Analytical solutions to the unsteady diffusion equation in spherical geometry are presented for uniform and composite porous media. In this case, a Neumann (prescribed flux) boundary condition is assumed as opposed to a Dirichlet (prescribed concentration) boundary condition used in previously published derivations. For radionuclides that have very high solubility under a given set of geochemical conditions, such as 99Tc and 79Se under oxidizing conditions, a prescribed flux boundary condition is more appropriate.