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首页> 外文期刊>Mathematical Problems in Engineering >Variational Approach for Resolving the Flow of Generalized Newtonian Fluids in Circular Pipes and Plane Slits
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Variational Approach for Resolving the Flow of Generalized Newtonian Fluids in Circular Pipes and Plane Slits

机译：求解圆形管和平面缝中广义牛顿流体流动的变分方法

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摘要

We use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile, and volumetric flow rate.
机译：我们使用通用和通用变分方法来获得广义牛顿流体通过圆管和平面缝的流动的解。新方法不是基于使用Euler-Lagrange变分原理的，因此它完全独立于我们以前基于该原理的方法。取而代之的是，该方法采用了一种非常通用和通用的优化方法，尽管这不是唯一可能的理论上的证明，但可以通过Dirichlet原理对其进行证明。使用九种类型的流体从新方法获得的结果在一定限制内与传统流体力学方法以及以前的变分方法获得的结果完全一致。除了本身是解决圆形管道和平面狭缝中流场的有用方法外，新的变分方法还为旧的变分方法以及一般使用变分原理来解决流体流动提供了更多支持。广义牛顿流体并获得流场的所有量，包括剪切应力，局部粘度，应变率，速度分布和体积流率。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第12期|714136.1-714136.10|共10页
  • 作者

    Sochi Taha;

  • 作者单位

    UCL, Dept Phys & Astron, London WC1E 6BT, England.;

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