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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >A series solution of the boundary value problem arising in the application of fluid mechanics
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A series solution of the boundary value problem arising in the application of fluid mechanics

机译：流体力学应用中产生的边值问题的级数解

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Purpose - This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM). Design/methodology/approach - The governing Navier-Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs. Findings - It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that they component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number. Originality/value - To the best of the author's knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.
机译：目的-本文旨在利用同伦扰动法（HPM）研究多孔通道中二级流体的二维稳态磁流体动力流。设计/方法/方法-通过适当的相似度转换，将控制流的Navier-Stokes方程简化为三阶非线性常微分方程。使用HPM获得所得微分方程的解析解。 Mathematica软件用于可视化流动行为。通过适当的曲线图分析了各种参数对速度场的影响。发现-发现当横向变量的范围从0到0.2时，速度的x分量随Hartman数的增加而增加，并且当横向变量的值在0.2到0.5之间时观察到相反的行为。注意，它们的速度分量随横向变量的增加而迅速增加。速度的y分量随哈特曼数M的增加而略有增加。雷诺数R对速度的x和y分量的影响与哈特曼数对速度的x和y分量的影响完全相反。速度和参数对速度的x和y分量的影响与雷诺数相似。原创性/价值-据作者所知，没有人尝试过使用HPM在多孔通道中二维地磁流体流体的二维稳态磁流体动力流动。

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