In a recent article by Pantokratoras and Fang (Transport in Porous Media, doi:10.1007/s11242-009-9470-6, 2009), the title problem for the fully developed flow regime was considered, and exact solutions for two types of boundary conditions were reported. However, for a certain parameter combination, some terms of these exact solutions become singular. As a consequence, the solutions cannot be evaluated by a direct substitution of the respective parameter values. The aim of the present note is to (i) show how the singularities can be removed, (ii) give the corresponding nonsingular solutions in an explicit form, and (iii) discuss the physical meaning of the singular cases.