The present paper is a study on dispersion of reactive solute in an oscillatory flow of a Two-fluid, three-layer Casson-Newtonian continuum using Aris-Barton’ s approach. A Two-fluid model of blood flow has been considered, the fluid in the central region is taken to be a Casson fluid (a core of red blood cell suspension) and a peripheral layer of plasma modelled as Newtonian fluid. The governing equations for the velocity distribution have been solved using a perturbation technique, and the effective dispersion coefficient has been evaluated numerically (FDM) by solving the moment equations. Using the Hermite polynomial representation of central moments the axial distribution of mean concentration is determined. The main objective is to look into the impact of yield stress, peripheral layer thickness, irreversible and reversible reaction rate on the dispersion process. The study has significant applications on the transport of species in a blood flow system.