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# Treatment of Wall Emission in the Narrow-Band Based Multiscale Full-Spectrum $k$-Distribution Method

[+] Author and Article Information
Liangyu Wang

Department of Mechanical and Nuclear Engineering,  The Pennsylvania State University, University Park, PA 16802

Michael F. Modest1

Department of Mechanical and Nuclear Engineering,  The Pennsylvania State University, University Park, PA 16802MFModest@psu.edu

1

Corresponding author.

J. Heat Transfer 129(6), 743-748 (Sep 27, 2006) (6 pages) doi:10.1115/1.2717936 History: Received October 18, 2005; Revised September 27, 2006

## Abstract

The multiscale full-spectrum $k$-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper a new scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission by distributing this emission across the different gas scales. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission distribution function is introduced and two approaches of evaluating the function are outlined. The first approach involves line-by-line integration of the spectral absorption coefficients and is, therefore, impractical. The second approach employs a narrow-band $k$-distribution database to calculate all parameters as in the original narrow-banded based MSFSK formulation and is, therefore, efficient. This distribution scheme of wall emission is evaluated and the two approaches are compared by conducting sample calculations for radiative heat transfer in strongly inhomogeneous media using both the MSFSK method and the line-by-line method.

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## Figures

Figure 1

Nondimensional heat flux leaving a homogeneous layer containing 20% CO2 and 20% H2O at 1000K

Figure 2

Nondimensional heat flux leaving an inhomogeneous layer at 1000K with step changes in mole fraction: 20% CO2 and 2% H2O in the left layer, with the composition switched in the right layer

Figure 3

Radiative heat source distribution for an inhomogeneous layer at 1000K with step changes in mole fraction: 20% CO2 and 2% H2O in the left layer, with the composition switched in the right layer

Figure 4

Nondimensional heat flux leaving an inhomogeneous layer with step change in mole fraction and temperature: 20% CO2 and 2% H2O at 1000K in the left layer and 2% CO2 and 20% H2O at 500K in the right layer

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