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An exact solution for tube and slit flow of a FENE-P fluid

机译:FENE-P流体管和狭缝流动的精确解决方案

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A fully analytical solution is derived for rectilinear flow of a nonlinear viscoelastic fluid obeying the constitutive FENE-P model, under fully developed conditions. Both the plane case (slit flow) and the axisymmetric case (tube flow) are considered. Physical interpretation of the results is provided. The normal stress profile is found to vary in a non-monotone way with the dimensionless parameter characterizing viscoelasticity, the Deborah number (De). For Deborah numbers below a critical value (dependent on the extensibility parameter of the model L-2) the normal stress raises with elasticity, but this trend is reversed for values above the critical one. This effect is due to the competing influence of elasticity and shear thinning. Also, as a consequence of shear thinning the velocity profile becomes flatter as De increases and L-2 decreases, leading to higher flow rates for the same pressure drop. [References: 17]
机译:在充分发展的条件下,遵循本构FENE-P模型,得出了非线性粘弹性流体的直线流动的完全解析解。同时考虑了平面情况(缝流)和轴对称情况(管流)。提供了结果的物理解释。发现法向应力分布以非单调方式变化,其特征在于表征粘弹性的无量纲参数Deborah数(De)。对于低于临界值的Deborah数(取决于模型L-2的可扩展性参数),法向应力随弹性而增大,但对于高于临界值的值,此趋势将相反。这种效果是由于弹性和剪切稀化的竞争影响所致。同样,由于剪切变稀的结果,速度曲线会随着De的增加和L-2的减小而变得更平坦,从而导致相同压降下的流速更高。 [参考:17]

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