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Heat transfer to laminar flow of nongray gases through a circular tube

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Abstract

Analyses are presented for infrared radiative energy transfer in gases when other modes of energy transfer simultaneously occur. Fully developed laminar flow of an absorbing emitting gas in a circular tube is considered under the conditions of uniform wall heat flux. Nongray as well as gray formulations are presented, and results are obtained for illustrative cases. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. The influence of variable wall emittance (gray and nongray) upon radiative energy transfer in nongray gases is investigated. In particular, nongray results are obtained, in the large path length limit, for the flow of CO2 through stainless steel tubes of various compositions. Finally, a correlation is presented which can be utilized to extend all nongray results for the parallel plate geometry, already available in literature, to yield results for the corresponding case of a circular tube.

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Abbreviations

A, A i :

total band absorptance, cm−1

A 0, A 0i :

correlation quantity, cm−1

Ā, Ā i :

dimensionless band absorptance, A i /A 0i

B 2, B 2 i :

correlation quantity

B w (T w ):

spectral surface radiosity (watts - cm−2)/cm−1

C 20 , C 20i :

correlation quantity, atm−1 cm−1

D :

diameter of a circular tube, cm

e w :

Planck's function (watts-cm−2)/cm−1

e wc , e wi :

Planck's function evaluated at the band center

e wc (T w ):

Planck's function evaluated at temperature T w

M 2 :

quantity defined by (16)

N :

quantity defined by (15)

P :

pressure, atm

q :

wall heat flux, watts/cm2

q R :

total radiative heat flux, watts/cm2

\(qRw,{\text{ }}qRwi\) :

spectral radiative flux (watts-cm−2)/cm−1

r :

physical coordinate for circular tube

r 0 :

radius of the tube

T :

temperature, K

T 1, T w :

wall temperature, K

T b :

bulk temperature, K

u, u i :

dimensionless coordinate, C 20 Pr

u 0, u 0i :

dimensionless path length, C 20 Pr 0

v x :

velocity, cm/sec

v m :

mean velocity

β, β i :

line structure parameter

γ 2 :

quantity defined by (15)

ɛ,ɛ i ,ɛ ω :

surface emittance

θ T :

dimensionless temperature (2)

θ bT :

dimensionless bulk temperature (11)

K w :

equilibrium spectral absorption coefficient, cm−1

κ P :

Planck mean coefficient, cm−1

ξ :

dimensionless coordinate, r/r 0

σ :

Stefan-Boltzmann constant

τ 0 :

optical thickness, κ P r 0 or κ P D

ω c , ω i :

wave number at the band center, cm−1

References

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Author notes

  1. S. N. Tiwari

    Present address: , ODU- VARC Campus 12070 Jefferson Avenue, 23 606, Newport News, Va., USA

Authors and Affiliations

  1. College of Engineering, State University of New York, 11790, Stony Brook, N.Y., USA

    S. N. Tiwari & R. D. Cess

Authors
  1. S. N. Tiwari
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  2. R. D. Cess
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Additional information

This work was supported by the National Science Foundation through Grant No. GK-16755.

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Tiwari, S.N., Cess, R.D. Heat transfer to laminar flow of nongray gases through a circular tube. Appl. Sci. Res. 25, 155–170 (1972). https://doi.org/10.1007/BF00382292

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  • DOI: https://doi.org/10.1007/BF00382292

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