The impact of heterogeneous (kinetic reversible phase exchange and irreversible absorption) chemical reactions along with a homogeneous first-order reaction is considered for the dispersion of a solute in a solvent flowing through an annular pipe under a periodic pressure gradient. A Casson model is used to describe the non-Newtonian viscosity of the liquid. The Aris–Barton method of moments is employed to study the behavior of the dispersion coefficient. The axial distribution of the mean concentration is determined using the Hermite polynomial representation of central moments. This study focuses on the transport phenomena in terms of the dispersion coefficient due to multiple kinds of reaction, yield stress, radius ratio, etc., which could be useful for analysis of flow of physiological blood-like liquids. © 2019, Springer Nature B.V.