An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments’, under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper. The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer. A significant change from previous modelling exercises in the study of hydrodynamic dispersion, different molecular diffusivity has been considered for the different region yet to be constant. For all time period, finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation. The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter, yield stress, viscosity ratio, peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers. This kind of study may be useful for understanding the dispersion process in the blood flow analysis. © 2017 Elsevier B.V.