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Magnetohydrodynamic Free Convective Flow Past an Infinite Vertical Porous Plate with Magnetic Induction

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Abstract

The steady two-dimensional magnetohydrodynamic free convective laminar flow of an electrically conducting, viscous and incompressible fluid with finite electrical conductivity past an infinite heated vertical porous plate has been investigated. The coupled ordinary differential equations governing the velocity, the temperature and induced magnetic field distributions are solved analytically. The effects of Prandtl number (P r ), Grashof number (Gr), magnetic field parameter (M), and suction parameter (\( \overline{V}_{0} \)) on the flow field are analysed using graphs. The study reveals that the increase of the Prandtl number (Pr) and the suction velocity (\( \overline{V}_{0} \)) lead to a decrease in the temperature, velocity and the induced magnetic field in the boundary layer region whereas increase in Grashof number and magnetic field parameter lead to increased induced magnetic field.

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Abbreviations

C p :

Specific heat at constant pressure

η :

Non-dimensional distance

Gr :

Grashof number

g :

Gravitational acceleration

\( \overrightarrow {H} \) :

Magnetic field

\( \overrightarrow {H}_{0} \) :

Applied magnetic field

\( H_{x} \) :

Induced magnetic field in the x-direction

\( \overrightarrow {H}_{x} \) :

Non-dimensional induced magnetic field

k :

Thermal conductivity

L :

Characteristic length

M :

Magnetic field parameter

μ :

Coefficient of viscosity

μ B :

Magnetic permeability

υ :

Kinematic viscosity

P m :

Magnetic Prandtl number

Pr :

Prandtl number

ρ :

Density of the fluid

σ :

Electrical conductivity of the fluid

T :

Dimensional temperature

T w :

Temperature at the wall

T ∞ :

Temperature at the free stream

Θ:

Non-dimensional temperature

u :

Velocity in the x-direction

\( \overline{u} \) :

Non-dimensional velocity in the x-axis direction

v :

Velocity in the y-direction

\( \overrightarrow {V} \) :

Velocity vector

V 0 :

Suction velocity

\( \overline{V}_{0} \) :

Suction parameter

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, P.O. Box 62000-00200, Nairobi, Kenya

    J. K. Kwanza

  2. Department of Mathematics and Computer Science, Catholic University of Eastern Africa, P.O. Box 62157-00200, Nairobi, Kenya

    J. A. Balakiyema

Authors
  1. J. K. Kwanza
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  2. J. A. Balakiyema
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Correspondence to J. K. Kwanza.

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Kwanza, J.K., Balakiyema, J.A. Magnetohydrodynamic Free Convective Flow Past an Infinite Vertical Porous Plate with Magnetic Induction. J Fusion Energ 31, 352–356 (2012). https://doi.org/10.1007/s10894-011-9475-3

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  • DOI: https://doi.org/10.1007/s10894-011-9475-3

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