In this work, a forcing strategy based on a cyclic flow reversal of a dyeing process of bobbin threads is investigated through numerical simulation. Convection, dispersion, and adsorption of dye on the threads are modeled considering that the system is operated by a cyclic reversal of the flow direction through the bobbins. The periodic forcing is modeled by an ad hoc discontinuous periodic function, and a mathematical model that takes it into account is developed. The mathematical model is a set of partial differential equations that is reduced to a system of ordinary differential equations by an orthogonal collocation on finite elements technique. The comparison between forced and unforced processes has been carried out analyzing the dye distribution factor and the total amount of adsorbed dye during the transient regime for both of the processes. The main effect of periodic forcing is to enhance a more even dye distribution.