KSME International Journal

, Volume 16, Issue 6, pp 861–869 | Cite as

Narrow band radiative solutions within a cubical enclosure filled with real gas mixtures

  • Won-Hee Park
  • Tae-Kuk Kim


Radiative transfer by nongray gas mixtures with nonuniform concentration and temperature profiles is studied by using the statistical narrow-band model and the ray-tracing method with the sufficiently accurate T60 quadrature set. Transmittances through the nonhomogeneous gas mixtures are calculated by using the Curtis-Godson approximation. Three different cases with different temperature and concentration profiles are considered to obtain benchmark solutions for the radiative transfer by nongray gas mixtures. The solutions obtained from this study are verified and found to be very well matched with the previous solutions for uniform gas mixtures. The results presented in this paper can be used as benchmark solutions in developing various solution methods for radiative transfer by nongray gas mixtures.

Key Words

Radiative Transfer Nongray Gas Ray-Tracing Method Narrow Band Model Curtis-Godson Approximation Tn Quadrature Set Nonuniform Gas 



Absorption coefficient,m -1


Blackbody fraction


Average intensity, W/(m2 · sr)


Radiative intensity, W/(m2 · sr)


System dimension,m


Total number of the discrete directions (=8N2 forTN quadrature)


Number of nodes along a path

\(\hat n\)

Unit vector normal to the wall


Partial pressure


Net radiative wall heat flux, W/m2




Absolute temperature,K

x, y, z



Angular weight form th discrete direction


μ, ξ, η

x, y, z direction cosines


Width of the band


Distance of the ray in them th discrete direction


Stefan-Boltzmann constant, 5.67 x 10-8 W/(μm · K4)









Bottom wall


Exact solution


ith band


Lower limit of the band


Maximum value


Minimum value


Order of the quadrature set


Estimation point


Side wall


Top wall


Upstream point


Upper limit of the band








Band averaged


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2003

Authors and Affiliations

  1. 1.Mechanical EngineeringChung-Ang UniversitySeoulKorea

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