Higher-order temporal scheme for ground heat exchanger analytical models

Abstract

Several models have been proposed in the literature to simulate and design earth heat exchangers, mostly used in the context of ground-source heat pump systems. Some models were based on numerical approaches and other on analytical solutions. The analytic models are mostly based on a convolution of response factors, with a stepwise function assuming a constant heat load during each time step. In this work, Duhamel’s theorem is used to derive the analytical expression of the infinite line source, the infinite cylindrical source and the finite line source, and to obtain analytical expressions integrating high-order temporal schemes allowing the load to vary linearly between successive time steps. It is shown that when the load varies with time, and long-time steps are required, a high-order temporal scheme can be advantageous. The proposed method can be applied to the models where the temporal superposition of pulses was used previously.