Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.