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New classes of periodic and non-periodic exact solutions for Newtonian and non-Newtonian fluid flows
International Journal of Engineering Science ( IF 6.6 ) Pub Date : 2022-09-02 , DOI: 10.1016/j.ijengsci.2022.103740
Subin P. Joseph

Two different families of planar exact solutions for second grade fluid flows are derived in this paper. Exact solutions for Newtonian fluid flows are derived as particular case when normal stress moduli vanish. The novelty of the solutions is that they are obtained by assuming the stream functions as a finite sum of functions with different arguments. An important property of the derived solutions is that solutions in a given family are all superposable flows. The first family of solutions can be considered as a generalization of rectangular array of Taylor vortices as these classical solutions are special cases of the derived exact solutions. A subfamily of spatially periodic exact solutions for both Newtonian and non-Newtonian fluid flows are also derived. The complex structures of the two dimensional vortices are illustrated in several cases.



中文翻译:

牛顿和非牛顿流体流动的周期和非周期精确解的新类别

本文推导了二级流体流动的两个不同系列的平面精确解。当正应力模量消失时,牛顿流体流动的精确解是作为特例推导出来的。解决方案的新颖之处在于它们是通过将流函数假设为具有不同参数的函数的有限和来获得的。派生解的一个重要特性是给定族中的解都是可叠加的流。第一类解可以被认为是泰勒涡旋矩形阵列的推广,因为这些经典解是导出的精确解的特例。还推导出了牛顿和非牛顿流体流动的空间周期精确解的子族。二维涡旋的复杂结构在几个案例中得到了说明。

更新日期:2022-09-02
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