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Adomian decomposition method simulation of von Kármán swrling bioconvection nanofluid flow

生物对流纳米流体流动的von Kármán 分解法模拟

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Abstract

The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk. It is known that the deformation of the disk is along the radial direction. In addition to that Stefan blowing is considered. The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit. The primitive mass conservation equation, radial, tangential and axial momentum, heat, nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall (disk surface) and free stream boundary conditions. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system. The emerging 11th order system features an extensive range of dimensionless flow parameters, i.e., disk stretching rate, Brownian motion, thermophoresis, bioconvection Lewis number, unsteadiness parameter, ordinary Lewis number, Prandtl number, mass convective Biot number, Péclet number and Stefan blowing parameter. Solutions of the system are obtained with developed semi-analytical technique, i.e., Adomian decomposition method. Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.

摘要

本研究分析了纳米流体从旋转圆盘中流过时的三维黏性时变旋流生物对流。圆盘的变形沿径向 进行,同时考虑Stefan 吹气,通过对Buongiorno 纳米流体模型的分析,发现布朗运动和热泳动在纳 米尺度上起着主导作用。在适当的壁面(圆盘表面)和自由流边界条件下,建立了原始质量守恒方程、 径向动量、切向动量和轴向动量、热量、纳米粒子浓度和微生物密度函数。将这个高度非线性、强耦 合的非定常偏微分方程系统用经典的von Kármán 和其他变换进行归一化,从而将边值问题转化为一 个常微分系统。产生的11 阶系统包括多种无量纲流动参数,即生物对流Lewis 数、不稳定参数、普 通Lewis 数、Prandtl 数、质量对流Biot 数、Peclet 数、Stefan 吹气参数。利用先进的半解析方法得到 了系统的解,即Adomian 分解法。利用Runge-Kutta 拍摄技术计算的早期文献对上述问题进行了验证。

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Authors and Affiliations

  1. Department of Mathematics, Vaagdevi College of Engineering, Warangal, Telangana, India

    M D Shamshuddin

  2. Department of Mathematics, Siksha ‘O’ Anusandhan Deemed to be University, Khandagiri, Bhubaneswar, Odisha, India

    S R Mishra

  3. Department of Aeronautical and Mechanical Engineering, University of Salford, Manchester, England, UK

    O Anwar Beg & A Kadir

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  1. M D Shamshuddin
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Correspondence to M D Shamshuddin.

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Shamshuddin, M.D., Mishra, S.R., Anwar Beg, O. et al. Adomian decomposition method simulation of von Kármán swrling bioconvection nanofluid flow. J. Cent. South Univ. 26, 2797–2813 (2019). https://doi.org/10.1007/s11771-019-4214-4

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