We present a method for solving moving-boundary problems in the presence of nonuniformities and nonlinearities. The method is based on the spectral decomposition of the concentration field of reacting/diffusing species in a suitable system of eigenfunctions and on the solution of the corresponding system of ordinary differential equations for the Fourier coefficients by means of fixed-point methods. The method proposed by Selim and Seagrave is improved upon and extended to solve moving-boundary problems in the presence of position-dependent diffusion coefficients and nonlinearities in kinetic rates. We apply this method to solve isothermal and nonisothermal shrinking-core models for fluid-solid noncatalytic reactions by focusing on the influence of spatial nonuniformities in the solid reactant distribution.