Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder

Muhammad Umar Farooq; Abdul Rehman; Naveed Sheikh

doi:doi:10.11648/j.ajmp.20231203.12

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Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder

Muhammad Umar Farooq^*, Abdul Rehman, Naveed Sheikh

Published in American Journal of Modern Physics (Volume 12, Issue 3)

Received: 14 November 2023 Accepted: 4 December 2023 Published: 14 December 2023

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Abstract

The present investigation deals with the study of annular axisymmetric stagnation flow and heat transfer of a Casson fluid through porous medium in a moving cylinder. The inner cylinder is rotating with a fixed angular velocity and is also translating along axial axis with constant axial velocity while the outer cylinder is assumed fixed. Fluid is injected from the top surface of the fixed outer cylinder towards the translating and rotating inner cylinder. The motion of the Casson fluid is assumed under the influence of some porous media. The governing nonlinear partial differential equations of conservation of mass, conservation of li near momentum and heat transfer are obtained and then simplified with the help of a set of suitable similarity transformations which reduces the original set of partial differential equations into a new simplified set of ordinary differential equations. The resulting system of ordinary differential equations is then solved numerically with the aid of fifth order Runge-Kutta Fehlberg method. A comparison of special cases of the present numerical solution with the already available work is also included through tables. The behavior of important involved physical non-dimensional parameters like Prandtl numbers, porosity parameter and Reynolds numbers is also presented at the end.

Published in	American Journal of Modern Physics (Volume 12, Issue 3)
DOI	10.11648/j.ajmp.20231203.12
Page(s)	47-53
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), 2023. Published by Science Publishing Group

Keywords

Axisymmetric Stagnation Flow, Casson Fluid, Moving Cylinder, Porous Medium

References

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APA Style

Farooq, M. U., Rehman, A., Sheikh, N. (2023). Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. American Journal of Modern Physics, 12(3), 47-53. https://doi.org/10.11648/j.ajmp.20231203.12

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ACS Style

Farooq, M. U.; Rehman, A.; Sheikh, N. Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. Am. J. Mod. Phys. 2023, 12(3), 47-53. doi: 10.11648/j.ajmp.20231203.12

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AMA Style

Farooq MU, Rehman A, Sheikh N. Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. Am J Mod Phys. 2023;12(3):47-53. doi: 10.11648/j.ajmp.20231203.12

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@article{10.11648/j.ajmp.20231203.12,
  author = {Muhammad Umar Farooq and Abdul Rehman and Naveed Sheikh},
  title = {Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder},
  journal = {American Journal of Modern Physics},
  volume = {12},
  number = {3},
  pages = {47-53},
  doi = {10.11648/j.ajmp.20231203.12},
  url = {https://doi.org/10.11648/j.ajmp.20231203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20231203.12},
  abstract = {The present investigation deals with the study of annular axisymmetric stagnation flow and heat transfer of a Casson fluid through porous medium in a moving cylinder. The inner cylinder is rotating with a fixed angular velocity and is also translating along axial axis with constant axial velocity while the outer cylinder is assumed fixed. Fluid is injected from the top surface of the fixed outer cylinder towards the translating and rotating inner cylinder. The motion of the Casson fluid is assumed under the influence of some porous media. The governing nonlinear partial differential equations of conservation of mass, conservation of li near momentum and heat transfer are obtained and then simplified with the help of a set of suitable similarity transformations which reduces the original set of partial differential equations into a new simplified set of ordinary differential equations. The resulting system of ordinary differential equations is then solved numerically with the aid of fifth order Runge-Kutta Fehlberg method. A comparison of special cases of the present numerical solution with the already available work is also included through tables. The behavior of important involved physical non-dimensional parameters like Prandtl numbers, porosity parameter and Reynolds numbers is also presented at the end.
},
 year = {2023}
}

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TY  - JOUR
T1  - Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder
AU  - Muhammad Umar Farooq
AU  - Abdul Rehman
AU  - Naveed Sheikh
Y1  - 2023/12/14
PY  - 2023
N1  - https://doi.org/10.11648/j.ajmp.20231203.12
DO  - 10.11648/j.ajmp.20231203.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 47
EP  - 53
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20231203.12
AB  - The present investigation deals with the study of annular axisymmetric stagnation flow and heat transfer of a Casson fluid through porous medium in a moving cylinder. The inner cylinder is rotating with a fixed angular velocity and is also translating along axial axis with constant axial velocity while the outer cylinder is assumed fixed. Fluid is injected from the top surface of the fixed outer cylinder towards the translating and rotating inner cylinder. The motion of the Casson fluid is assumed under the influence of some porous media. The governing nonlinear partial differential equations of conservation of mass, conservation of li near momentum and heat transfer are obtained and then simplified with the help of a set of suitable similarity transformations which reduces the original set of partial differential equations into a new simplified set of ordinary differential equations. The resulting system of ordinary differential equations is then solved numerically with the aid of fifth order Runge-Kutta Fehlberg method. A comparison of special cases of the present numerical solution with the already available work is also included through tables. The behavior of important involved physical non-dimensional parameters like Prandtl numbers, porosity parameter and Reynolds numbers is also presented at the end.

