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

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 l...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-01, Vol.7 (1), p.81
Main Authors: Siddiqui, Abdul Majeed, Zeb, Muhammad, Haroon, Tahira, Azim, Qurat-ul-Ain
Format: Article
Language:English
Subjects:
Boundary conditions
Computational fluid dynamics
exact solution
Exact solutions
Flow velocity
Fluid flow
Geometry
Heat conductivity
Heat transfer
heat transfer flow
Incompressible flow
mathematical modeling
Mathematics
Newtonian fluids
Non-Newtonian fluids
ordinary differential equations
Pipes
PTT fluid
Rheology
Shear stress
Temperature profiles
Velocity
Viscoelasticity
Viscosity
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7010081