Axisymmetric Flow Through a Cylinder with Porous Medium

Muhammad Umar Farooq; Abdul Rehman; Naveed Sheikh; Manzoor Iqbal

doi:doi:10.11648/j.ijssam.20200503.12

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Axisymmetric Flow Through a Cylinder with Porous Medium

Muhammad Umar Farooq, Abdul Rehman, Naveed Sheikh, Manzoor Iqbal

Published in International Journal of Systems Science and Applied Mathematics (Volume 5, Issue 3)

Received: 2 October 2020 Accepted: 20 October 2020 Published: 27 October 2020

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Abstract

The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.ijssam.20200503.12
Page(s)	32-35
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), 2020. Published by Science Publishing Group

Keywords

Moving Cylinder, Porous Medium, Runge-Kutta 4^th Order Shooting Method

References

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[3]	W. A. Khan, I. Pop, Boundary layer flow past a wedge moving in a nanofluid. Mathematical Problems in Engineering, (2013).
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[10]	S. Nadeem, Abdul Rehman, Changhoon Lee, Jinho Lee, Boundary layer flow of second grade fluid in a cylinder with heat transfer, Mathematical Problems in Engineering, Volume 2012, Article ID 640289.
[11]	S. Nadeem, Abdul Rehman, K. Vajravelu, Jinho Lee, Changhoon Lee, Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder, Mathematical Problems in Engineering, Volume 2012, Article ID 378259.
[12]	Abdul Rehman, S. Nadeem, Mixed convection heat transfer in micropolar nanofluid over a vertical slender cylinder, Chin. Phy. Lett. 29 (12) (2012) 124701-5.
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[14]	Abdul Rehman, S. Nadeem, M. Y. Malik, Stagnation flow of couple stress nanofluid over an exponentially stretching sheet through a porous medium, J. Power Tech. 93 (2) (2013) 122-132.
[15]	Abdul Rehman, S. Nadeem, M. Y. Malik, Boundary layer stagnation-point flow of a third grade fluid over an exponentially stretching sheet, Braz. J. Che. Eng. 30 (3) (2013) 611-618.
[16]	Abdul Rehman, S. Nadeem, Heat transfer analysis of the boundary layer flow over a vertical exponentially stretching cylinder, Global J. Sci. Fron. Res. 13 (11) (2013) 73-85.
[17]	M. Y. Malik, M. Naseer, S. Nadeem, Abdul Rehman, The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder, Appl. NanoSci. DOI: 10.1007/s13204-012-0267-0.
[18]	Abdul Rehman, S. Nadeem, S. Iqbal, M. Y. Malik, M. Naseer, Nanoparticle effect over the boundary layer flow over an exponentially stretching cylinder, J. NanoEngineering and NanoSystems (2014) 1-6.
[19]	M. Y. Malik, M. Naseer, S. Nadeem, Abdul Rehman, The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alexandria Eng. J., 53 (2014) 747-750.
[20]	Abdul Rehman, R. Bazai, S. Achakzai, S. Iqbal, M. Naseer, Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder, App Comp Math, 4 (6) (2015) 424-430.
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[26]	Haroon Rasheed, Abdul Rehman, Naveed Sheikh, Saleem Iqbal, MHD Boundary Layer Flow of Nanofluid over a Continuously Moving Stretching Surface, Applied and Computational Mathematics, 2017; 6 (6): 265-270.
[27]	Najeeb Alam Khan, Umair Bin Saeed, Faqiha Sultan, Saif Ullah, and Abdul Rehman, Study of velocity and temperature distributions in boundary layer flow of fourth grade fluid over an exponential stretching sheet, AIP ADVANCES 8, 025011 (2018).
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APA Style

Muhammad Umar Farooq, Abdul Rehman, Naveed Sheikh, Manzoor Iqbal. (2020). Axisymmetric Flow Through a Cylinder with Porous Medium. International Journal of Systems Science and Applied Mathematics, 5(3), 32-35. https://doi.org/10.11648/j.ijssam.20200503.12

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ACS Style

Muhammad Umar Farooq; Abdul Rehman; Naveed Sheikh; Manzoor Iqbal. Axisymmetric Flow Through a Cylinder with Porous Medium. Int. J. Syst. Sci. Appl. Math. 2020, 5(3), 32-35. doi: 10.11648/j.ijssam.20200503.12

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AMA Style

Muhammad Umar Farooq, Abdul Rehman, Naveed Sheikh, Manzoor Iqbal. Axisymmetric Flow Through a Cylinder with Porous Medium. Int J Syst Sci Appl Math. 2020;5(3):32-35. doi: 10.11648/j.ijssam.20200503.12

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@article{10.11648/j.ijssam.20200503.12,
  author = {Muhammad Umar Farooq and Abdul Rehman and Naveed Sheikh and Manzoor Iqbal},
  title = {Axisymmetric Flow Through a Cylinder with Porous Medium},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {32-35},
  doi = {10.11648/j.ijssam.20200503.12},
  url = {https://doi.org/10.11648/j.ijssam.20200503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20200503.12},
  abstract = {The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.},
 year = {2020}
}

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TY  - JOUR
T1  - Axisymmetric Flow Through a Cylinder with Porous Medium
AU  - Muhammad Umar Farooq
AU  - Abdul Rehman
AU  - Naveed Sheikh
AU  - Manzoor Iqbal
Y1  - 2020/10/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20200503.12
DO  - 10.11648/j.ijssam.20200503.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 32
EP  - 35
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20200503.12
AB  - The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.
VL  - 5
IS  - 3
ER  -

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Author Information

Muhammad Umar Farooq

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Abdul Rehman

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Naveed Sheikh

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Manzoor Iqbal

Department of Mathematics, University of Balochistan, Quetta, Pakistan

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Plain Text BibTeX RIS

APA Style

Muhammad Umar Farooq, Abdul Rehman, Naveed Sheikh, Manzoor Iqbal. (2020). Axisymmetric Flow Through a Cylinder with Porous Medium. International Journal of Systems Science and Applied Mathematics, 5(3), 32-35. https://doi.org/10.11648/j.ijssam.20200503.12

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ACS Style

Muhammad Umar Farooq; Abdul Rehman; Naveed Sheikh; Manzoor Iqbal. Axisymmetric Flow Through a Cylinder with Porous Medium. Int. J. Syst. Sci. Appl. Math. 2020, 5(3), 32-35. doi: 10.11648/j.ijssam.20200503.12

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AMA Style

Muhammad Umar Farooq, Abdul Rehman, Naveed Sheikh, Manzoor Iqbal. Axisymmetric Flow Through a Cylinder with Porous Medium. Int J Syst Sci Appl Math. 2020;5(3):32-35. doi: 10.11648/j.ijssam.20200503.12

Copy | Download

@article{10.11648/j.ijssam.20200503.12,
  author = {Muhammad Umar Farooq and Abdul Rehman and Naveed Sheikh and Manzoor Iqbal},
  title = {Axisymmetric Flow Through a Cylinder with Porous Medium},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {32-35},
  doi = {10.11648/j.ijssam.20200503.12},
  url = {https://doi.org/10.11648/j.ijssam.20200503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20200503.12},
  abstract = {The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Axisymmetric Flow Through a Cylinder with Porous Medium
AU  - Muhammad Umar Farooq
AU  - Abdul Rehman
AU  - Naveed Sheikh
AU  - Manzoor Iqbal
Y1  - 2020/10/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20200503.12
DO  - 10.11648/j.ijssam.20200503.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 32
EP  - 35
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20200503.12
AB  - The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.
VL  - 5
IS  - 3
ER  -

Copy | Download