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Wärme - und Stoffübertragung

, Volume 3, Issue 2, pp 114–119 | Cite as

Nongrey radiant heat transfer corrections to thermal conductivity measurements

  • W. Leidenfrost
  • R. J. Latko
Article

Abstract

A numerical investigation is presented to determine the influence of radiative transfer on experimental thermal conductivity measurements. The analysis is simplified by approximating the thermal conductivity test cell configuration by a parallel plate model. The problem is rigorously formulated in terms of a nonlinear integrodifferential equation, and the solution is obtained by the method of successive approximations. Both grey and nongrey results are presented. For water vapor at atmospheric pressure and 700 ‡K, it is shown that radiative transfer between black surfaces may affect thermal conductivity measurements by 35 percent.

Keywords

Heat Transfer Water Vapor Radiative Transfer Successive Approximation Radiant Heat Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Dn

Integral of the normalized Planck function defined by Eq. (10)

Eb

Blackbody emissive power

En

Exponential integral function defined by Eq. (5)

Ii

Integral defined by Eq. (22)

I0

Integral defined by Eq. (23)

k

Thermal conductivity of test fluid

L

Spacing between plates

N

Dimensionless conduction-radiation interaction parameter kx/4n2σT i 3

n

Index of refraction

qr

Radiative heat flux

qt

Total (conductive+radiative) heat flux

R

Radiosity or radiant energy leaving (emitted+reflected) a surface

sgn(x)

Sign functionx > 0, sgn(x)=1x < 0, sgn(x)=− 1

T

Temperature

T

Average temperature between plates

δT

Temperature difference between plates

t

Dummy integration variable

y

Position coordinate

Greek symbols

α

Magnitude of nongrey band, ϰλp

ɛ

Emissivity

θ

Nondimensional temperature,T/T i

ϰλ

Spectral absorption coefficient

xp

Planck mean absorption coefficient defined by Eq. (11)

λ

Wavelength

ξ

Dimensionless distance,y/L

σ

Stefan-Boltzmann constant

τλ

Optical depth defined by Eq. (3)

τ0,λ

Optical thickness defined by Eq. (4)

Φ

Dimensionless radiation flux,q r /n 2 σT i 4

χ

Dimensionless radiosity,R/n2σT i 4

ψ, Ω

Functions defined by Eq. (26)

Subscripts

i

wall aty=0

o

wall aty=L

Superscripts

n

nth frequency interval

Zusammenfassung

Der Strahlungseinflu\ auf die experimentelle Bestimmung der Wärmeleitzahl wird untersucht für den vereinfachten Fall einer Plattenapparatur. Das Problem wird durch eine nichtlineare Integral-Differentialgleichung beschrieben, die nach der Methode der schrittweisen AnnÄherung gelöst wird. Ergebnisse werden sowohl für graue als auch nicht graue Versuchskörper angegeben. Für Wasserdampf unter normalem Druck wird gezeigt, da\ die Strahlung die Wärmeleitzahlmessungen in einer Apparatur mit schwarzen Wänden bis zu 35% beeinflussen kann.

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References

  1. 1.
    Leidenfrost, W.: An attempt to measure the thermal conductivity of liquids, gases and vapors with a high degree of accuracy over wide ranges of temperature (−180 to 500 ‡C) and pressure (vacuum to 500 atm). Intern. J. Heat Mass Transfer 7 (1964) p. 447.Google Scholar
  2. 2.
    Kohler, M.: Einflu\ der Strahlung auf den Wärmetransport durch eine Flüssigkeitsschicht. Angew. Phys. 18 (1965) p. 356.Google Scholar
  3. 3.
    Poltz, H.: Die WärmeleitfÄhigkeit von Flüssigkeiten II. Der Strahlungsanteil der effektiven WärmeleitfÄhigkeit. Intern. J. Heat Mass Transfer 8 (1965) p. 515.Google Scholar
  4. 4.
    Tien, C. L.: Thermal radiation properties of gases. In Advances in Heat Transfer Vol. 5, New York Academic Press (1968) p. 253.Google Scholar
  5. 5.
    Cess, R. D., P. Mighdoll andS. N. Tiwari: Infrared radiation heat transfer in nongray gases. Intern. J. Heat Mass Transfer 10 (1967) p. 1521.Google Scholar
  6. 6.
    Hildebrand, F. B.: Introduction to Numerical Analysis, New York: McGraw-Hill, Inc. 1956.Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • W. Leidenfrost
    • 1
  • R. J. Latko
    • 2
  1. 1.Purdue UniversityLafayette
  2. 2.Systems, Science and SoftwareLa Jolla

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