Abstract
The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non‐Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second‐order in dimensionless Weissenberg number (We). The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number (We). The obtained results demonstrate that for shear‐thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We. Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non‐Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio‐mathematical studies.
Highlights
Academic Editor: Dan Selisteanu e current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. e flow governing equations are derived under the consideration of mild stenosis
Mathematical analysis has been carried out by considering the blood as non-Newtonian nature. en, the analytical solution has been investigated by using the regular perturbation technique. e solutions obtained by this perturbation are up to the second-order in dimensionless Weissenberg number (We). e performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number (We). e obtained results demonstrate that for shear-thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We
Introduction e study of artery constriction due to the development of stenosis has attained prime importance in fluid dynamics [1,2,3,4]. e blood flow in the vessels is a result of the delicate relationship between pressure and area of the fluid. e size of the stenosis determines the flow type. ree types of flow have been studied: mild stenosis as the flow is laminar, moderate stenosis as the flow is a combination of turbulent and laminar, and thirdly the flow depicts turbulent nature when the size of the stenosis is increased. e characteristics of the blood flow depend on the shape and size of the stenosis
Summary
Academic Editor: Dan Selisteanu e current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. e flow governing equations are derived under the consideration of mild stenosis. E current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. E flow governing equations are derived under the consideration of mild stenosis.
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