The long-term time evolution of the mean surface temperature of the most critical BHE, for BHE fields with arbitrarily given monthly heat loads and no groundwater flow, is studied by means of finite-element computations performed through COMSOL Multiphysics and the superposition of effects. A unit step heat load, with duration of one month, is considered, and its effects are evaluated. Then, the effects of any periodic heat load with a period of one year and given monthly heat loads can be obtained by a weighted sum of the effects of the unit step heat load, properly displaced in time. The result of the computations is a set of dimensionless equations that, properly superimposed, yield the time evolution of the dimensionless temperature at the interface between the most critical BHE and the ground, for a period of 50 years, for several typical configurations of BHE fields.
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