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
Volume 3, Issue 5, October 2014, Pages: 247-255
Received: Sep. 11, 2014;
Accepted: Sep. 22, 2014;
Published: Oct. 20, 2014
Views 3029 Downloads 186
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
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.
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, Applied and Computational Mathematics.
Vol. 3, No. 5,
2014, pp. 247-255.
O. D. Makinde and T. Chinyoka, “Analysis of nonlinear dispersion of a pollutant ejected by an external source into a channel flow,” Math. Prob. in Engng, vol. 2010, Article ID 827363, 17 pages, 2010.
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.
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.
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.
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.
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.
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.
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.
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.
S. Mukhopadhyay, “Heat transfer in a moving fluid over a moving nonisothermal flat surface,” Chin. Phys. Lett., vol. 8, no.12, ID124706, 2011.
D.A. Nield and A. Bejan, Convection in Porous Media, 3rd Ed., Springer Science + Business Media, Inc., N. York, 2006.
D.B. Ingham and I. Pop, Transport Phenomena in Porous Media, Elsevier, Oxford, UK , 2005.
I. Pop and D.B. Ingham, Convective Heat Transfer, Pergamon, Amsterdam, The Netherland, 2001.
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.
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.
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.
O.D. Makinde, “Computational modelling of mhd unsteady flow and heat transfer toward a flat plate with Navier slip and Newtonian heating,” Braz. J. Chem. Engng, vol. 29, No. 01, pp. 159 – 166, 2012.
K. Bhattacharyya, S. Mukhopadhya, G.C Layek, “Similarity solution of mixed convection boundary layer slip flow over a vertical plate,” Ain Shams J.(Mech. Engng), vol. 4, pp.299-305. 2013.
S.Y. Ibrahim and O.D. Makinde, “Radiation effect on chemically reacting magnetohydrodynamics (mhd) boundary layer flow of heat and mass transfer through a porous vertical flat plate, Int. J. of Phy. Sci., vol. 6, issue 6, pp.1508-1516, 2011
P. Dulal and P.S. Hiremath, “ Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium," Meccanica..Vol. 45, issue 3, pp. 415-524, 2009.