Research Papers: Radiative Heat Transfer

On Multilayer Modeling of Radiative Transfer for Use With the Multisource k-Distribution Method for Inhomogeneous Media

[+] Author and Article Information
John Tencer

Sandia National Laboratories,
1515 Eubank,
Albuquerque, NM 87123
e-mail: jtencer@sandia.gov

John R. Howell

University of Texas at Austin,
Austin, TX 78712
e-mail: jhowell@mail.utexas.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 5, 2012; final manuscript received January 21, 2014; published online March 10, 2014. Assoc. Editor: He-Ping Tan.

J. Heat Transfer 136(6), 062703 (Mar 10, 2014) (7 pages) Paper No: HT-12-1539; doi: 10.1115/1.4026554 History: Received October 05, 2012; Revised January 21, 2014

A nonisothermal medium is modeled using the multilayer approach in which the continuous temperature distribution in a one-dimensional system as modeled as being piecewise constant. This has been shown to provide accurate results for a surprisingly small number of layers. Analysis is performed on a nonisothermal gray medium to attempt to characterize the ways in which the errors introduced by the multilayer modeling change with various physical parameters namely, the optical thickness and the temperature or emissive power gradient. A demonstration is made of how the multisource k-distribution method is capable of evaluating the heat flux within a one-dimensional system with piecewise constant temperature distribution with line-by-line accuracy with a significant decrease in computational expense. The k-distribution method for treating the spectral properties of an absorbing–emitting medium represents a powerful alternative to line-by-line calculations by reducing the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of 10 without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. The multisource k-distribution method extends the k-distribution method to problems with piecewise constant temperature and optical properties.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Buckius, R. O., and Lee, H., 1986, “Combined Mode Heat Transfer Analysis Utilizing Radiation Scaling,” ASME J. Heat Transfer, 108, pp. 626–632. [CrossRef]
Lee, H. S., Menart, J. A., and Fakheri, A., 1990, “Multilayer Radiation Solution for Boundary-Layer Flow of Gray Gases,” AIAA J. Thermophys. Heat Transfer, 4, pp. 180–185. [CrossRef]
Kim, T. K., Menart, J. A., and Lee, H. S., 1991, “Nongray Radiative Gas Analysis Using the S–N Techniques,” ASME J. Heat Transfer, 113, pp. 945–952. [CrossRef]
Solovjov, V. P., and Webb, B. W., 2008, “Multilayer Modeling of Radiative Transfer by SLW and CW Methods in Non-Isothermal Gaseous Medium,” J. Quant. Spectrosc. Radiative Transfer, 109, pp. 245–257. [CrossRef]
Denison, M. K., and Webb, B. W., 1993, “The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers,” ASME J. Heat Transfer, 115, pp. 1004–1012. [CrossRef]
Maurente, A., Franca, F. H. R., Miki, K., and Howell, J. R., 2012, “Application of Approximations for Joint Cumulative k-Distributions for Mixtures to FSK Radiation Heat Transfer in Multi-Component High Temperature Non-LTE Plasmas,” J. Quant. Spectrosc. Radiat. Transfer, 113, pp. 1521–1535. [CrossRef]
Modest, M. F., and Zhang, H., 2000, “The Full Spectrum Correlated-k Distribution and Its Relationship to the Weighted-Sum-of-Gray-Gases Method,” IMECE, ASME, Orlando, FL, pp. 75–84.
Modest, M. F., and Zhang, H., 2002, “The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures,” ASME J. Heat Transfer, 124, p. 30–38. [CrossRef]
Lacis, A. A., and Oinas, V., 1991, “A Description of the Correlated-k Distribution Method for Modeling Nongray Gaseous Absorption, Thermal Emission, and Multiple Scattering in Vertically Inhomogeneous Atmospheres,” J. Geophys. Res., 96, pp. 9027–9063. [CrossRef]
Goody, R., West, R., Chen, L., and Crisp, D., 1989, “The Correlated-k Method for Radiation Calculations in Nonhomogeneous Atmospheres,” J. Quant. Spectrosc. Radiat. Transfer, 42, pp. 539–550. [CrossRef]
Riviere, Ph., Soufiani, A., and Taine, J., 1992, “Correlated-k and Fictitious Gas Methods for H2O Near 2.7 mm,” J. Quant. Spectrosc. Radiat. Transfer, 48, pp. 187–203. [CrossRef]
Riviere, Ph., Soufiani, A., and Taine, J., 1995, “Correlated-k and Fictitious Gas Model for H2O Infrared Radiation in the Voigt Regime,” J. Quant. Spectrosc. Radiat. Transfer, 53, pp. 335–346. [CrossRef]
Taine, J., and Soufiani, A., 1999, “Gas IR Radiative Properties: From Spectroscopic Data to Approximate Models,” Adv. Heat Transfer, 33, pp. 295–414. [CrossRef]
Pal, G., Modest, M. F., and Wang, L., 2008, “Hybrid Full-Spectrum Correlated k-Distribution Method for Radiative Transfer in Strongly Nonhomogeneous Gas Mixtures,” ASME J. Heat Transfer, 130, p. 082701. [CrossRef]
Zhang, H., and Modest, M. F., 2003, “Scalable Multi-Group Full-Spectrum Correlated-k Distributions for Radiative Transfer Calculations,” ASME J. Heat Transfer, 125, pp. 454–461. [CrossRef]
Tencer, J. T., and Howell, J. R., 2012, “A Multi-Source Full Spectrum K-Distribution Method for 1-D Inhomogeneous Media,” EUROTHERM SEMINAR No. 95 Computational Thermal Radiation in Participating Media IV, Nancy, France.
Rothman, L. S., Jacquemart, D., Barbe, A., Benner, D. C., Birk, M., Brown, L. R., Carleer, M. R., Chackerian, C., Jr., Chance, K., Couder, L. H., Dana, V., Devi, V. M., Flaud, J. M., Gamache, R. R., Godman, A., Hartmann, J. M., Jucks, K. W., Maki, A. G., Mandin, J. Y., Massie, S. T., Orphal, J., Perrin, A., Rinsland, C. P., Smith, M. A. H., Tennysn, J., Tolchenv, R. N., Toth, R. A., Auwera, J. V., Varanasi, P., and Wagner, G., 2005, “The HITRAN 2004 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer, 96, pp. 139–204. [CrossRef]


Grahic Jump Location
Fig. 3

Local error in radiative flux normalized by the volume-averaged radiative flux as a function of optical depth (physical location) for a linear emissive power temperature profile

Grahic Jump Location
Fig. 4

Global error convergence for a variety of temperature profiles using layers distributed uniformly over the optical coordinate

Grahic Jump Location
Fig. 2

Local error in radiative flux normalized by the volume-averaged radiative flux as a function of optical depth (physical location) for a linear temperature distribution

Grahic Jump Location
Fig. 1

Schematic illustration of multilayer system and geometric nomenclature [4]

Grahic Jump Location
Fig. 5

Global error convergence for a variety of temperature profiles using layers distributed uniformly throughout the range of emissive powers

Grahic Jump Location
Fig. 6

Effect of emissive power gradient on multilayer approximation error behavior

Grahic Jump Location
Fig. 7

k-Distribution demonstration [6]

Grahic Jump Location
Fig. 8

k-Distribution results for a homogeneous isothermal medium with cold black walls

Grahic Jump Location
Fig. 9

k-Distribution results for a purely absorbing medium subject to a known spectral boundary flux



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In