Study of steady pipe and channel flows of a single-mode Phan-Thien-Tanner fluid

Analytical solutions are derived for the steady state channel and pipe flows of viscoelastic fluids obeying the complete single-mode Phan-Thien-Tanner (PTT) constitutive equation with a linear stress coefficient in the absence of a solvent viscosity contribution. The results include the profiles of all relevant stresses, the axial velocity and the viscosity across the gap. The three material functions of the single-mode PTT model in steady Couette flow are also given and it is shown that the conditions of the maximum point in the shear stress versus shear rate curve are related to the conditions for existence of steady state solutions in the channel and pipe flows. The range of model parameters for which a classical steady solution exists is established. (C) 2001 Elsevier Science B.V. All rights reserved.