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首页> 外文期刊>International Journal of Engineering Science >An exact solution of the governing equation of a fluid of second-grade for three-dimensional vortex flow
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An exact solution of the governing equation of a fluid of second-grade for three-dimensional vortex flow

机译：三维涡流二级流体控制方程的精确解

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摘要

Three-dimensional vortex flow of a fluid of second-grade, for which the velocity field is in the form of υ_r =f(r), υ_θ - g(r), υ_z = zh(r), where r, θ, z are cylindrical polar coordinates, is considered and an exact solution of the governing equation is given. It is an important fact that for this type of flow of a Newtonian fluid, the axial gradient of radial distribution of pressure does not exist and this is unrealistic in many problems of rotational flow. It is found that the axial gradient of radial distribution of pressure exists for this type of flow of a fluid of second grade. It is emphasized that there are exact solutions for the velocity field considered of the governing equation for an Oldroyd type fluid and a Maxwell type one. For some special cases of the velocity field closed form solution of the governing equation are investigated.
机译：二级流体的三维涡流，其速度场的形式为υ_r= f（r），υ_θ-g（r），υ_z= zh（r），其中r，θ，z考虑圆柱极坐标，并给出控制方程的精确解。一个重要的事实是，对于这种牛顿流体流，不存在径向径向分布的轴向梯度，这在许多旋转流问题中是不现实的。已经发现，对于第二类流体的这种类型的流动存在压力的径向分布的轴向梯度。要强调的是，对于Oldroyd型流体和Maxwell型流体的控制方程，存在针对速度方程的精确解。对于某些特殊情况，研究了控制方程的速度场闭式解。

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