Heat transfer around a buried coil heat source is studied analytically in detail on the background of its potential application in the pile ground heat exchanger for ground-coupled heat pump systems. Advanced from our previous studies of this problem on the basis of pure conduction models, combined conductive and advective heat transfer models are presented in this paper, taking the groundwater movement in the porous medium of the strata into consideration. The methodology to obtain analytical solutions of such combined conduction and convection problems is expatiated based on the Green’s function theory and moving heat source concept. While various simplifications are assumed to describe the shape of the buried coil with increasing sophistication, models of the line heat source, cylindrical heat source, ring-coil heat source and spiral-coil heat source are introduced step by step. Both infinite length and finite length heat sources are also taken into account to discuss the impact of the ground surface and limited length of the heat source on the heat transfer process. Explicit expressions of the analytical solutions are obtained for eight cases studied, and computation on these solutions has confirmed effectiveness of this approach to deal with sophisticated combined conduction and advection heat transfer problems.