A Mathematical Model Of Blood Flow Of A Stenosed Artery In Variable Shape
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Abstract
In this theoretical study, a mathematical model is developed to carry out a systematic analysis of flow behaviour in a two-dimensional vessel (modeled as artery) with a locally variable shaped constriction. An artificial artery, which containing a viscous incompressible fluid that representing the flowing blood can be treated as inflexible vessel. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section is perpendicular to the axis of the vessel. The constricted vessel is resolved into a straight vessel and the entire resulting equations are solved by a numerical method with Reynolds number and ‘n’, a number giving the shape of the constriction as parameters. The impacts of these parameters on wall shear stress, pressure gradient and velocity have been analysed. It is found that the flow resistance decreases as the shape of a smooth stenosis changes and extreme resistance is attained for the symmetric stenosis. But the length of separation increases for the asymmetric constrictions and the oscillation in the shear layer appears earlier for asymmetric constriction than that in the case of symmetric constriction. The extreme resistance is attained for inflexible stenosed vessel rather than the flexible one.
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