistance capacity model for short-term borehole heat exchanger simulation with non-stiff ordinary differential equations

Abstract In the present study, a new thermal resistance capacity circuit for the heat transfer modeling in borehole heat exchanger with low computation time is developed. Generally, the thermal circuit models result in sets of ordinary differential equations which are solved numerically. The system of equations derived from the traditional thermal resistance capacity model (TRCM) are usually stiff and lead to unstable results unless for a very small time steps which can increase the computation time significantly. Meanwhile, the system of ordinary differential equations derived from the present model is non-stiff and there is no time step limitation for the stability of the results. It is shown that the present model yields accurate and stable results even for large time steps. Finally, the two-dimensional model is extended to the three-dimensional model. The results of the three-dimensional solution of the present model are in good agreement with the numerical results and experimental measurements reported in the literature.

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