Time evolution of the ground temperature around a set of Borehole Heat Exchangers with unbalanced seasonal loads and no groundwater movement

The time evolution of the mean surface temperature of the most critical BHE, for BHE fields with unbalanced seasonal loads and no groundwater flow, is studied by means of finite-element computations performed through COMSOL Multiphysics and the superposition of effects. Two dimensionless heat loads with period of one year are adopted, such that their superposition yields any heat load varying in time with a sinusoidal law during each half year. A time period of 50 years is considered in numerical computations. The results, in the form of tables of coefficients of two dimensionless equations, allow a quick evaluation of the time evolution of the dimensionless temperature at the surface of the most critical BHE, for any BHE field (such as a single line, a double line, a square or rectangular field) which can be considered as a part of a 5 × 5 square field.