Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Mark Kimathi; Surindar Mohan Uppal

doi:doi:10.11648/j.acm.20200901.11

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Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal

Published in Applied and Computational Mathematics (Volume 9, Issue 1)

Received: 3 February 2020 Accepted: 13 February 2020 Published: 25 February 2020

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Abstract

In this study, the magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid through a convergent-divergent channel in the presence of an oblique variable magnetic field to the flow with a case of suction and injection on the walls has been investigated. The velocity profiles, temperature profiles, the effects of injection and suction, time, induced magnetic field and the effects of varying various parameters on the flow have been investigated. The equations governing the MHD flow are solved by the collocation method and the results presented in graphs. The velocity, temperature, and magnetic induction increases with the increase in the suction parameter and decrease in the wedge angle while velocity, temperature, and magnetic induction reduce with the increase in the injection parameter. The velocity, temperature and magnetic induction increase with the increase in the Hartmann number. The results of this study will be useful information to the engineers to improve the performance and efficiency of machines in the industrial, environmental, aerospace, chemical, civil, mechanical and biomechanical engineering applications.

Published in	Applied and Computational Mathematics (Volume 9, Issue 1)
DOI	10.11648/j.acm.20200901.11
Page(s)	1-13
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

Jeffrey-Hamel Flow, Newtonian Fluid, Inclined Magnetic Field, Unsteadiness Parameter

References

[1]	Jeffery, G. B. "L. The two-dimensional steady motion of a viscous fluid." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 29, no. 172 (1915): 455-465.
[2]	Hamel, Georg. "Spiralförmige Bewegungen zäher Flüssigkeiten." Jahresbericht der Deutschen mathematiker-Vereinigung 25 (1917): 34-60.
[3]	W. I. Axford, “The magnetohydrodynamic Jeffrey-Hamel problem for a weakly conducting fluid,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 14, pp. 335–351, 1961.
[4]	G. Domairry and A. Aziz, “Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by a homotopy perturbation method,” Mathematical Problems in Engineering, vol. 2009, Article ID 603916, 19 pages, 2009.
[5]	Imani, A. A., Rostamian, Y., Ganji, D. D., & Rokni, H. B. (2012). Analytical investigation of Jeffery-Hamel flows with high magnetic field and nanoparticle by rvim.
[6]	Asadullah, M., Khan, U., Manzoor, R., Ahmed, N., & Mohyud-Din, S. T. (2013). MHD flow of a Jeffery fluid in converging and diverging channels. Int. J. Mod. Math. Sci, 6 (2), 92-106.
[7]	Khan, U., Ahmed, N., Zaidi, Z. A., Jan, S. U., & Mohyud-Din, S. T. (2013). On Jeffery–Hamel flows. Int J Mod Math Sci, 7 (3), 236-247.
[8]	Sheikholeslami, M., Mollabasi, H., & Ganji, D. D. (2015). Analytical investigation of MHD Jeffery–Hamel nanofluid flow in non-parallel walls. International Journal of Nanoscience and Nanotechnology, 11 (4), 241-248.
[9]	Zubair Akbar, M., Ashraf, M., Farooq Iqbal, M., & Ali, K. (2016). Heat and mass transfer analysis of unsteady MHD nanofluid flow through a channel with moving porous walls and medium. AIP Advances, 6 (4), 045222.
[10]	Alam, M. S., Haque, M. M., & Uddin, M. J. (2016). The convective flow of nanofluid along with a permeable stretching/shrinking wedge with second-order slip using Buongiorno’s mathematical model. International Journal of Advanced in Applied Mathematics and Mechanics, 3 (3), 79-91.
[11]	Nagler, J. (2017). Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction. Applied Mathematics and Mechanics, 38 (6), 815-830.
[12]	Ochieng, F. O., Kinyanjui, M. N., & Kimathi, M. E. (2018). Hydromagnetic Jeffery-Hamel Unsteady Flow of a Dissipative Non-Newtonian Fluid with Nonlinear Viscosity and Skin Friction. Global Journal of Pure and Applied Mathematics, 14 (8), 1101-1119.
[13]	Sattar, M. A. (2013). Derivation of the similarity equation of the 2-D unsteady boundary layer equations and the corresponding similarity conditions. American Journal of Fluid Dynamics, 3 (5), 135.
[14]	Alam, M. S., & Huda, M. N. (2013). A new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface. International Journal of Advances in Applied Mathematics and Mechanics, 1 (2), 39-52.
[15]	Alam, M. D. S., Khan, M. A. H., & Alim, M. A. (2016). Magnetohydrodynamic Stability of Jeffery-Hamel Flow using Different Nanoparticles. Journal of Applied Fluid Mechanics, 9 (2).

