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Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

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Abstract

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.

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Abbreviations

B 0 :

magnetic induction

C fx :

local skin friction

e :

electronic charge

g :

gravitational acceleration

Gr x :

modified Grashof number

J :

electric current density

m :

Hall parameter

M :

magnetic parameter

κ :

thermal conductivity

τ :

collision time of electrons with ions

Nu x :

local Nusselt number

p :

pressure

Pr :

Prandtl number

T :

temperature of the fluid

T ∞ :

free stream temperature

x,y,z :

coordinate directions

u,υ,w :

velocity components in the x-, y, and z-directions

V 0 :

transpiration velocity

q″w :

uniform wall heat flux

ω :

cyclotron frequency of electron

α :

thermal diffusivity

β :

volumetric expansion coefficient for temperature

ψ :

stream function

θ :

dimensionless temperature function

ρ :

density

ν :

kinematic viscosity

µ:

dynamic viscosity

ζ :

local transpiration parameter

η :

pseudo similarity variable

w:

conditions at wall

∞:

conditions far away from wall

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Authors and Affiliations

  1. Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    L. K. Saha

  2. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, 44000, Pakistan

    S. Siddiqa & M. A. Hossain

Authors
  1. L. K. Saha
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  2. S. Siddiqa
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  3. M. A. Hossain
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Correspondence to M. A. Hossain.

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Saha, L.K., Siddiqa, S. & Hossain, M.A. Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux. Appl. Math. Mech.-Engl. Ed. 32, 1127–1146 (2011). https://doi.org/10.1007/s10483-011-1487-9

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  • DOI: https://doi.org/10.1007/s10483-011-1487-9

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