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

A. M. Siddiqui; A. Walait; T. Allison; T. Haroon

doi:10.4236/ojfd.2018.84024

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Open Journal of Fluid Dynamics > Vol.8 No.4, December 2018

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

A. M. Siddiqui¹, A. Walait², T. Allison¹, T. Haroon¹

¹Deparment of Mathematics, Pennsylvania State University, York Campus, York, PA, USA.
²Department of Mathematics, Riphah International University Islamabad Campus, Pakistan.

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

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.

Keywords

Exact Solution, Two-Layer Flow, PTT Fluids

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.

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