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Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation

Received: 08 July 2018    Accepted: 19 July 2018    Published: 21 August 2018
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Abstract

The various industrial, biological and engineering applications of third grade fluid have in recent times propel continuous research on the flow dynamics and heat transfer characteristics of the non-Newtonian fluid. In this work, effects of nonlinear hydrodynamic slip and temperature-jump conditions on pipe flow and heat transfer of third grade fluid with nonlinear temperature-dependent viscosities and internal heat generation are presented. The developed nonlinear governing equations are solved using regular perturbation method. In order to verify the accuracy of the solution methodology, the results of the approximate analytical solution are compared with the results of the numerical solutions using Runge-Kutta fourth-order coupled with shooting method. Good agreements are obtained between the analytical and the numerical results. Thereafter, the obtained approximate analytical solutions are used to investigate the effects of variable viscosity, non-Newtonian parameter, viscous dissipation and pressure gradient on the flow and heat transfer characteristics of the third-grade fluid in the pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. The present results can be used to advance the analysis and study of the behaviour of third grade fluid flow and steady state heat transfer processes such as found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.

DOI 10.11648/j.se.20180603.11
Published in Software Engineering (Volume 6, Issue 3, September 2018)
Page(s) 69-88
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Third-Grade Fluid, Pipe Flow, Non-Linear Viscosities, Non-Linear Internal Heat Generation, Nonlinear Boundary Conditions

References
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[2] S. N. Majhi and V. R. Nair Flow of a third grade fluid over a sternosed tubes, Indian national science academy, volume 60 (3) (1994), 535.
[3] M. Massoudi and I. Christie Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe, International journal of nonlinear mechanics, volume 30 (1995) 687.
[4] M. Yurusoy M. and Pakdemirli. Approximate analytical solution for the flow of a third grade fluid in a pipe, International journal of nonlinear mechanics, volume 37 (2002). 187-195.
[5] K. Vajrevelu, J. r. Cannon, D. Rollins and J. Leto on solutions of some non-Linear differential equations arising in third grade fluid flows, International journal of engineering science, volume 40 (2002), 1791.
[6] T. Hayat, S. Nadeem, S. Asghar, and A. M. Siddiqui. Fluctuating flow of a third order fluid on a porous plate in a rotating medium, International journal of nonlinear mechanics, volume 36 (2002), 901-916.
[7] Y. Muhammet. Similarity solutions to boundary layer equations for third grade non-Newtonian fluid in special channel coordinate system, Journal of theoretical and applied mechanics, volume 41 (4) (2003) 775-787.
[8] M. Yurusoy. Flow of a third grade fluid between concentric cylinder, Journal of mathematical and computational applications, volume 9 (1) (2004), 11-12.
[9] M. Pakdemirli and B. S. Yilbas Entropy generation for a pipe flow of a third grade fluid with Vogel model viscosity, International journal of nonlinear mechanics, volume 43 (3) (2006). 432-437.
[10] M. Sajid, R. Mahmood and T. Hayat (2008) Finite element solution for flow of a third grade fluid past a horizontal porous plate with partial slip, International journal for computer and mathematics with applications, volume 56, 1236.
[11] R. Elahi, T. Hayat, F. M. Mahomed and S. Asghar. Effects of slip on the nonlinear flow of the third grade fluid, Journal of the nonlinear analysis, volume 11, (2010) 139-146.
[12] O. J. Jayeoba, and S. S. Okoya. Approximate analytical solutions for pipe flow of a third grade fluid with variable model of viscosities and heat generation/absorption, Journal of the Nigerian mathematical society, volume 31 (2012), 207-227.
[13] B. Y. Ogunmola, A. T. Akinshilo and M. G. Sobamowo. Perturbation Solutions for Hagen–Poiseuille Flow and Heat transfer of Third Grade Fluid with Temperature-Dependent Viscosities and Internal Heat Generation. Article in Press, International Journal of Engineering Mathematics, Hindawi, 2016.
[14] S. S. Abbasbandy, T. Hayat, R. Ellahi and S. Asghar. Numerical results of a flow in third grade fluid between two porous walls, Verlagderzeitschrift fur Naturforschurg, volume 0932 (2008), 51.
[15] I. Nayak, A. K. Nayak and J. Padhy Numerical solutions for the flow and heat transfer of a third grade fluid past a porous vertical plate, Journal for advanced studies theoretical physics, volume 6, (2012), 615.
[16] Y. M. Aiyesimi, G. T. Okedayo and O. W. Lawal. Unsteady magneto hydrodynamic (MHD) thin film flow of a third grade fluid with heat transfer and no slip boundary condition down an inclined plane, International journal of physical sciences, volume 8 (19) (2013), 946.
[17] A. W. Ogunsola and B. A. Peter. Effect of variable viscosity on third grade fluid flow over a radiative surface with Arrhenius reaction, International journal of pure and applied sciences and technology, Volume 22 (1) (2014), 1-2.
[18] M. Yurusoy, M. Pakdemirli and B. S. Yilbas. Perturbation solution for third grade fluid flowing between parallel plates, Proceedings of the institute of Mechanical Engineering, volume 222 Part C, (2007). 653.
[19] M. G. Sobamowo, L. O. Jayesimi and M. A. Waheed. Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method. Karbala International Journal of Modern Science. volume 4 (2018), 107-118.
[20] M. G. Sobamowo, A. T. Akinshilo and A. A. Yinusa. Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip, and Temperature Jump Conditions. Modeling and Simulation in Engineering. volume 2018, Article ID 7364634, 18 pages.
[21] M. G. Sobamowo, L. O. Jayesimi and M. A. Waheed. Axisymmetric Magnetohydrodynamic Squeezing flow of nanofluid in a porous medium under the influence of slip boundary conditions. Transport Phenomena in nano and micro Scales. volume 6 (2) (2018), 122-132.
[22] M. G. Sobamowo and A. T. Akinshilo. Analysis of flow, heat transfer and entropy generation in a pipe conveying fourth grade fluid with temperature-dependent viscosities and internal heat generation. Journal of Molecular Liquids, volume 241 (2018), 188-198.
[23] M. G. Sobamowo. Singular perturbation and differential transform methods to two-dimensional flow of nanofluid in a porous channel with expanding/contracting walls subjected to a uniform transverse magnetic field. Thermal Science and Engineering Progress. volume 4 (2017), 71-84.
[24] M. G. Sobamowo. On the analysis of laminar flow of viscous fluid through a porous channel with suction/injection at slowly expanding or contracting walls. Journal of Computational Applied Mechanics. volume 48 (2) (2017), 319-330. Publication of Tehran, University.
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[26] M. G. Sobamowo, L. O. Jayesimi and M. A. Waheed (2017). On the Squeezing flow of nanofluid through a porous medium with slip boundary and magnetic field: A comparative study of three approximate analytical methods. Global Journal of Engineering, volume 17 (6), 61-76.
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Author Information
  • Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria

  • Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria

  • Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria

  • Department of Electrical Engineering, the Polytechnic, Ibadan, Nigeria

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    Gbeminiyi Sobamowo, Akinbowale Akinshilo, Ahmed Yinusa, Oluwatoyin Adedibu. (2018). Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation. Software Engineering, 6(3), 69-88. https://doi.org/10.11648/j.se.20180603.11

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    ACS Style

    Gbeminiyi Sobamowo; Akinbowale Akinshilo; Ahmed Yinusa; Oluwatoyin Adedibu. Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation. Softw. Eng. 2018, 6(3), 69-88. doi: 10.11648/j.se.20180603.11

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    AMA Style

    Gbeminiyi Sobamowo, Akinbowale Akinshilo, Ahmed Yinusa, Oluwatoyin Adedibu. Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation. Softw Eng. 2018;6(3):69-88. doi: 10.11648/j.se.20180603.11

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  • @article{10.11648/j.se.20180603.11,
      author = {Gbeminiyi Sobamowo and Akinbowale Akinshilo and Ahmed Yinusa and Oluwatoyin Adedibu},
      title = {Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation},
      journal = {Software Engineering},
      volume = {6},
      number = {3},
      pages = {69-88},
      doi = {10.11648/j.se.20180603.11},
      url = {https://doi.org/10.11648/j.se.20180603.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.se.20180603.11},
      abstract = {The various industrial, biological and engineering applications of third grade fluid have in recent times propel continuous research on the flow dynamics and heat transfer characteristics of the non-Newtonian fluid. In this work, effects of nonlinear hydrodynamic slip and temperature-jump conditions on pipe flow and heat transfer of third grade fluid with nonlinear temperature-dependent viscosities and internal heat generation are presented. The developed nonlinear governing equations are solved using regular perturbation method. In order to verify the accuracy of the solution methodology, the results of the approximate analytical solution are compared with the results of the numerical solutions using Runge-Kutta fourth-order coupled with shooting method. Good agreements are obtained between the analytical and the numerical results. Thereafter, the obtained approximate analytical solutions are used to investigate the effects of variable viscosity, non-Newtonian parameter, viscous dissipation and pressure gradient on the flow and heat transfer characteristics of the third-grade fluid in the pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. The present results can be used to advance the analysis and study of the behaviour of third grade fluid flow and steady state heat transfer processes such as found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation
    AU  - Gbeminiyi Sobamowo
    AU  - Akinbowale Akinshilo
    AU  - Ahmed Yinusa
    AU  - Oluwatoyin Adedibu
    Y1  - 2018/08/21
    PY  - 2018
    N1  - https://doi.org/10.11648/j.se.20180603.11
    DO  - 10.11648/j.se.20180603.11
    T2  - Software Engineering
    JF  - Software Engineering
    JO  - Software Engineering
    SP  - 69
    EP  - 88
    PB  - Science Publishing Group
    SN  - 2376-8037
    UR  - https://doi.org/10.11648/j.se.20180603.11
    AB  - The various industrial, biological and engineering applications of third grade fluid have in recent times propel continuous research on the flow dynamics and heat transfer characteristics of the non-Newtonian fluid. In this work, effects of nonlinear hydrodynamic slip and temperature-jump conditions on pipe flow and heat transfer of third grade fluid with nonlinear temperature-dependent viscosities and internal heat generation are presented. The developed nonlinear governing equations are solved using regular perturbation method. In order to verify the accuracy of the solution methodology, the results of the approximate analytical solution are compared with the results of the numerical solutions using Runge-Kutta fourth-order coupled with shooting method. Good agreements are obtained between the analytical and the numerical results. Thereafter, the obtained approximate analytical solutions are used to investigate the effects of variable viscosity, non-Newtonian parameter, viscous dissipation and pressure gradient on the flow and heat transfer characteristics of the third-grade fluid in the pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. The present results can be used to advance the analysis and study of the behaviour of third grade fluid flow and steady state heat transfer processes such as found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.
    VL  - 6
    IS  - 3
    ER  - 

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