Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions

Adetunji Adeniyan; Joshua Aanuoluwapo Adigun

doi:doi:10.11648/j.acm.20140305.19

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Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions

Adetunji Adeniyan, Joshua Aanuoluwapo Adigun

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

Received: 11 September 2014 Accepted: 22 September 2014 Published: 20 October 2014

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Abstract

The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta method with a shooting technique and depicted graphically for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.

Published in	Applied and Computational Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.acm.20140305.19
Page(s)	247-255
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), 2014. Published by Science Publishing Group

Keywords

Forced Convection, Permeable Sheet, Porous Medium, Pollutant Concentration, Magnetohydrodynamics, Convective Boundary Condition

References

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[2]	O. D. Makinde, R.J. Moitsheki, and B. A. Tau, “Similarity reductions of equations for river pollution,” Appl. Math. Comput. vol.188 , pp. 1267-1273, 2007.
[3]	R.J. Moitsheki and O.D. Makinde, “Symmetry reductions and solutions for pollutant diffusion in a cylindrical system,” Nonlinear Anal. RWA, vol. 10, pp. 3420-3427, 2009.
[4]	R.J. Moitsheki and O.D Makinde, “Computational modelling and similarity reduction of equations for transient fluid flow and heat transfer with variable properties,” Adv. in Mech. Engng, vol. 2013, Article ID 983962, 8 pages , 2013.
[5]	T. Chinyoka and O.D. Makinde, “ Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration,”Computers and Mathematics with Applications, vol. 60, pp. 642-652, 2010.
[6]	K. Lakshminarayanachari, C.M. Suresha, M.S. Prasad and C. Pandurangappa, “A two dimensional numerical model of primary pollutant emitted from an urban area source with wet deposition and mesoscale wind,” Int. J. Sci. Env. and Tech. vol. 2, no 1, pp: 60 – 79, 2013.
[7]	M. Shekhu and C. Sulochana. “Time dependent mathematical model of air pollutants emitted from time-dependent elevated line source into a stable atmospheric boundary layer,” J. Chem. Engng. and Mat. Sci., vol. 4, issue 8, pp. 103-115 , 2013.
[8]	H.I.Andersson, J.B. Aarseth and B.S. Dandapat, “Heat transfer in a liquid film on an unsteady stretching surface,” Int. J. Heat and Mass Trans., vol. 43, no. 1, pp. 69–74, 2000.
[9]	M.S. Abel, N. Mahesha and J. Tawade, “Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field,” Appl. Mathematical Modelling, vol.33, pp. 3430-3441, 2009.
[10]	S. Mukhopadhyay, “Heat transfer in a moving fluid over a moving nonisothermal flat surface,” Chin. Phys. Lett., vol. 8, no.12, ID124706, 2011.
[11]	D.A. Nield and A. Bejan, Convection in Porous Media, 3rd Ed., Springer Science + Business Media, Inc., N. York, 2006.
[12]	D.B. Ingham and I. Pop, Transport Phenomena in Porous Media, Elsevier, Oxford, UK , 2005.
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[14]	A. Ishak, N.A Yacob and N. Bachok,. “Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition,” Meccanica doi:10.1007/s11012-010-9338-4, 2010.
[15]	P.O. Olanrewaju, F.I. Alao, A. Adeniyan, S.A. Bishop, “Double-diffusive convection from a permeable vertical surface under convective boundary condition in the presence of heat generation and thermal radiation,” Nonlinear Sci. Lett. A., vol. 4, No.3 pp. 76-90, 2013.
[16]	A. Adeniyan and J.A. Adigun, “Effects of chemical reaction on stagnation point mhd flow over a vertical plane with convective boundary conditions in the presence of a transverse uniform magnetic field,” The Inter. J. Engng and Sci. (IJES), vol. 2 issue 4 pp.14-18, 2013.
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APA Style

Adetunji Adeniyan, Joshua Aanuoluwapo Adigun. (2014). Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Applied and Computational Mathematics, 3(5), 247-255. https://doi.org/10.11648/j.acm.20140305.19

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ACS Style

Adetunji Adeniyan; Joshua Aanuoluwapo Adigun. Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Appl. Comput. Math. 2014, 3(5), 247-255. doi: 10.11648/j.acm.20140305.19

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AMA Style

Adetunji Adeniyan, Joshua Aanuoluwapo Adigun. Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Appl Comput Math. 2014;3(5):247-255. doi: 10.11648/j.acm.20140305.19

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@article{10.11648/j.acm.20140305.19,
  author = {Adetunji Adeniyan and Joshua Aanuoluwapo Adigun},
  title = {Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {247-255},
  doi = {10.11648/j.acm.20140305.19},
  url = {https://doi.org/10.11648/j.acm.20140305.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.19},
  abstract = {The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta  method with a shooting technique and depicted graphically  for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.},
 year = {2014}
}

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TY  - JOUR
T1  - Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions
AU  - Adetunji Adeniyan
AU  - Joshua Aanuoluwapo Adigun
Y1  - 2014/10/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.19
DO  - 10.11648/j.acm.20140305.19
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 247
EP  - 255
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.19
AB  - The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta  method with a shooting technique and depicted graphically  for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.
VL  - 3
IS  - 5
ER  -

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Author Information

Adetunji Adeniyan

Department of Mathematics, University of Lagos, Akoka, Yaba, Lagos State, Nigeria
Joshua Aanuoluwapo Adigun

Department of Physical Sciences, Bells University of Technology, Ota, Ogun State, Nigeria

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APA Style

Adetunji Adeniyan, Joshua Aanuoluwapo Adigun. (2014). Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Applied and Computational Mathematics, 3(5), 247-255. https://doi.org/10.11648/j.acm.20140305.19

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ACS Style

Adetunji Adeniyan; Joshua Aanuoluwapo Adigun. Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Appl. Comput. Math. 2014, 3(5), 247-255. doi: 10.11648/j.acm.20140305.19

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AMA Style

Adetunji Adeniyan, Joshua Aanuoluwapo Adigun. Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions. Appl Comput Math. 2014;3(5):247-255. doi: 10.11648/j.acm.20140305.19

Copy | Download

@article{10.11648/j.acm.20140305.19,
  author = {Adetunji Adeniyan and Joshua Aanuoluwapo Adigun},
  title = {Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {247-255},
  doi = {10.11648/j.acm.20140305.19},
  url = {https://doi.org/10.11648/j.acm.20140305.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.19},
  abstract = {The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta  method with a shooting technique and depicted graphically  for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions
AU  - Adetunji Adeniyan
AU  - Joshua Aanuoluwapo Adigun
Y1  - 2014/10/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.19
DO  - 10.11648/j.acm.20140305.19
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 247
EP  - 255
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.19
AB  - The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta  method with a shooting technique and depicted graphically  for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.
VL  - 3
IS  - 5
ER  -

Copy | Download