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Research Papers: Radiative Heat Transfer

Inverse Estimation of Main Parameters of Spectral Line-Based Weighted Sum of Gray Gases Model With Few Gray Gases to Simulate the Radiation in Nongray Media

[+] Author and Article Information
A. Dehghanian

Mechanical Engineering Department,
Shahid Bahonar University of Kerman,
Kerman 76175-133, Iran

S. M. Hosseini Sarvari

Mechanical Engineering Department,
Shahid Bahonar University of Kerman,
Kerman 76175-133, Iran
e-mail: sarvari@uk.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 5, 2016; final manuscript received June 8, 2017; published online August 29, 2017. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 140(2), 022701 (Aug 29, 2017) (10 pages) Paper No: HT-16-1630; doi: 10.1115/1.4037496 History: Received October 05, 2016; Revised June 08, 2017

The aim of this study is to present a reduced spectral line-based weighted sum of gray gases (SLW) model to simulate the radiation heat transfer in nongray media at high temperatures. Inverse approach is used to divide the absorption cross section band into a clear gas with one gray gas and two gray gases, which are called the S-1 and S-2 approaches, respectively. The unknown absorption cross sections are determined from the knowledge of measured total incident intensities received by wall surfaces. In order to simulate the exact solution of radiation heat transfer in nongray gaseous media, the discrete transfer method (DTM) in combination with S-20 model is used, where the nongray medium is replaced with a set of a clear gas and 20 gray gases. The inverse problem is formulated as an optimization problem to minimize a least square objective function, which is solved by the conjugate gradient method (CGM). The accuracy of the present method is verified by comparing with previous researches and the S-20 approach with a large number of gray gases. The effects of noisy data on the inverse solution are investigated by considering an extreme case with large measurement error. The results show that the unknown absorption cross sections are retrieved well, even for noisy data.

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Figures

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Fig. 1

Schematic of the plane-parallel nongray medium with diffuse–gray walls

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Fig. 2

(a) The S-1 spectral model and (b) the S-2 spectral model

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Fig. 3

(a) The divergence of radiative heat flux and (b) the radiative heat flux, throughout the medium by using the ALBDF coefficients proposed by Denison and Webb [2] for example 1

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Fig. 4

(a) The divergence of radiative heat flux and (b) the radiative heat flux, throughout the medium by using the ALBDF coefficients proposed by Pearson et al. [11] for example 1

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Fig. 5

Comparison of the results for different measurements error by using the ALBDF coefficients proposed by Pearson et al. [11] for example 1: (a) the divergence of radiative heat flux and (b) the radiative heat flux

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Fig. 6

(a) The divergence of radiative heat flux and (b) the radiative heat flux, throughout the medium for example 2

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Fig. 7

(a) The divergence of radiative heat flux and (b) the radiative heat flux, throughout the medium for example 3

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