Purpose

Cilia serves numerous biological functions in the human body. Malfunctioning of nonmotile or motile cilia will have different kinds of consequences for human health. More specifically, the directed and rhythmic beat of motile cilia facilitates the unidirectional flow of fluids that are crucial in both homeostasis and the development of ciliated tissues. In cilia-dependent hydrodynamic flows, tapering geometries look a lot like the structure of biological pathways and vessels, like airways and lymphatic vessels. In this paper, the Carreau fluid model through the cilia-assisted tapered channel (asymmetric) under the influence of induced magnetic field and convective heat transfer is investigated.

Design/methodology/approach

Lubrication theory is a key player in the mathematical formulation of momentum, magnetic field and energy equations. The formulated nonlinear and coupled differential equations are solved with the aid of the homotopy perturbation method (HPM). The graphical results are illustrated with the help of the computational software “Mathematica.”

Findings

The impact of diverse emerging physical parameters on velocity, induced magnetic field, pressure rise, current density and temperature profiles is presented graphically. It is observed that the cilia length parameter supported the velocity and current density profiles, while the Hartman number and Weissenberg number were opposed. A promising effect of emerging parameters on streamlines is also perceived.

Originality/value

The study provides novel aspects of cilia-driven induced magnetohydrodynamics flow of Carreau fluid under the influence of induced magnetic field and convective heat transfer through the asymmetric tapered channel.

中文翻译：

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使用纤毛衰减流上的磁化非牛顿卡罗流体模型进行霍尔电流的对流换热

 目的

纤毛在人体中具有多种生物学功能。非运动或运动纤毛的功能障碍将对人类健康产生不同的后果。更具体地说，运动纤毛的定向和有节奏的跳动促进了液体的单向流动，这对于纤毛组织的稳态和发育至关重要。在依赖纤毛的流体动力学流动中，逐渐变细的几何形状看起来很像生物通路和血管的结构，如气道和淋巴管。本文研究了在感应磁场和对流传热的影响下通过纤毛辅助锥形通道（不对称）的卡罗流体模型。

设计/方法论/途径

润滑理论在动量、磁场和能量方程的数学公式中发挥着关键作用。借助同伦微扰法 (HPM) 求解公式化的非线性和耦合微分方程。图形结果在计算软件“Mathematica”的帮助下进行说明。

 发现

以图形方式呈现各种新兴物理参数对速度、感应磁场、压力上升、电流密度和温度曲线的影响。据观察，纤毛长度参数支持速度和电流密度分布，而哈特曼数和魏森伯格数则相反。新兴参数对流线的良好影响也被认为是有希望的。

 原创性/价值

该研究提供了在感应磁场和通过不对称锥形通道的对流传热影响下纤毛驱动的卡罗流体感应磁流体动力学流动的新颖方面。