The shear-augmented dispersion of solute in blood flow through (i) a circular pipe and (ii) channel between two parallel flat plates in the presence of chemical reaction is analyzed mathematically, treating the blood as Herschel-Bulkley fluid model. The convective diffusion equation is solved with the help of the appropriate boundary conditions and the expressions for the mean velocity of solvent fluid in the plug flow region and non-plug (outer) flow region, the effective axial diffusivity and the relative axial diffusivity of the solute are derived. It is noted that when the yield stress of the blood increases, the effective axial diffusivity of the solute decreases slowly and the relative axial diffusivity of the solute decreases significantly. It is also found that the effective axial diffusivity and relative axial diffusivity decrease marginally with the increase of the power-law index. It is also recorded that the effective axial diffusivity and relative axial diffusivity of the solute decrease marginally with the increase of the rate of chemical reaction parameter. The effective axial diffusivity and relative axial diffusivity of the solute are considerably higher when it disperses in Herschel-Bulkley fluid flow than when it disperses in Casson fluid flow.

blood flow, chemical reaction, solute dispersion, flow in pipe and channel, Herschel-Bulkley fluid, relative axial diffusivity, effective axial diffusivity.