Meccanica

, Volume 46, Issue 5, pp 1103–1112 | Cite as

Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate

Article

Abstract

In this paper, the steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of an incompressible, viscous and electrically conducting fluid over a stretching vertical flat plate is theoretically investigated with Hall effects taken into account. The governing equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the magnetic parameter, the Hall parameter and the buoyancy parameter on the velocity profiles, the cross flow velocity profiles and the temperature profiles are presented graphically and discussed. Investigated results indicate that the Hall effect on the temperature is small, and the magnetic field and Hall currents produce opposite effects on the shear stress and the heat transfer at the stretching surface.

Keywords

Stretched flat plate Hall effect Magnetohydrodynamic Mixed convection Boundary layer 

Nomenclature

a,c

constants

B0

the strength of the imposed magnetic field

Cfx

skin friction coefficient in x-direction

Cfz

skin friction coefficient in z-direction

e

electric charge (C)

f

dimensionless stream function

g

acceleration due to gravity (m s−2)

Grx

local Grashof number

H0

external magnetic field

m

Hall parameter

me

the mass of an electron (kg)

M

magnetic parameter

ne

electron number density

Pr

Prandtl number

Rex

local Reynolds number

T

fluid temperature (K)

Te

electron collision time (s)

Tw

surface temperature (K)

T

ambient temperature (K)

u,v,w

velocity components along the x, y and z directions, respectively (m s−1)

uw(x)

velocity of the stretching plate (m s−1)

x,y,z

Cartesian coordinates along the stretching surface, normal to it, and transverse to the xy plane, respectively (m)

Greek Letters

α

thermal diffusivity (m2 s−1)

β

thermal expansion coefficient (1/K)

λ

constant buoyancy or mixed convection parameter

θ

dimensionless temperature

ν

kinematic viscosity (m2 s−1)

μ

dynamic viscosity (kg m−1 s−1)

μe

magnetic permeability (H m−1)

ρ

fluid density (kg m−3)

τw

wall shear stress (Pa)

