Simulation of 2D Heat Transfer in a Horizontal Plane with Thermal Resistance-Capacitance Model

Abstract

In this paper, a thermal resistance capacitance model (TRCM) technique is developed for studying the heat transport in the horizontal plane of a borehole heat exchanger (BHE) array for a seasonal thermal energy storage (STES) system. We started from the TRCM model previously developed from other studies for a single BHE borehole and expanded it to have an azimuthal sense with a hexagonal element to represent a single BHE. Then we use it as an element to form a honey comb shaped collections to model the heat transport in a horizontal plane of a BHE array at a representative depth by solving an ordinary differential equation set. We validated the approach by comparison with the results generated by the finite element method for the same model and the results have reached excellent agreement. The major findings and conclusive remarks are: 1) a novel TRCM model is developed with the capability to model heat transport in a horizontal plane for the study of the temperature evolution in the soil formations in a STEMM BHE system; 2) This newly developed TRCM model is much faster than the FEM for the same model so that it is cost-effective and practical for modeling long term (weeks to decades) thermal evolution in a BHE array; 3) Using the newly developed TRCM approach we studied the ‘partition by partition’ heating scenario and the results show a higher temperature concentrated in the center of the BHE array, a results desired for the system for reducing the loss of heat energy from the periphery of the BHE array.