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Arterial Blood Flow Through a Nonsymmetrical Stenosis with Applications

The problem of blood flow through an axially nonsymmetric but radially symmetric stenosed tube when blood is represented by a Casson fluid and a Newtonian fluid, is investigated. The equations governing the flow obtained from the proposed model are solved and closed-form expressions for blood flow characteristics, namely, the dimensionless resistance to flow, the wall shear stress and the shearing stress on the wall at the maximum height of the stenosis, are derived. The results obtained are discussed in brief both qualitatively and quantitatively by comparing with related studies in the literature. It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape and that the maximum resistance is attained in the case of symmetric stenosis. The magnitudes of the resistance to flow are always higher in the case of a Casson fluid model than in the case of a Newtonian fluid model. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to the Casson fluid parameter; however, the latter is independent of the stenosis shape and the former posseses a character different from the resistance to flow with respect to the parameter determining the stenosis shape. The analysis results are finally used to estimate the blood flow characteristics in different blood vessels using the numerical data from literature.