Abstract
A two-dimensional model is used to analyze the unsteady pulsatile flow of blood through a tapered artery with stenosis. The rheology of the flowing blood is captured by the constitutive equation of Carreau model. The geometry of the time-variant stenosis has been used to carry out the present analysis. The flow equations are set up under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave. A radial coordinate transformation is employed to immobilize the effect of the vessel wall. The resulting partial differential equations along with the boundary and initial conditions are solved using finite difference method. The dimensionless radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for normal and diseased artery with particular focus on variation of these quantities with non-Newtonian parameters.
Highlights
It is generally accepted that the rheological behavior of blood is assumed as Newtonian for values of shear rate greater than 100 s−1 and such situation occur in larger arteries
The geometry of the time-variant stenosis has been used to carry out the present analysis
The accumulation of cholesterols, fats and smooth muscle cells in blood vessels causes partial occlusion known as stenosis
Summary
The present study generalizes the results of Mandal[24] and Ali et al.[33] In Ref. 24, Mandal used power-law to analyze the effects of the non-Newtonian rheology of blood, the vessel tapering, the severity of stenosis and the wall deformability on flow characteristics while Ali et al.[33] generalized the Mandal’s Analysis by utilizing the constitutive equation of Sisko model. Akbar and Nadeem[34] analyzed steady flow Carreau fluid in an artery under the assumption of mild stenosis. They have obtained the solution of governing equation using perturbation approach.
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