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Mathematics 2019, 7(1), 81; https://doi.org/10.3390/math7010081

Exact Solution for the Heat Transfer of Two Immiscible PTT Fluids Flowing in Concentric Layers through a Pipe

1
Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403, USA
2
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock 43600, Pakistan
3
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Defence Road, Lahore 54000, Pakistan
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 7 January 2019 / Accepted: 8 January 2019 / Published: 14 January 2019
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Abstract

This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer. View Full-Text
Keywords: PTT fluid; heat transfer flow; mathematical modeling; ordinary differential equations; exact solution PTT fluid; heat transfer flow; mathematical modeling; ordinary differential equations; exact solution
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Siddiqui, A.M.; Zeb, M.; Haroon, T.; Azim, Q.-U.-A. Exact Solution for the Heat Transfer of Two Immiscible PTT Fluids Flowing in Concentric Layers through a Pipe. Mathematics 2019, 7, 81.

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