YANG Xu, LIANG Yingjie, SUN Hongguang, CHEN Wen. A Study on the Constitutive Relation and the Flow of Spatial Fractional NonNewtonian Fluid in Circular Pipes[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1213-1226. doi: 10.21656/1000-0887.390153
Citation: YANG Xu, LIANG Yingjie, SUN Hongguang, CHEN Wen. A Study on the Constitutive Relation and the Flow of Spatial Fractional NonNewtonian Fluid in Circular Pipes[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1213-1226. doi: 10.21656/1000-0887.390153

A Study on the Constitutive Relation and the Flow of Spatial Fractional NonNewtonian Fluid in Circular Pipes

doi: 10.21656/1000-0887.390153
Funds:  The National Science Fund for Distinguished Young Scholars of China(11125208);The National Natural Science Foundation of China(11572112; 41628202; 11528205)
  • Received Date: 2018-05-25
  • Rev Recd Date: 2018-09-26
  • Publish Date: 2018-11-01
  • A thorough understanding of the flow behavior of non-Newtonian fluid is the first step for analyzing, predicting and controlling of pipe flow. Experiments indicate that non-Newtonian fluid is historically dependent on the procedure of shear flow. The constitutive model for fractional non-Newtonian fluid was established via the spatial fractional calculus approach. The velocity profile, the flux, the mean velocity, the pressure drop and the mean Reynolds number of the proposed model were also derived. In addition, a novel criterion for the flow state of fractional non-Newtonian fluid was proposed. The results show that, the shear stress of the non-Newtonian fluid can be described by the axial velocity distribution. For the fractional non-Newtonian fluid without yield shear stress, the larger the fractional order is, the more uniform the velocity distribution will be and the stronger the memory of the fluid will be. The magnitude of the fractional order reflects the memory of the fluid with respect to the global space. For the fractional non-Newtonian fluid with yield shear stress, the larger the fractional order is, the more uniform the velocity distribution in the velocity gradient region will be, and the smaller of the velocity in the core region will be. In this case, the magnitude of the fractional order reflects the memory of the fluid with respect to the local region. This study offers a new method for the modeling of memory characteristics of non-Newtonian fluid.
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