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Hydromagnetic natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion

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Acta Physica Academiae Scientiarum Hungaricae

Abstract

Natural convection of an electrically conducting fluid produced by the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and chemical species in the presence of a uniform transverse magnetic field is discussed. On thermal boundary layer thickness, concentration boundary layer thicknessX t andX c have been calculated for different values of Prandtl number. A direct relation between the film thickness and distance travelled is presented and it is found that the film thickness approaches the uniform film thickness asymptotically.

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Abbreviations

u :

velocity component inx-direction

v :

velocity component iny-direction

x :

vertical distance along the surface

y :

horizontal distance from the surface

α:

thermal molecular diffusivity

β:

volumetric coefficient of thermal expansion

β* :

volumetric coefficient of expansion with concentration

ϱ:

fluid density

δ(x):

boundary layer thickness for velocity

η:

dimensionless distance from the wall (=y/ϱ(x))

μ:

dynamic viscosity of the fluid

v :

kinematic viscosity of the fluid

g :

acceleration due to gravity

δ t (x):

boundary layer thickness for temperature

δ c (x):

boundary layer thickness for concentration

σ:

electric conductivity (assumed to be constant)

q :

flow rate per unit width of wall

C :

nondimensional species concentration

Pr :

Prandtl number (v/α)

Sc :

Schmidt number (v/D)

D :

chemical molecular diffusivity

F x :

component of the magnetic body force (—σu B 20 )

V:

the velocity vector with componentsu andv

J:

the current density

F:

Lorentz body force

E:

electric field

Gr :

Grashof number

T :

fluid temperature

Δ:

Gr+Gr′

Le :

Lewis number (Sc/Pr)

Δ m :

dimensionless symbol

X :

dimensionless length

0:

at the surface

∞:

in the undisturbed fluid

p :

at the plate surface

t :

based on temperature

c :

based on species concentration

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Authors and Affiliations

  1. Applied Mathematics Section, Institute of Technology, Banaras hindu University, 221 005, Varanasi, India

    P. C. Ram, S. S. Singh & H. L. Agarwal

Authors
  1. P. C. Ram
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  2. S. S. Singh
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  3. H. L. Agarwal
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Ram, P.C., Singh, S.S. & Agarwal, H.L. Hydromagnetic natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Acta Physica 42, 49–57 (1977). https://doi.org/10.1007/BF03157198

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  • DOI: https://doi.org/10.1007/BF03157198

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