VL  - 12
IS  - 3
ER  -

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Author Information

Muhammad Umar Farooq

Department of Mathematics, University of Balochistan, Quetta, Pakistan

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Abdul Rehman

Department of Mathematics, University of Balochistan, Quetta, Pakistan

Contact Email
Naveed Sheikh

Department of Mathematics, University of Balochistan, Quetta, Pakistan

Contact Email

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APA Style

Farooq, M. U., Rehman, A., Sheikh, N. (2023). Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. American Journal of Modern Physics, 12(3), 47-53. https://doi.org/10.11648/j.ajmp.20231203.12

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ACS Style

Farooq, M. U.; Rehman, A.; Sheikh, N. Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. Am. J. Mod. Phys. 2023, 12(3), 47-53. doi: 10.11648/j.ajmp.20231203.12

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AMA Style

Farooq MU, Rehman A, Sheikh N. Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder. Am J Mod Phys. 2023;12(3):47-53. doi: 10.11648/j.ajmp.20231203.12

Copy | Download

@article{10.11648/j.ajmp.20231203.12,
  author = {Muhammad Umar Farooq and Abdul Rehman and Naveed Sheikh},
  title = {Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder},
  journal = {American Journal of Modern Physics},
  volume = {12},
  number = {3},
  pages = {47-53},
  doi = {10.11648/j.ajmp.20231203.12},
  url = {https://doi.org/10.11648/j.ajmp.20231203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20231203.12},
  abstract = {The present investigation deals with the study of annular axisymmetric stagnation flow and heat transfer of a Casson fluid through porous medium in a moving cylinder. The inner cylinder is rotating with a fixed angular velocity and is also translating along axial axis with constant axial velocity while the outer cylinder is assumed fixed. Fluid is injected from the top surface of the fixed outer cylinder towards the translating and rotating inner cylinder. The motion of the Casson fluid is assumed under the influence of some porous media. The governing nonlinear partial differential equations of conservation of mass, conservation of li near momentum and heat transfer are obtained and then simplified with the help of a set of suitable similarity transformations which reduces the original set of partial differential equations into a new simplified set of ordinary differential equations. The resulting system of ordinary differential equations is then solved numerically with the aid of fifth order Runge-Kutta Fehlberg method. A comparison of special cases of the present numerical solution with the already available work is also included through tables. The behavior of important involved physical non-dimensional parameters like Prandtl numbers, porosity parameter and Reynolds numbers is also presented at the end.
},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Annular Axisymmetric Stagnation Flow of a Casson Fluid Through Porous Media in a Moving Cylinder
AU  - Muhammad Umar Farooq
AU  - Abdul Rehman
AU  - Naveed Sheikh
Y1  - 2023/12/14
PY  - 2023
N1  - https://doi.org/10.11648/j.ajmp.20231203.12
DO  - 10.11648/j.ajmp.20231203.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 47
EP  - 53
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20231203.12
AB  - The present investigation deals with the study of annular axisymmetric stagnation flow and heat transfer of a Casson fluid through porous medium in a moving cylinder. The inner cylinder is rotating with a fixed angular velocity and is also translating along axial axis with constant axial velocity while the outer cylinder is assumed fixed. Fluid is injected from the top surface of the fixed outer cylinder towards the translating and rotating inner cylinder. The motion of the Casson fluid is assumed under the influence of some porous media. The governing nonlinear partial differential equations of conservation of mass, conservation of li near momentum and heat transfer are obtained and then simplified with the help of a set of suitable similarity transformations which reduces the original set of partial differential equations into a new simplified set of ordinary differential equations. The resulting system of ordinary differential equations is then solved numerically with the aid of fifth order Runge-Kutta Fehlberg method. A comparison of special cases of the present numerical solution with the already available work is also included through tables. The behavior of important involved physical non-dimensional parameters like Prandtl numbers, porosity parameter and Reynolds numbers is also presented at the end.

VL  - 12
IS  - 3
ER  -

Copy | Download