Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal

doi:doi:10.11648/j.ajam.20150305.11

| Peer-Reviewed

Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal

Published in American Journal of Applied Mathematics (Volume 3, Issue 5)

Received: 11 August 2015 Accepted: 22 August 2015 Published: 3 September 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.ajam.20150305.11
Page(s)	206-214
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), 2015. Published by Science Publishing Group

Keywords

Pressure Gradient, Suction and Injection, Magnetohydrodynamic (MHD)

References

[1]	Bég O. A, Zueco J. and Takhar H.S (2009). Unsteady magnetohydrodynamic Hartmann-Couette flow and heat transfer in a Darcian channel with Hall current, ionslip, viscous and Joule heating effects. Network numerical solutions, Nonlinear Science Numerical Simulation. 14 (4), pp. 1082-1097.
[2]	Chinyoka, T., and Makinde, O.D., (2012).Unsteady hydromagnetic flow of a reactive variable viscosity third-grade fluid in a channel with convective cooling. International journal for numerical Methods in Fluids, Vol. 69(2), pp. 353-365
[3]	D. Vieru and Siddique I. (2010). Axial Flow of Several Non-Newtonian Fluids through a Circular Cylinder Journal: International Journal of Applied Mechanics. Vol. 02, pp.543
[4]	David J Griffiths (1999). Introduction to electrodynamics (Third edition.). Prentice Hall. pp. 559–562.
[5]	Govindrajulu T., (1969). Unsteady flow of an incompressible and electrically conducting fluid between two infinite discs rotating in the presence of a uniform axial magnetic field. Journal: ActaMechanica - ACTA MECH, vol. 8, no. 1, pp. 53-62,
[6]	Hayat, T., Ahmed, N. and Sajid M. (2008).Analytic Solution for MHD Flow of a Third Order Fluid in a Porous Channel. J. Comput. Appl. Maths., Vol. 214, p. 572-582.
[7]	Katagiri, M., (1962). Flow Formation in Couette Motion in Magnetohydrodynamics. Phys. Soc. Jpn., Vol. 17, p. 393-396.
[8]	Khan, M., Fetecau, C. and Hayat, T. (2007). “MHD Transient Flows in a Channel of Rectangular Cross-Section with Porous Medium. Physics Letters A, Vol. 369, p. 44.
[9]	Khan, M., Maqbool, K. and Hayat, T., (2006). Influence of Hall Current on the Flows of a Generalized Oldroyd-B Fluid in a Porous Space. Acta Mech., Vol. 184, p. 1.
[10]	Mishra SP and Muduli JC (1980). Unsteady flow through two porous flat walls in the presence of a magnetic field. Rev. Roum. des Sci Tech. Serie de Mech. Appl., 25, pp. 21-27.
[11]	Muhuri, P. K., (1963). Flow Formation in Couette Motion in Magnetohydrodynamics with Suction. J. Phys. Soc. Jpn., Vol. 18, p. 1671-1675.
[12]	Seth G. S., Ansari S. and Nandkeolyar R., (2011). Unsteady Hydromagnetic Couette flow within a porous channel. Tamkang journal of Science and Engineering. Vol. 14. No. 1, pp. 7-14
[13]	Singh, A. K. and Kumar, N., (1983). Unsteady Magneto- hydrodynamic Couette Flow. Wear, Vol. 89, p. 125-129.
[14]	Soundalgekar V.M. (1967). On the flow of an electrically conducting incompressible fluid near an accelerated plate in the presence of a parallel plate, under transverse magnetic field. Proc. Ind. Acad. Sci., 65A, pp. 179-187.
[15]	Tao LN (1960). Magnetohydrodynamic effects on the formation of Couette flow. J. Aerospace Sci., 27, pp. 334-338.
[16]	M. Sheikholeslami, D. D. Ganji, (2013) Heat transfer of Cu-water nanoﬂuid ﬂow between parallel plates, Powder Technol. 235 pp 873–879.
[17]	Guchhait, S., Das, S., Jana, R. N. and Ghosh, S. K. (2011). Combined effects of Hall current and rotation on unsteady Couette flow in porous channel. World J. Mech., Vol. 1. pp. 87-99.
[18]	Prasad, B. G. and Kumar, R. (2012). Unsteady hydromagnetic Couette flow through a porous medium in a rotating system, Theo.Appl. Mech. Letters, Vol. 1. DOI: 10.1063/2.1104205.
[19]	Seth, G. S., Nandkeolyar, R. and Ansari, Md. S. (2012). Effects of Hall current and rotation on unsteady MHD Couette flow in the presence of an inclined magnetic field, J. Appl. Fluid Mech., Vol. 5, No. 2, pp. 67-74.
[20]	Seth, G. S. and Singh, J. K. (2012). Unsteady MHD Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system, Int. J. Appl. Mech. Eng., Vol. 17, No. (2/3). (To appear in 2012).
[21]	Jha, B. K. and Apere, C. A. (2011). Hall and ion-slip effects on unsteady MHD Couette flow in a rotating system with suction and injection, J. Phys. Soc. Japan, 80, DOI:10.1143/JPSJ.80.114401.
[22]	S. Ahmed and K. Kalita, (2013) Magnetohydrodynamic transient flow through a porous medium bounded by a hot vertical plate in presence of radiation: A theoretical analysis, J. Eng. Phys. Thermophys. 86 pp31-39.

