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

Gbeminiyi Sobamowo; Akinbowale Akinshilo; Ahmed Yinusa; Oluwatoyin Adedibu

doi:doi:10.11648/j.se.20180603.11

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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

Gbeminiyi Sobamowo, Akinbowale Akinshilo, Ahmed Yinusa, Oluwatoyin Adedibu

Published in Software Engineering (Volume 6, Issue 3)

Received: 8 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.

Published in	Software Engineering (Volume 6, Issue 3)
DOI	10.11648/j.se.20180603.11
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), 2018. 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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[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.
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[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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APA Style

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://article.sciencepublishinggroup.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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Author Information

Gbeminiyi Sobamowo

Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Akinbowale Akinshilo

Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Ahmed Yinusa

Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Oluwatoyin Adedibu

Department of Electrical Engineering, the Polytechnic, Ibadan, Nigeria

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APA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

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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