TEMPERATURE DISTRIBUTION AROUND A SET OF CYLINDRICAL SURFACES SUBJECTED TO A TIME DEPENDENT HEAT FLUX

The analytical solution for the temperature field in an infinite solid medium which surrounds a cylindrical surface, determined by Carlslaw and Jaeger for the case of constant heat flux, is extended to the case of any time dependent heat flux. Then, with reference to a sinusoidally varying heat flux, the analytical solution is employed to validate a finite-element solution of the same problem, performed through COMSOL Multiphysics. Finally, the long term behaviour of BHE fields subjected to completely unbalanced winter and summer heat loads, in the absence of groundwater movement, is investigated by means of finite element simulations performed through COMSOL Multiphysics and a simple method based on the superposition of effects. Fields with few BHEs are considered, to complement the results of a recent study which refers to an infinite line, double line or square field.