MHD Chemically Reacting Viscous Fluid Flow towards a Vertical Surface with Slip and Convective Boundary Conditions
MHD chemically reacting viscous fluid flow towards
a vertical surface with slip and convective boundary conditions has
been conducted. The temperature and the chemical species
concentration of the surface and the velocity of the external flow are
assumed to vary linearly with the distance from the vertical surface.
The governing differential equations are modeled and transformed
into systems of ordinary differential equations, which are then solved
numerically by a shooting method. The effects of various parameters
on the heat and mass transfer characteristics are discussed. Graphical
results are presented for the velocity, temperature, and concentration
profiles whilst the skin-friction coefficient and the rate of heat and
mass transfers near the surface are presented in tables and discussed.
The results revealed that increasing the strength of the magnetic field
increases the skin-friction coefficient and the rate of heat and mass
transfers toward the surface. The velocity profiles are increased
towards the surface due to the presence of the Lorenz force, which
attracts the fluid particles near the surface. The rate of chemical
reaction is seen to decrease the concentration boundary layer near the
surface due to the destructive chemical reaction occurring near the
surface.
[1] S. Y. Ibrahim and O.D. Makinde, Chemically Reacting MHD Boundary
Layer Flow of Heat and Mass Transfer past a Low-Heat-Resistant Sheet
moving vertically downwards, Sci. Res. & Essays, 6(22): 4762 – 4775
(2011).
[2] S.Y. Ibrahim and O.D. Makinde, Chemically Reacting MHD Boundary
Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate
with Suction, Sci. Res. & Essays, 5(19): 2875 – 2882 (2010).
[3] K. Cao and J. Baker, Slip effects on mixed convective flow and heat
transfer from a vertical plate”, Int. J. Heat Mass Transf., Vol. 52 Nos 15-
16, pp. 3829-3841 (2009).
[4] J. Zhu, L.C. Zheng and Z.G. Zhang, Analytical solution to stagnationpoint
flow and heat transfer over a stretching sheet based on homotopy
analysis”, Appl. Math. Mech. Engl. Ed., Vol. 30, No. 4, pp. 463-474
(2009).
[5] I. A. Hassanien and R. S. R. Gorla, Combined forced and free
convection in stagnation flows of micropolar fluids over vertical nonisothermal
surfaces”, Int. J. Eng. Sci., Vol. 28 No. 8, pp. 783-792
(1990).
[6] C. Y. Wang, Stagnation slip flow and heat transfer on a moving plate”,
Chem. Eng. Sci., Vol. 61 No. 23, pp. 7668-7672 (2006).
[7] S. A. Kechil, I. Hashim, Series solution of flow over nonlinearly
stretching sheet with chemical reaction and magnetic field, Physics
Letters B, 372, 2258-2263 (2008).
[8] J. Zhu, L.C. Zheng and Z.G. Zhang, The effect of the slip condition on
the MHD stagnation-point over a power-law stretching sheet, Appl.
Math. Mech. Vol. 31 No.4, pp.439-448 (2010).
[9] O. D. Makinde, Computational modeling of MHD unsteady flow and
heat transfer over a flat plate with Navier slip and Newtonian heating”,
Brazilian J. Chem. Eng., Vol.29 No.1, pp.159-166, (2012).
[10] O. D. Makinde and P. Sibanda, Effects of chemical reaction on boundary
layer flow past a vertical stretching surface in the presence of internal
heat generation, Inter. J. of Num. Methods for Heat & Fluid Flow, Vol.
21 No. 6, pp. 779-792, (2011).
[11] C. Michele and C. Fabrizio, Influence of a magnetic field on liquid metal
free convection in an internally heated cubic enclosure, Int. J. of Num.
Methods for Heat & Fluid Flow, Vol. 12 No. 6, pp. 687-715 (2002).
[12] S.R.G. Rama, A. Slaouti and H.S. Takhar, Mixed convection in non-
Newtonian fluids along a vertical plate in porous media with surface
mass transfer, Int. J. of Num. Methods for Heat and Fluid Flow, Vol. 7
No. 6, pp. 598-608 (1997).
[13] E. M. Arthur, Y. I. Seini and A. Seidu, On chemically reacting
hydromagnetic flow over a flat surface in the presence of radiation with
viscous dissipation and convective boundary conditions, American J.
Appl. Maths; 2(5): 179-185 (2014).
[14] E. M. Arthur and Y. I. Seini, MHD thermal stagnation point-flow
towards a stretching porous surface, Math. Theory and Modeling, Vol.4,
No.5, 163 – 169 (2014).
[15] 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”. Int. J. Comp.
& Appl. Maths, 9(2), 101-118 (2014).
[16] 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, Int. J. Num. Methods and Fluid Flow; 24(3): 643 – 653
(2014).
[17] Y. Y. Lok, N. Amin and I. Pop, Unsteady mixed convection flow of a
micropolar fluid near the stagnation-point on a vertical surface, Int. J.
Therm. Sci., Vol. 45 No. 12, pp. 1149-1157 (2006).
