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Abstract

The two-phase flow of blood in a small diameter blood vessel under mild stenotic condition is investigated in this mathematical analysis, modelling the densely concentrated red cells in the inner phase region as Herschel-Bulkley fluid and the plasma with depleted red cells in the peripheral phase region as Newtonian fluid. The analytic solutions for the velocity profile, rate of flow, slip velocity, shear stress at the blood vessel’s wall, resistive impedance to flow and core fluid’s viscosity are obtained. It is found that when the stenosis length ratio and the flow index parameter increase, the slip velocity increases significantly and an opposite behavior is noticed for the core fluid’s viscosity. It is also recorded that the percentage of difference between the core fluid’s viscosity in the two-phase Herschel-Bulkley fluid model and the corresponding experimental values in the blood vessel’s of diameter and are found to be 1.27% and 0.32% respectively and the respective differences observed by Ponalagausamy and Tamil Selvi (2011) in their two-layered Casson fluid model are 3.75% and 6.86% respectively. The estimated slip velocity values of two-phase Herschel-Bulkley fluid model in the blood vessels of diameter and are recoded as 1.202 cm/s and 0.7405 cm/s respectively and these values are in good alignment with the respective values obtained by Ponalagusamy and Tamil Selvi (2011) for two-fluid Casson model. The estimates of the core fluid’s viscosity in two-phase Herschel-Bulkley fluid model increase gradually when the flow index parameter increases in the blood vessels of diameter and this behavior is reversed in the blood vessels of diameter.