A computational model of a heat pump system with a hemispherical surface tank as the ground heat source

A computational model for a space heating system utilising a heat pump with a hemispherical surface tank as the ground heat source is presented. An analytical solution is obtained for the transient temperature field outside a hemispherical surface tank by an application of the Complex Finite Fourier Transform (CFFT) and the Finite Bessel Transform (FBT) techniques. This analytical solution, when utilized with expressions valid for the heat pump work and space heat load, leads to the prediction of the annual variation of water temperature in the surface tank as well as the transient earth temperature field surrounding the surface tank. Monthly and annual heat pump work requirements are predicted and presented.