[1] S. Y. Ibrahim and O.D. Makinde, Chemically Reacting MHD Boundary
Layer Flow of Heat and Mass Transfer past a Low-Heat-Resistant Sheet
moving vertically downwards, Sci. Res. & Essays, 6(22): 4762 – 4775
(2011).
[2] S.Y. Ibrahim and O.D. Makinde, Chemically Reacting MHD Boundary
Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate
with Suction, Sci. Res. & Essays, 5(19): 2875 – 2882 (2010).
[3] K. Cao and J. Baker, Slip effects on mixed convective flow and heat
transfer from a vertical plate”, Int. J. Heat Mass Transf., Vol. 52 Nos 15-
16, pp. 3829-3841 (2009).
[4] J. Zhu, L.C. Zheng and Z.G. Zhang, Analytical solution to stagnationpoint
flow and heat transfer over a stretching sheet based on homotopy
analysis”, Appl. Math. Mech. Engl. Ed., Vol. 30, No. 4, pp. 463-474
(2009).
[5] I. A. Hassanien and R. S. R. Gorla, Combined forced and free
convection in stagnation flows of micropolar fluids over vertical nonisothermal
surfaces”, Int. J. Eng. Sci., Vol. 28 No. 8, pp. 783-792
(1990).
[6] C. Y. Wang, Stagnation slip flow and heat transfer on a moving plate”,
Chem. Eng. Sci., Vol. 61 No. 23, pp. 7668-7672 (2006).
[7] S. A. Kechil, I. Hashim, Series solution of flow over nonlinearly
stretching sheet with chemical reaction and magnetic field, Physics
Letters B, 372, 2258-2263 (2008).
[8] J. Zhu, L.C. Zheng and Z.G. Zhang, The effect of the slip condition on
the MHD stagnation-point over a power-law stretching sheet, Appl.
Math. Mech. Vol. 31 No.4, pp.439-448 (2010).
[9] O. D. Makinde, Computational modeling of MHD unsteady flow and
heat transfer over a flat plate with Navier slip and Newtonian heating”,
Brazilian J. Chem. Eng., Vol.29 No.1, pp.159-166, (2012).
[10] O. D. Makinde and P. Sibanda, Effects of chemical reaction on boundary
layer flow past a vertical stretching surface in the presence of internal
heat generation, Inter. J. of Num. Methods for Heat & Fluid Flow, Vol.
21 No. 6, pp. 779-792, (2011).
[11] C. Michele and C. Fabrizio, Influence of a magnetic field on liquid metal
free convection in an internally heated cubic enclosure, Int. J. of Num.
Methods for Heat & Fluid Flow, Vol. 12 No. 6, pp. 687-715 (2002).
[12] S.R.G. Rama, A. Slaouti and H.S. Takhar, Mixed convection in non-
Newtonian fluids along a vertical plate in porous media with surface
mass transfer, Int. J. of Num. Methods for Heat and Fluid Flow, Vol. 7
No. 6, pp. 598-608 (1997).
[13] E. M. Arthur, Y. I. Seini and A. Seidu, On chemically reacting
hydromagnetic flow over a flat surface in the presence of radiation with
viscous dissipation and convective boundary conditions, American J.
Appl. Maths; 2(5): 179-185 (2014).
[14] E. M. Arthur and Y. I. Seini, MHD thermal stagnation point-flow
towards a stretching porous surface, Math. Theory and Modeling, Vol.4,
No.5, 163 – 169 (2014).
[15] 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”. Int. J. Comp.
& Appl. Maths, 9(2), 101-118 (2014).
[16] 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, Int. J. Num. Methods and Fluid Flow; 24(3): 643 – 653
(2014).
[17] Y. Y. Lok, N. Amin and I. Pop, Unsteady mixed convection flow of a
micropolar fluid near the stagnation-point on a vertical surface, Int. J.
Therm. Sci., Vol. 45 No. 12, pp. 1149-1157 (2006).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:70954", author = "Ibrahim Yakubu Seini and Oluwole Daniel Makinde", title = "MHD Chemically Reacting Viscous Fluid Flow towards a Vertical Surface with Slip and Convective Boundary Conditions", abstract = "MHD chemically reacting viscous fluid flow towards
a vertical surface with slip and convective boundary conditions has
been conducted. The temperature and the chemical species
concentration of the surface and the velocity of the external flow are
assumed to vary linearly with the distance from the vertical surface.
The governing differential equations are modeled and transformed
into systems of ordinary differential equations, which are then solved
numerically by a shooting method. The effects of various parameters
on the heat and mass transfer characteristics are discussed. Graphical
results are presented for the velocity, temperature, and concentration
profiles whilst the skin-friction coefficient and the rate of heat and
mass transfers near the surface are presented in tables and discussed.
The results revealed that increasing the strength of the magnetic field
increases the skin-friction coefficient and the rate of heat and mass
transfers toward the surface. The velocity profiles are increased
towards the surface due to the presence of the Lorenz force, which
attracts the fluid particles near the surface. The rate of chemical
reaction is seen to decrease the concentration boundary layer near the
surface due to the destructive chemical reaction occurring near the
surface.", keywords = "Boundary layer, surface slip, MHD flow, chemical
reaction, heat transfer, mass transfer.", volume = "9", number = "10", pages = "592-7", }