Cite This Article

Plain Text BibTeX RIS

APA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. (2015). Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. American Journal of Applied Mathematics, 3(5), 206-214. https://doi.org/10.11648/j.ajam.20150305.11

Copy | Download

ACS Style

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am. J. Appl. Math. 2015, 3(5), 206-214. doi: 10.11648/j.ajam.20150305.11

Copy | Download

AMA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am J Appl Math. 2015;3(5):206-214. doi: 10.11648/j.ajam.20150305.11

Copy | Download

@article{10.11648/j.ajam.20150305.11,
  author = {Edward Richard Onyango and Mathew Ngugi Kinyanjui and Surindar Mohan Uppal},
  title = {Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {5},
  pages = {206-214},
  doi = {10.11648/j.ajam.20150305.11},
  url = {https://doi.org/10.11648/j.ajam.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.11},
  abstract = {This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate
AU  - Edward Richard Onyango
AU  - Mathew Ngugi Kinyanjui
AU  - Surindar Mohan Uppal
Y1  - 2015/09/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150305.11
DO  - 10.11648/j.ajam.20150305.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 206
EP  - 214
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150305.11
AB  - This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.
VL  - 3
IS  - 5
ER  -

Copy | Download

Author Information

Edward Richard Onyango

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

Dept. Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Surindar Mohan Uppal

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. (2015). Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. American Journal of Applied Mathematics, 3(5), 206-214. https://doi.org/10.11648/j.ajam.20150305.11

Copy | Download

ACS Style

Edward Richard Onyango; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am. J. Appl. Math. 2015, 3(5), 206-214. doi: 10.11648/j.ajam.20150305.11

Copy | Download

AMA Style

Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am J Appl Math. 2015;3(5):206-214. doi: 10.11648/j.ajam.20150305.11

Copy | Download

@article{10.11648/j.ajam.20150305.11,
  author = {Edward Richard Onyango and Mathew Ngugi Kinyanjui and Surindar Mohan Uppal},
  title = {Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {5},
  pages = {206-214},
  doi = {10.11648/j.ajam.20150305.11},
  url = {https://doi.org/10.11648/j.ajam.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.11},
  abstract = {This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate
AU  - Edward Richard Onyango
AU  - Mathew Ngugi Kinyanjui
AU  - Surindar Mohan Uppal
Y1  - 2015/09/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150305.11
DO  - 10.11648/j.ajam.20150305.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 206
EP  - 214
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150305.11
AB  - This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.
VL  - 3
IS  - 5
ER  -

Copy | Download