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

Author

Listed:
  • Abdul Majeed Siddiqui

    (Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403, USA)

  • Muhammad Zeb

    (Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock 43600, Pakistan)

  • Tahira Haroon

    (Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403, USA)

  • Qurat-ul-Ain Azim

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Defence Road, Lahore 54000, Pakistan)

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.

Suggested Citation

  • Abdul Majeed Siddiqui & Muhammad Zeb & Tahira Haroon & Qurat-ul-Ain Azim, 2019. "Exact Solution for the Heat Transfer of Two Immiscible PTT Fluids Flowing in Concentric Layers through a Pipe," Mathematics, MDPI, vol. 7(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:81-:d:197548
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    Cited by:

    1. Muhammad Sulaiman & Naveed Ahmad Khan & Fahad Sameer Alshammari & Ghaylen Laouini, 2023. "Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks," Mathematics, MDPI, vol. 11(5), pages 1-19, February.

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