Non-linear mathematical models for blood flow through tapered tubes

In this paper, the steady flow of blood through tapered tube has been analyzed assuming blood as (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for pressure drop, wall shear stress and resistance to flow have been obtained. The effects of tapering of the tube and the non-Newtonian nature of the fluid on pressure drop, wall shear stress and resistance to flow are discussed. For all fluids, the pressure drop increases with increasing angle of taper from 0.5° to 1° for a given value of yield stress θ and tapered tube Reynolds number Reψ. The resistance to flow as well as the wall shear stress increase with increasing yield stress for Herschel-Bulkley fluid and also for Casson's fluid when the other parameters held constant. Both for Herschel-Bulkley fluid and Casson's fluid, the wall shear stress as well as the resistance to flow increase with increasing axial distance for a given tapered tube Reynolds number Reψ, angle of taper ψ and yield stress θ.