The main aim of this research work is to establish, under fully developed conditions, an analytical solution for viscoelastic fluids flow obeying the constitutive Phan–Thien–Tanner (PTT) and Finely Extensible Nonlinear Elastic-Peterlin (FENE-P) models. In fact, a unified formulation for laminar, stationary and fully developed flow in the cases of circular and flat ducts geometries is obtained for velocity profile involving PTT and FENE-P models. In this investigation, the effect of pressure gradient on velocity profile, shear stress, shear rate and shear viscosity is explored. Effects of pressure gradient and Weissenberg number on normal stress are also studied and discussed.

这项研究工作的主要目的是在完全发达的条件下建立粘弹性流体流动的解析解，并遵循本构潘-坦-坦纳（PTT）模型和精细可扩展非线性弹性-彼得林（FENE-P）模型。实际上，对于涉及PTT和FENE-P模型的速度剖面，在圆形和扁平管道几何形状的情况下，获得了层流，固定流和充分展开流的统一公式。在这项研究中，探讨了压力梯度对速度分布，剪切应力，剪切速率和剪切粘度的影响。还研究和讨论了压力梯度和魏森伯格数对正应力的影响。