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APA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal. (2020). Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Applied and Computational Mathematics, 9(1), 1-13. https://doi.org/10.11648/j.acm.20200901.11

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ACS Style

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Mark Kimathi; Surindar Mohan Uppal. Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Appl. Comput. Math. 2020, 9(1), 1-13. doi: 10.11648/j.acm.20200901.11

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AMA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal. Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Appl Comput Math. 2020;9(1):1-13. doi: 10.11648/j.acm.20200901.11

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@article{10.11648/j.acm.20200901.11,
  author = {Edward Richard Onyango and Mathew Ngugi Kinyanjui and Mark Kimathi and Surindar Mohan Uppal},
  title = {Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.acm.20200901.11},
  url = {https://doi.org/10.11648/j.acm.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200901.11},
  abstract = {In this study, the magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid through a convergent-divergent channel in the presence of an oblique variable magnetic field to the flow with a case of suction and injection on the walls has been investigated. The velocity profiles, temperature profiles, the effects of injection and suction, time, induced magnetic field and the effects of varying various parameters on the flow have been investigated. The equations governing the MHD flow are solved by the collocation method and the results presented in graphs. The velocity, temperature, and magnetic induction increases with the increase in the suction parameter and decrease in the wedge angle while velocity, temperature, and magnetic induction reduce with the increase in the injection parameter. The velocity, temperature and magnetic induction increase with the increase in the Hartmann number. The results of this study will be useful information to the engineers to improve the performance and efficiency of machines in the industrial, environmental, aerospace, chemical, civil, mechanical and biomechanical engineering applications.},
 year = {2020}
}

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TY  - JOUR
T1  - Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection
AU  - Edward Richard Onyango
AU  - Mathew Ngugi Kinyanjui
AU  - Mark Kimathi
AU  - Surindar Mohan Uppal
Y1  - 2020/02/25
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200901.11
DO  - 10.11648/j.acm.20200901.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200901.11
AB  - In this study, the magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid through a convergent-divergent channel in the presence of an oblique variable magnetic field to the flow with a case of suction and injection on the walls has been investigated. The velocity profiles, temperature profiles, the effects of injection and suction, time, induced magnetic field and the effects of varying various parameters on the flow have been investigated. The equations governing the MHD flow are solved by the collocation method and the results presented in graphs. The velocity, temperature, and magnetic induction increases with the increase in the suction parameter and decrease in the wedge angle while velocity, temperature, and magnetic induction reduce with the increase in the injection parameter. The velocity, temperature and magnetic induction increase with the increase in the Hartmann number. The results of this study will be useful information to the engineers to improve the performance and efficiency of machines in the industrial, environmental, aerospace, chemical, civil, mechanical and biomechanical engineering applications.
VL  - 9
IS  - 1
ER  -

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Author Information

Edward Richard Onyango

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mathew Ngugi Kinyanjui

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mark Kimathi

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya; Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya
Surindar Mohan Uppal

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal. (2020). Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Applied and Computational Mathematics, 9(1), 1-13. https://doi.org/10.11648/j.acm.20200901.11

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ACS Style

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Mark Kimathi; Surindar Mohan Uppal. Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Appl. Comput. Math. 2020, 9(1), 1-13. doi: 10.11648/j.acm.20200901.11

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AMA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Mark Kimathi, Surindar Mohan Uppal. Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Appl Comput Math. 2020;9(1):1-13. doi: 10.11648/j.acm.20200901.11

Copy | Download

@article{10.11648/j.acm.20200901.11,
  author = {Edward Richard Onyango and Mathew Ngugi Kinyanjui and Mark Kimathi and Surindar Mohan Uppal},
  title = {Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.acm.20200901.11},
  url = {https://doi.org/10.11648/j.acm.20200901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200901.11},
  abstract = {In this study, the magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid through a convergent-divergent channel in the presence of an oblique variable magnetic field to the flow with a case of suction and injection on the walls has been investigated. The velocity profiles, temperature profiles, the effects of injection and suction, time, induced magnetic field and the effects of varying various parameters on the flow have been investigated. The equations governing the MHD flow are solved by the collocation method and the results presented in graphs. The velocity, temperature, and magnetic induction increases with the increase in the suction parameter and decrease in the wedge angle while velocity, temperature, and magnetic induction reduce with the increase in the injection parameter. The velocity, temperature and magnetic induction increase with the increase in the Hartmann number. The results of this study will be useful information to the engineers to improve the performance and efficiency of machines in the industrial, environmental, aerospace, chemical, civil, mechanical and biomechanical engineering applications.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection
AU  - Edward Richard Onyango
AU  - Mathew Ngugi Kinyanjui
AU  - Mark Kimathi
AU  - Surindar Mohan Uppal
Y1  - 2020/02/25
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200901.11
DO  - 10.11648/j.acm.20200901.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200901.11
AB  - In this study, the magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid through a convergent-divergent channel in the presence of an oblique variable magnetic field to the flow with a case of suction and injection on the walls has been investigated. The velocity profiles, temperature profiles, the effects of injection and suction, time, induced magnetic field and the effects of varying various parameters on the flow have been investigated. The equations governing the MHD flow are solved by the collocation method and the results presented in graphs. The velocity, temperature, and magnetic induction increases with the increase in the suction parameter and decrease in the wedge angle while velocity, temperature, and magnetic induction reduce with the increase in the injection parameter. The velocity, temperature and magnetic induction increase with the increase in the Hartmann number. The results of this study will be useful information to the engineers to improve the performance and efficiency of machines in the industrial, environmental, aerospace, chemical, civil, mechanical and biomechanical engineering applications.
VL  - 9
IS  - 1
ER  -

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