Subscripts

w

condition at the surface

ambient condition

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Banks WHH, Zaturska MB (1986) Eigensolutions in boundary-layer flow adjacent to a stretching wall. IMA J Appl Math 36:263–273 MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Sparrow EM, Abraham JP (2005) Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid. Int J Heat Mass Transf 48:3047–3056 CrossRefMATHGoogle Scholar
  3. 3.
    Abraham JP, Sparrow EM (2005) Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface. Int J Heat Fluid Flow 26:289–295 CrossRefGoogle Scholar
  4. 4.
    Lakshmisha KN, Venkateswaran S, Nath G (1988) Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface. J Heat Transf 110:590–595 CrossRefGoogle Scholar
  5. 5.
    Kumari M, Takhar HS, Nath G (1990) MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux. Wärme- Stoffübertrag 25:331–336 ADSCrossRefGoogle Scholar
  6. 6.
    Taylor GI (1959) The dynamics of thin sheets of fluid. Proc R Soc A 253:289–295 ADSCrossRefMATHGoogle Scholar
  7. 7.
    Stuart JT (1966) Double boundary layers in oscillatory viscous flow. J Fluid Mech 24:673–687 ADSMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Moffatt HK (1982) High frequency excitation of liquid metal systems. In: IUTAM symposium: metallurgical applications of magnetohyrodynamics, Cambridge Google Scholar
  9. 9.
    Sakiadis BC (1961) Boundary-layer behaviour on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 7:26–28 CrossRefGoogle Scholar
  10. 10.
    Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645–647 CrossRefGoogle Scholar
  11. 11.
    Sato H (1961) The Hall effect in the viscous flow of ionized gas between parallel plates under transverse magnetic field. J Phys Soc Jpn 16:1427–1433 ADSCrossRefMATHGoogle Scholar
  12. 12.
    Sutton GW, Sherman A (1965) Engineering magnetohydrodynamics. McGraw-Hill, New York Google Scholar
  13. 13.
    Pop I (1971) The effect of Hall currents on hydromagnetic flow near an accelerated plate. J Math Phys Sci 5:375–385 MATHGoogle Scholar
  14. 14.
    Raptis A, Ram PC (1984) Effects of Hall current and rotation. Astrophys Space Sci 106:257–264 ADSCrossRefMATHGoogle Scholar
  15. 15.
    Hossain MA, Rashid RIMA (1987) Hall effect on hydromagnetic free convection flow along a porous flat plate with mass transfer. J Phys Soc Jpn 56:97–104 ADSCrossRefGoogle Scholar
  16. 16.
    Watanabe T, Pop I (1995) Hall effects on magnetohydrodynamic boundary layer flow over a continuous moving flat plate. Acta Mech 108:35–47 CrossRefMATHGoogle Scholar
  17. 17.
    Gupta AS, Takhar HS (2003) Hall effects on MHD flow and heat transfer over a stretching surface. J Appl Mech Eng 8(2):219–232 MATHGoogle Scholar
  18. 18.
    Pop I, Ghosh SK, Nandi DK (2001) Effects of the Hall current on free and forced convection flows in a rotating channel in the presence of an inclined magnetic field. Magnetohydrodynamics 37(4):348–359 ADSGoogle Scholar
  19. 19.
    Ghosh SK, Pop I (2003) Hall effects on unsteady hydromagnetic flow in a rotating system with oscillating pressure gradient. Int J Appl Mech Eng 8(1):43–56 MATHGoogle Scholar
  20. 20.
    Ezzat M, Zakaria M, Moursy M (2004) Magnetohydrodynamic boundary layer flow past a stretching plate and heat transfer. J Appl Math 1:9–21 MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Zakaria M (2004) Magnetohydrodynamic viscoelastic boundary layer flow past a stretching plate and heat transfer. Appl Math Comput 155:165–177 MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Yih KA (1999) Free convection effect on MHD coupled heat and mass transfer of a moving permeable vertical surface. Int Commum Heat Mass Transf 26:95–104 CrossRefGoogle Scholar
  23. 23.
    Abo-Eldahab EM (2005) Hydromagnetic three-dimensional flow over a stretching surface with heat and mass transfer. Heat Mass Transf 41:734–743 ADSCrossRefGoogle Scholar
  24. 24.
    Ishak A, Nazar R, Pop I (2006) Magnetohydrodynamic stagnation-point flow towards a stretching vertical sheet. Magnetohydrodynamics 42(1):77–90 ADSMATHGoogle Scholar
  25. 25.
    Ishak A, Nazar R, Pop I (2007) Magnetohydrodynamic stagnation-point flow towards a stretching vertical sheet in a micropolar fluid. Magnetohydrodynamics 43(1):83–97 ADSMathSciNetGoogle Scholar
  26. 26.
    Hossain MA (1986) Effect of Hall current on unsteady hydromagnetic free convection flow near an infinite vertical porous plate. J Phys Soc Jpn 55(7):2183–2190 ADSCrossRefGoogle Scholar
  27. 27.
    Hossain MA, Mahammad K (1988) Effect of Hall current on hydromagnetic free convection flow near an accelerated porous plate. Jpn J Appl Phys 27(8):1531–1535 ADSCrossRefGoogle Scholar
  28. 28.
    Ram PC (1988) Hall effect on free convective flow and mass transfer through a porous medium. Wärme- Stoffübertrag 22:223–225 ADSCrossRefGoogle Scholar
  29. 29.
    Megahed AA, Komy SR, Afify AA (2003) Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate. Int J Non-Linear Mech 38:513–520 CrossRefMATHGoogle Scholar
  30. 30.
    Abo-Eldahab EM, Abd El-Aziz M, Salem AM, Jaber KK (2007) Hall currenteffect on MHD mixed convection flow from an inclined continuously stretching surface with blowing/suction and internal heat generation/absorption. Appl Math Model 31:1829–1846 CrossRefMATHGoogle Scholar
  31. 31.
    Salem AM, Abd El-Aziz M (2008) Effect of Hall currents and chemical reaction on a hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption. Appl Math Model 32(7):1236–1254 MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Ghosh SK, Anwar Bég O, Narahari M (2009) Hall effects on MHD flow in a rotating system with heat transfer characteristics. Meccanica 44:741–765 MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Abd El-Aziz M (2010) Flow and heat transfer over an unsteady stretching surface with Hall effect. Meccanica 45:97–109 MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Cowling TG (1957) Magnetohydrodynamics. Interscience, New York MATHGoogle Scholar
  35. 35.
    Cebeci T, Bradshaw P (1988) Physical and computational aspects of convective heat transfer. Springer, New York CrossRefMATHGoogle Scholar
  36. 36.
    Ishak A, Nazar R, Pop I (2008) Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat Mass Transf 44:921–927 ADSCrossRefGoogle Scholar
  37. 37.
    Grubka LJ, Bobba KM (1985) Heat transfer characteristics of a continuous stretching surface with variable temperature. ASME J Heat Transf 107:248–250 CrossRefGoogle Scholar
  38. 38.
    Ali ME (1994) Heat transfer characteristics of a continuous stretching surface. Wärme- Stoffübertr 29:227–234 ADSCrossRefGoogle Scholar
  39. 39.
    Schlichting H, Gersten K (2000) Boundary layer theory. Springer, Berlin CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversiti Putra MalaysiaUPM SerdangMalaysia
  2. 2.School of Mathematical Sciences, Faculty of Science & TechnologyUniversiti Kebangsaan MalaysiaUKM BangiMalaysia
  3. 3.Department of Mathematics & Institute for Mathematical ResearchUniversiti Putra MalaysiaUPM SerdangMalaysia
  4. 4.Faculty of MathematicsUniversity of ClujClujRomania

Personalised recommendations