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

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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.

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Abbreviations

a,c :

constants

B 0 :

the strength of the imposed magnetic field

C fx :

skin friction coefficient in x-direction

C fz :

skin friction coefficient in z-direction

e :

electric charge (C)

f :

dimensionless stream function

g :

acceleration due to gravity (m s−2)

Gr x :

local Grashof number

H 0 :

external magnetic field

m :

Hall parameter

m e :

the mass of an electron (kg)

M :

magnetic parameter

n e :

electron number density

Pr :

Prandtl number

Re x :

local Reynolds number

T :

fluid temperature (K)

T e :

electron collision time (s)

T w :

surface temperature (K)

T ∞ :

ambient temperature (K)

u,v,w :

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

u w (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)

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)

μ e :

magnetic permeability (H m−1)

ρ :

fluid density (kg m−3)

τ w :

wall shear stress (Pa)

w :

condition at the surface

∞:

ambient condition

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Authors and Affiliations

  1. Department of Mathematics, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia

    F. M. Ali

  2. School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor, Malaysia

    R. Nazar

  3. Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia

    N. M. Arifin

  4. Faculty of Mathematics, University of Cluj, 3400, Cluj, CP 253, Romania

    I. Pop

Authors
  1. F. M. Ali
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  2. R. Nazar
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  3. N. M. Arifin
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  4. I. Pop
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Correspondence to R. Nazar.

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Ali, F.M., Nazar, R., Arifin, N.M. et al. Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate. Meccanica 46, 1103–1112 (2011). https://doi.org/10.1007/s11012-010-9371-3

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  • DOI: https://doi.org/10.1007/s11012-010-9371-3

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