Exact Solution for Pressure Driven Flow of Two Immiscible Phan-Thien-Tanner Fluids in a Pipe

DOI: 10.4236/ojfd.2018.84024   PDF   HTML   XML   711 Downloads   1,082 Views   Citations


This paper provides the exact solutions for the fully developed two layer pressure driven flows of incompressible Phan-Thien-Tanner fluids in a horizontal cylindrical pipe. Exact equations are formulated and solved for important kinematic properties, such as, velocity profiles, normal and shear stresses, total volume fluxes through a circular cross-section and average velocities. Graphical results are provided and discussed for the different flow parameters. A comparison of Upper Convected Maxwell (UCM), Linear Phan-Thien-Tanner (LPTT) and Exponential Phan-Thien-Tanner (EPTT) shows that UCM is a low viscosity fluid as compared to LPTT, and EPTT and LPTT is lighter than EPTT.

Share and Cite:

Siddiqui, A. , Walait, A. , Allison, T. and Haroon, T. (2018) Exact Solution for Pressure Driven Flow of Two Immiscible Phan-Thien-Tanner Fluids in a Pipe. Open Journal of Fluid Dynamics, 8, 378-391. doi: 10.4236/ojfd.2018.84024.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Bird, R.B., Armstrong, R.C. and Hassager, O. (1987) Dynamics of Polymeric Liquids. In: Vol. 1 Fluid Mechanics, 2nd Edition, John Wiley and Sons, Inc., Hoboken, New Jersey.
[2] Phan-Thien, N. and Tanner, R.I. (1977) A New Constitutive Equation Derived from Network Theory. Journal of Non-Newtonian Fluid Mechanics, 2, 353-365.
[3] Tanner, R.I. (2000) Engineering Rheology. Clarendon Press, Oxford.
[4] Oliveira, P.J. and Pinho, F.T. (1999) Analytical Solution for the Fully-Developed Channel and Pipe Flow of Phan-Thien-Tanner Fluids. Journal of Fluid Mechanics, 387, 271-280.
[5] Pinho, F.T. and Oliveira, P.J. (2000) Analysis of Forced Convection in Pipes and Channels with Simplified Phan-Thien-Tanner Fluid. International Journal of Heat and Mass Transfer, 43, 2273-2287. https://doi.org/10.1016/S0017-9310(99)00303-8
[6] Pinho, F.T. and Oliveria, P.J. (2000) Axial Annular Flow of a Nonlinear Viscoelastic Fluid: An Analytical Solution. Journal of Non-Newtonian Fluid Mechanics, 93, 325-337.
[7] Alves, M.A., Pinho, F.T. and Oliveira, P.J. (2001) Study of Steady Pipe and Channel Flows of Single-Mode Phan-Thien-Tanner Fluid. Journal of Non-Newtonian Fluid Mechanics, 101, 55-76.
[8] Letelier, M.F. and Siginer, D.A. (2005) On the Fully Developed Tube Flow of a Class of Non-Linear Viscoelastic Fluids. International Journal of Non-Linear Mechanics, 40, 485-493.
[9] Siddiqui, A.M., Mahmood, R. and Ghori, Q.K. (2006) Some Exact Solutions for the Thin Film Flow of a PTT Fluid. Physics Letters A, 356, 353-356.
[10] Packham, B.A. and Shall, R. (1971) Stratified Laminar Flow of Two Immiscible Fluids. Mathematical Proceedings of the Cambridge Philosophical Society, 69, 443-448.
[11] Brauner, N. (1991) Two-Phase Liquid-Liquid Annular Flow. International Journal of Multiphase Flow, 17, 59-76. https://doi.org/10.1016/0301-9322(91)90070-J
[12] Kapur, J.N. and Shukla, J.B. (1964) The Flow of Incompressible Immiscible Fluids between Two Plates. Applied Scientific Research, Section A, 13, 55-60.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.