Moatimid Galal M, Mohamed Mona A A, Elagamy Khaled
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
Sci Rep. 2022 Jul 4;12(1):11275. doi: 10.1038/s41598-022-15094-w.
The present study highlights the flow of an incompressible nanofluid following the non-Newtonian flow. The non-Newtonian fluid behavior is characterized by the Casson prototype. The flow occupies the conical gap between the rotating/stationary surfaces of the cone and the horizontal disc. Heat and mass transfer is also considered. The novelty of the proposed mathematical model is supplemented with the impacts of a uniform magnetic field imposed vertically upon the flow together with Ohmic dissipation and chemical reactions. The constitutive equations of the Casson fluid have been interpreted along with the cylindrical coordinates. The governing partial differential equations of momentum, energy, and concentration are converted into a set of nonlinear ordinary differential equations via appropriate similarity transformations. This scheme leads to a set of coupled nonlinear ordinary equations concerning velocity, temperature, and nanoparticles concentration distributions. These equations are analytically solved by means of the Homotopy perturbation method (HPM). The theoretical findings are presented in both graphical and tabular forms. The main objective of this study is to discuss the effects of the rotations of both cone and disc and the effects of the other parameters in the two cases of rotation alternatively. Additionally, the effect of the angle between the cone and the disk is one of our interesting points because of the importance of its effect in some engineering industry applications. The rotation parameters are found to have reduction effects on both the temperature and the radial velocity of the fluid, while they have an enhancing effect on the azimuthal velocity. The effects of other parameters with these rotations are found to be qualitatively the same as some earlier published studies. To validate the current mathematical model, a comparison with the previous scientific reports is made.
本研究着重探讨了遵循非牛顿流的不可压缩纳米流体的流动情况。非牛顿流体行为以卡森模型为特征。该流动占据了圆锥体与水平圆盘的旋转/静止表面之间的锥形间隙。同时还考虑了传热和传质。所提出的数学模型的新颖之处在于补充了垂直施加于流动的均匀磁场的影响以及欧姆耗散和化学反应。卡森流体的本构方程已结合柱坐标进行了解释。通过适当的相似变换，将动量、能量和浓度的控制偏微分方程转换为一组非线性常微分方程。该方案得到了一组关于速度、温度和纳米颗粒浓度分布的耦合非线性常微分方程。这些方程通过同伦摄动法（HPM）进行解析求解。理论结果以图形和表格形式呈现。本研究的主要目的是交替讨论在两种旋转情况下圆锥体和圆盘的旋转影响以及其他参数的影响。此外，圆锥体与圆盘之间夹角的影响是我们感兴趣的点之一，因为其在一些工程行业应用中的影响很重要。发现旋转参数对流体的温度和径向速度都有降低作用，而对方位角速度有增强作用。发现这些旋转情况下其他参数的影响在定性上与一些早期发表的研究相同。为了验证当前的数学模型，与先前的科学报告进行了比较。
