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通过有限元方法对涉及霍尔电流和离子滑移电流的加热旋转锥上的三维普朗特混合纳米材料进行建模。

Modeling of three dimensional Prandtl hybrid nano-material over a heated rotating cone involving hall and ion slip currents via finite element procedure.

作者信息

Sohail Muhammad, Nazir Umar, El-Zahar Essam R, Park Choonkil, Mukdasai Kanit, Iqbal Amjad

机构信息

Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, 64200, Pakistan.

Department of Applied Mathematics and Statistics, Institute of Space Technology, P.O. Box 2750, Islamabad, 44000, Pakistan.

出版信息

Sci Rep. 2022 Jul 16;12(1):12206. doi: 10.1038/s41598-022-16555-y.

Abstract

Flow in a rotating cone for magnetized Prandtl fluid model is inspected in this investigation. The momentum equation of Prandtl model is derived under the consideration of Hall and ion slip effects and heat transport phenomenon is considered with Joule heating and viscous dissipation effects. The model of Hamilton Crosser and Yamada Ota are considered for the empirical relations of nanofluid mixture. The flow presenting expression of Prandtl fluid model with thermal transport is modeled under boundary layer approximation in the form of partial differential equations (PDEs). The derived PDEs have been converted into set of coupled nonlinear ordinary differential equations (ODEs) by engaging an appropriate scaling group transformation and these converted nonlinear set of ODEs have been tackled numerically via finite element scheme (FES). Impact of different emerging parameters has been displayed graphically and the physics behind the observed phenomena is explained in detail. The convergence of FES is established by carrying the grid independent survey. From the performed investigation, it is recorded that the parameters appear due to Hall and Ion slip currents enhance the fluid velocity but the inverse behavior is recorded for temperature profile.

摘要

本研究考察了旋转圆锥中磁化普朗特流体模型的流动。在考虑霍尔效应和离子滑移效应的情况下推导了普朗特模型的动量方程,并考虑了焦耳热和粘性耗散效应下的热传输现象。对于纳米流体混合物的经验关系,考虑了汉密尔顿·克罗斯纳和山田·奥田的模型。在边界层近似下,以偏微分方程(PDEs)的形式对具有热传输的普朗特流体模型的流动呈现表达式进行建模。通过采用适当的标度群变换,将导出的偏微分方程转化为一组耦合的非线性常微分方程(ODEs),并通过有限元格式(FES)对这些转化后的非线性常微分方程组进行了数值求解。以图形方式展示了不同新出现参数的影响,并详细解释了观察到的现象背后的物理原理。通过进行网格无关性研究确定了有限元格式的收敛性。从所进行的研究中记录到,由于霍尔电流和离子滑移电流出现的参数会提高流体速度,但温度分布呈现相反的行为。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ba0d/9288551/b5e8d82ee914/41598_2022_16555_Fig1_HTML.jpg

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