A mathematical expression for the film thickness in a flat sample, reacting with a fluid, as a function of reaction time is derived. The formulation is based on a gas-solid reaction similar to the unreacted core shrinking model and takes into account two moving reaction frontiers, one due to the shrinking unreacted core, and one due to the changing thickness of the samples as a result of combustion. The equation of motion for the two reaction boundaries is solved exactly for flat samples applying a Lambert W function. The model for the flat samples is compared with experimental results.