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Laminar convection with an absorbing and emitting gas

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Abstract

The heat transfer and fluid flow are determined for fully developed laminar flow in a vertical channel. The effects of natural and forced convection and thermal radiation are included in the analysis. The spectral variation of the radiation properties are included through the use of the total band absorptance. The analysis is general and specific numerical results have been obtained for the 15 micron band of carbon dioxide. A simplified approach for large path is also presented which is in excellent agreement with the more exact results.

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Abbreviations

a, b :

exponential kernel approximation (0.9, 1.8, respectively)

c p :

specific heat at constant pressure

e ω :

black body spectral emissivity

f 2 :

pressure broadening parameter

g :

acceleration of gravity

K T :

thermal conductivity

k ω :

spectral absorption coefficient

L :

channel spacing

p :

static fluid pressure

q R :

radiant heat flux

q1, total:

total wall heat flux = (q1, conduction) with rad. present +q1, radiation

Ra :

Rayleigh =βgL 3 τ/να

T :

fluid temperature

u :

axial velocity

\(\bar u\) :

non-dimensional velocity

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} \) :

optical depth =C 20 ρ LY

x :

axial coordinate

y :

transverse coordinate

Y :

non-dimensional transverse coordinate

α :

thermal diffusivity

β :

thermal coefficient of volume expansivity

γ :

\( - \left( {\frac{1}{{\rho 0}}\frac{{\partial p}}{{\partial x}} + g} \right)\frac{{L^3 }}{{v\alpha }}\)

μ :

direction cosine

ν :

kinematic viscosity

ρ :

mass density

τ :

=L(dT 1/dx)

φ :

=(T 1−T)/τγ

0:

evaluated at origin

1:

evaluated at wall

ωc :

evaluated at band center

m :

mean value

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Authors and Affiliations

  1. Univ. of California, Berkeley

    T. E. Donovan & R. Greif

  2. Dept. of Mech. Eng., 94720, Berkeley, California, U.S.A.

    T. E. Donovan & R. Greif

Authors
  1. T. E. Donovan
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  2. R. Greif
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Donovan, T.E., Greif, R. Laminar convection with an absorbing and emitting gas. Appl. Sci. Res. 31, 110–122 (1975). https://doi.org/10.1007/BF01795830

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  • DOI: https://doi.org/10.1007/BF01795830

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