The energy pile technology has been widely used, and the solid cylindrical heat source (SCS) model is usually adopted to describe the heat transfer process between the energy pile and the surrounding soil. This paper investigates the SCS model with a convective boundary condition (SCS-3 model), and realistic conditions such as transversely isotropic ground and groundwater flow are all included in the model. An analytical solution for the problem is established using Green's function method and the theory of moving heat sources. Solutions for the SCS model with a boundary condition of the first kind (SCS-1 model) and for the line source (LS) model with a convective boundary condition (LS-3 model) are recovered as special cases of the solution in this paper. Computational examples are presented, and comparisons between different models are made. First, the SCS-1 model is compared with the SCS-3 model, showing the error caused by neglecting the surface convective effect. Second, the LS-3 model is compared with the SCS-3 model, showing the error associated with neglecting the size of heat source. The effects of groundwater flow velocity and convective heat transfer coefficient on the temporal and spatial variations of these errors are also investigated.