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Thermal instability induced by buoyancy and surface tension with radiative transfer

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Abstract

The onset of steady, cellular convection in a horizontal fluid layer heated from below is considered taking into account the possibility of radiative heat transfer in addition to conduction and convection. The radiation is found to have a stabilizing effect even in the presence of surface tension. The effect of surface viscosity and surface deflexion are also discussed. The coupling between the surface tension and buoyancy becomes weaker as the radiative heat transfer rate is increased.

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Abbreviations

a :

wave number

a R :

critical wavenumber for N ma=0

a M :

critical wavenumber for R=0

c v :

specific heat at constant volume

D :

d/dz

d :

depth

g :

acceleration of gravity

H :

rate of radiative heat per unit volume

I :

optical thickness of the layer

K :

absorption coefficient

k :

thermal diffusivity

M :

N ma

M*:

critical N ma when R=0

N cr :

Crispation group

N ma :

Marangoni number

N nu :

Nusselt number

N vi :

surface viscosity group

P :

pressure

R :

Rayleigh number

R*:

critical Rayleigh number for N ma=0

T m :

temperature of the upper surface

t :

time

v :

velocity vector

w :

vertical component of velocity

W :

defined in (4)

x, y, z :

rectangular co-ordinates (z-vertical)

α :

coefficient of volumetric expansion

β :

adverse temperature gradient

θ :

temperature

H :

defined in (4)

ε :

time constant

λ k :

(0, 0, 1), a unit vector in the z direction

ν :

coefficient of kinematic viscosity

ρ0:

reference value of density

σ :

Stefans constant

χ :

radiation number

References

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Authors and Affiliations

  1. Dept. of Math., Indian Inst. of Techn. Bombay, Bombay - 76, India

    C. V. Gopalakrishnan Nair & M. G. Palekar

Authors
  1. C. V. Gopalakrishnan Nair
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  2. M. G. Palekar
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Nair, C.V.G., Palekar, M.G. Thermal instability induced by buoyancy and surface tension with radiative transfer. Appl. Sci. Res. 30, 144–154 (1974). https://doi.org/10.1007/BF00386067

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  • DOI: https://doi.org/10.1007/BF00386067

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