Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition

Christian John Etwire; Yakubu Ibrahim Seini

doi:doi:10.11648/j.ajam.20140206.14

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Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition

Christian John Etwire, Yakubu Ibrahim Seini

Published in American Journal of Applied Mathematics (Volume 2, Issue 6)

Received: 10 December 2014 Accepted: 24 December 2014 Published: 4 January 2015

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Abstract

This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.ajam.20140206.14
Page(s)	214-220
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

Convective, Radiation, Magneto Hydrodynamic, Eckert Number, Magnetic Field, Biot Number

References

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[2]	M.S. Abel and M. Mareppa, MHD flow and heat transfer of the mixed hydrodynamic / thermal slip over a linear vertically stretching sheet International Journal of Mathematical Archive-4(5), 2013, 156-163
[3]	Y.I. Seini and O.D. Makinde, Hydromagnetic Flow with Dufour and Soret Effects past a Vertical Plate Embedded in Porous Media, Mathematical Theory and Modeling, 3 (12), 2013, 47 - 64
[4]	M. Abbasi, G.H. Navab, I.R. Petroudi, Analytic solution of hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid with convective surface boundary condition. Indian J. Sci. Res. 1(2), 2014, 241-247.
[5]	O.D. Makinde, Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition International Journal of the Physical Sciences Vol. 5(6), 2010, 700-710.
[6]	O.D. Makinde and A. Ogulu, The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chem. Eng. Commun. 195(12), 2008, 1575-1584.
[7]	A.Y. Ghaly and E.M.E. Elbarbary, Radiation effect on MHD free convection flow of a gas at a stretching surface with uniform free stream, J. Appl. Math., 2, 2002, 93
[8]	A.M. Emad, Radiation effect on heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream, J. Phys. D., Appl. Phys. 33, 2000, 3180.
[9]	M.E. Yazdi, A. Moradi and S. Dinarvand , Radiation Effects on MHD Stagnation-Point Flow in a Nanofluid, Research Journal of Applied Sciences, Engineering and Technology 5(22), 2013, 5201-5208
[10]	M.K. Mazumdar and R.K. Deka, MHD flow past an impulsively started infinite vertical plate in presence of thermal radiation, Romanian Journal of Physics, 52(5-6), 2007, 529-535
[11]	S. Srinivas and R. Muthuraj, Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method Fluid Dynamics Division, Communication in Nonlinear Science and Numerical Simulation, 15(8), 2010, 2098–2108.
[12]	M.A. Emmanuel, I.Y. Seini, A. Seidu, On chemically reacting hydromagnetic flow over a flat surface in the presence of radiation with viscous dissipation and convective boundary conditions, American Journal of Applied Mathematics, 2 (5), 2014, 179-185
[13]	M. A. Hossain and H. S. Takhar, “Radiation effect on mixed convection along a vertical plate with uniform surface temperature”, Heat mass transfer 31, 1996, 243 – 248.
[14]	R. Imoro, E.M. Arthur and Y.I. Seini, Heat and Mass Transfer over a Vertical Surface with Convective Boundary Conditions in the Presence of Viscous Dissipation and nth Order Chemical Reaction. International Journal of Computational and Applied Mathematics, RIP. ISSN 1819-4966 Volume 9, Number 2, 2014, pp. 101-118.
[15]	Y.I. Seini and O.D Makinde, Boundary layer flow near stagnation-points on a vertical surface with slip in the presence of transverse magnetic field. International Journal of Numerical Methods for Heat & Fluid Flow Vol. 24 No. 3, 2014, pp. 643-653.
[16]	S.Y. Ibrahim and O.D. Makinde, “MHD boundary layer flow due to exponential stretching surface with radiation and chemical reaction”, Mathematical Problems in Engineering, 2013. http://dx.doi.org/10.1155/2013/163614
[17]	O. D. Makinde and P. O. Olanrewaju, Buoyancy Effects on Thermal Boundary Layer Over a Vertical Plate With a Convective Surface Boundary Condition. Journal of Fluids Engineering, 2010, Vol. 132 / 044502-1

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APA Style

Christian John Etwire, Yakubu Ibrahim Seini. (2015). Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. American Journal of Applied Mathematics, 2(6), 214-220. https://doi.org/10.11648/j.ajam.20140206.14

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ACS Style

Christian John Etwire; Yakubu Ibrahim Seini. Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. Am. J. Appl. Math. 2015, 2(6), 214-220. doi: 10.11648/j.ajam.20140206.14

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AMA Style

Christian John Etwire, Yakubu Ibrahim Seini. Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. Am J Appl Math. 2015;2(6):214-220. doi: 10.11648/j.ajam.20140206.14

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@article{10.11648/j.ajam.20140206.14,
  author = {Christian John Etwire and Yakubu Ibrahim Seini},
  title = {Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {214-220},
  doi = {10.11648/j.ajam.20140206.14},
  url = {https://doi.org/10.11648/j.ajam.20140206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.14},
  abstract = {This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.},
 year = {2015}
}

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TY  - JOUR
T1  - Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition
AU  - Christian John Etwire
AU  - Yakubu Ibrahim Seini
Y1  - 2015/01/04
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20140206.14
DO  - 10.11648/j.ajam.20140206.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 214
EP  - 220
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.14
AB  - This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.
VL  - 2
IS  - 6
ER  -

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Author Information

Christian John Etwire

Faculty of Mathematical Sciences, University for Development Studies, P.O. Box 1350, Tamale - Ghana
Yakubu Ibrahim Seini

Faculty of Mathematical Sciences, University for Development Studies, P.O. Box 1350, Tamale - Ghana

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APA Style

Christian John Etwire, Yakubu Ibrahim Seini. (2015). Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. American Journal of Applied Mathematics, 2(6), 214-220. https://doi.org/10.11648/j.ajam.20140206.14

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ACS Style

Christian John Etwire; Yakubu Ibrahim Seini. Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. Am. J. Appl. Math. 2015, 2(6), 214-220. doi: 10.11648/j.ajam.20140206.14

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AMA Style

Christian John Etwire, Yakubu Ibrahim Seini. Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition. Am J Appl Math. 2015;2(6):214-220. doi: 10.11648/j.ajam.20140206.14

Copy | Download

@article{10.11648/j.ajam.20140206.14,
  author = {Christian John Etwire and Yakubu Ibrahim Seini},
  title = {Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {214-220},
  doi = {10.11648/j.ajam.20140206.14},
  url = {https://doi.org/10.11648/j.ajam.20140206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.14},
  abstract = {This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition
AU  - Christian John Etwire
AU  - Yakubu Ibrahim Seini
Y1  - 2015/01/04
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20140206.14
DO  - 10.11648/j.ajam.20140206.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 214
EP  - 220
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.14
AB  - This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.
VL  - 2
IS  - 6
ER  -

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