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Research Papers: Radiative Heat Transfer

Application of the WSGG Model to Solve the Radiative Transfer in Gaseous Systems With Nongray Boundaries

[+] Author and Article Information
Roberta Juliana Collet da Fonseca

Department of Mechanical Engineering,
Federal University of Rio Grande do Sul,
Sarmento Leite Street, 425,
Porto Alegre 90050-170, RS, Brazil
e-mail: roberta.fonseca@ufrgs.br

Guilherme Crivelli Fraga

Department of Mechanical Engineering,
Federal University of Rio Grande do Sul,
Sarmento Leite Street, 425,
Porto Alegre 90050-170, RS, Brazil
e-mail: guilhermecfraga@ufrgs.br

Rogério Brittes da Silva

Academic Coordination of Cachoeira do Sul,
Federal University of Santa Maria,
Ernesto Barros Street, 1345,
Cachoeira do Sul 96506-322, RS, Brazil
e-mail: rogerio.silva@ufsm.br

Francis Henrique Ramos França

Department of Mechanical Engineering,
Federal University of Rio Grande do Sul,
Sarmento Leite Street, 425,
Porto Alegre 90050-170, RS, Brazil
e-mail: frfranca@mecanica.ufrgs.br

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 11, 2017; final manuscript received October 16, 2017; published online February 21, 2018. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 140(5), 052701 (Feb 21, 2018) (10 pages) Paper No: HT-17-1205; doi: 10.1115/1.4038548 History: Received April 11, 2017; Revised October 16, 2017

This paper presents a methodology for the application of the weighted-sum-of-gray-gases (WSGG) model to systems where the medium is bounded by nongray surfaces. The method relies on the assumption that each gray gas absorption coefficient is randomly spread across the entire wavenumber spectrum. It follows that, in the spectral integration of the radiative transfer equation (RTE), the local emission term can be computed by the joint probability of emission from the subsections of the spectrum related to each gray gas coefficient and from each wall emissivity band. One advantage of the proposed methodology is that it allows the use without any modification of WSGG correlations that are available in the literature. The study presents a few test cases considering a one-dimensional (1D), nonuniform medium slab composed of H2O and CO2, bounded by nongray surfaces. The accuracy of the methodology is assessed by direct comparison with line-by-line (LBL) calculations.

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References

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Figures

Grahic Jump Location
Fig. 2

Representation of the subsections of the spectrum (the shaded areas) where the wall spectral emissivity is εk and the spectral pressure absorption coefficient of the medium is κp,j

Grahic Jump Location
Fig. 1

Schematic of the 1D medium slab bounded by two diffuse nongray walls

Grahic Jump Location
Fig. 6

(a) Radiative heat flux for test case 3 and (b) radiative heat source for test case 3

Grahic Jump Location
Fig. 5

(a) Radiative heat flux for test case 2 and (b) radiative heat source for test case 2

Grahic Jump Location
Fig. 7

(a) Radiative heat flux for test case 4 and (b) radiative heat source for test case 4

Grahic Jump Location
Fig. 3

(a) Profiles of medium temperature and molar concentration of CO2 and (b) wall emissivities with two-band and five-band stepwise variation

Grahic Jump Location
Fig. 4

(a) Radiative heat flux for test case 1 and (b) radiative heat source for test case 1

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