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 . 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 . 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 . 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.

中文翻译：

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在 Carreau 流体模型中研究非线性锥形狭窄动脉血流的分析方法

目前的研究提供了一种使用 Carreau 流体模型分析通过狭窄动脉的血流的分析方法。流量控制方程是在考虑轻度狭窄的情况下推导出来的。通过将血液视为非牛顿性质进行了数学分析。然后，利用正则微扰技术研究了解析解。通过这种扰动获得的解达到无量纲魏森伯格数的二阶。详细讨论了不同参数值的计算，例如速度、壁面剪应力、剪应力和狭窄喉部的阻力阻抗。得到的结果表明，对于剪切稀化流体，流体速度随着参数m的增加而增加，而随着参数m的增加，观察到相反的行为。因此，所提出的数值分析通过将血液视为非牛顿 Carreau 流体模型来揭示流动的许多方面，并且所提出的模型同样适用于其他生物数学研究。