ABSTRACT 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.
Cite this paper
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.
 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.
 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. https://doi.org/10.1016/0377-0257(77)80021-9
 Tanner, R.I. (2000) Engineering Rheology. Clarendon Press, Oxford.
 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. https://doi.org/10.1017/S002211209900453X
 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
 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.
 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. https://doi.org/10.1016/S0377-0257(01)00159-8
 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. https://doi.org/10.1016/j.ijnonlinmec.2004.07.009
 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. https://doi.org/10.1016/j.physleta.2006.03.071
 Packham, B.A. and Shall, R. (1971) Stratified Laminar Flow of Two Immiscible Fluids. Mathematical Proceedings of the Cambridge Philosophical Society, 69, 443-448. https://doi.org/10.1017/S0305004100046880
 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
 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.