## THERMAL SCIENCE

International Scientific Journal

### A COMPARISON OF TWO STATISTICAL NARROW BAND MODELS FOR NON-GRAY GAS RADIATION IN PLANAR PLATES

**ABSTRACT**

Non-gray gas radiation analysis and comparison are conducted by combining a ray tracing method and two statistical narrow band (SNB) spectral models, namely the Goody SNB model and the Malkmus SNB model. In this paper, gas radiation in real gas containing H2O, H2O/N2, or H2O/CO2/N2 mixtures at 1 atm in planar plates was studied. Comparisons between these models are performed using the latest narrow-band database. The present computations are validated by reproducing the published results in the literature. The radiative source term, the wall fluxes, the narrow-band radiation intensities along a line-of-sight and the computing time are all compared. From the comparisons, it is found that the Malkmus SNB model is somewhat superior to the Goody SNB model and the former is preferred in engineering application.

**KEYWORDS**

PAPER SUBMITTED: 2017-12-14

PAPER REVISED: 2018-01-22

PAPER ACCEPTED: 2018-01-24

PUBLISHED ONLINE: 2018-02-18

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Supplement 2**, PAGES [S777 - S784]

- Modest, M. F., Radiative heat transfer; second edition. 2003. San Diego Academic Press: New York.
- Song T. H. Comparison of Engineering Models of Nnon-Grey Behavior of Combustion Products, Int. J. Heat Mass Transfe, 36 (1993), pp. 3975-3982.
- Rothman, L. S., Gordon, I. E., Barbe, A., et al., The HITRAN 2008 Molecular Spectroscopic Database, JQSRT, 110 (2009), 533-572.
- Rothmana, L. S., Camy, P. C., Flaud, J. M., et al., HITEMP, the High-Temperature Molecular Spectroscopic Database. 2000. www.hitran.com .
- Edwards, D. K. and Balakrishnan, A., Thermal Radiation by Combustion Gases, Int. J. Heat Mass Transfer, 16 (1973), 25-40.
- Hottel, H.C. and Sarofim, A.F., Radiative Transfer. 1967. McGraw-Hill: New York.
- Modest, M. F., The Weighted-sum-of-grey-gases Model for Arbitrary Solution Methods in Radiative Transfer, ASME J. Heat Transfer , 113 (1991), 650-656.
- Soufim, A. and Djavdan, E., A Comparison BetweenWeighted Sum of Grey Gases and Statistical Narrow-Band Radiation Models for Combustion Aapplications, Combust. Flame, 97 (1994), 240- 250.
- Denison, M. K. and Webb, B. W., The Spectral Line-Based Weighted-Sum-of-Grey-Gases Model in Non-Isothermal Nonhomogeneous Media, ASME J. Heat Transfer, 117 (1995), 359-365.
- Modest, M. F. and Zhang, H., The Full-Spectrum Correlated-k Distribution for Thermal Radiation from Molecular Gas-particulate Mixtures, ASME J. Heat Transfer, 124 (2002), 30-38.
- Goody, R., A Statistical Model for Water Vapour Absorption, Quarterly Journal of the Royal Meteorological Society, 78 (1952), 165-169.
- Malkmus, W., Random Lorentz Band Aodel with Exponential-Tailed S-1 Line Intensity Distribution Function, J. Optical Society of America, 57 (1967), 323-329.
- Grosshandler, W. L., Radiative Heat Transfer in Nonhomogeneous Gases: a Simplified Approach, Int. J. Heat Mass Transfer, 23 (1980), 1447-1459.
- Kim, T. K., Menart, J. A., and Lee, H. S., Non-Grey Radiative Gas Analysis Using the S-N Discrete Ordinates Method, ASME J. Heat Transfer, 113 (1991), 946-952.
- Liu J. and Tiwari, S. N., Investigation of Radiative Transfer in Non-Grey Gases Using a Narrow Band Model and Monte Carlo Simulation, ASME J. Heat Transfer, 116 (1994), 160-166.
- Liu F., Gülder, Ö. L., Smallwood, G. J., and Ju Y., Non-Grey Gas Radiative Transfer Analyses Using the Statistical Narrow-Band Model, Int. J. Heat Mass Transfer, 41 (1998), 2227-2236.
- Lacis, A.A. and Oinas, V., A Description of the Correlated-k Distribution Method for Modeling Non- Grey Gaseous Absorption, Thermal Emission, and Multiple Scattering in Vertically Inhomogeneous Atmospheres, J. Geophysical Research, 96 (1991), 9027-9063.
- Soufiani, A. and Taine, J., High Temperature Gas Radiative Property Parameters of Statistical Narrow Band Model for H2O,CO2 and CO, and Correlated k Model for H2O and CO2, Int. J. Heat Mass Transfer, 40 (1997), 987-991.
- Liu F., Smallwood, G. J., and Gülder, Ö. L., Band Lumping Strategy for Radiation Heat Transfer Calculations Using a Narrowband Model, J. Thermophys Heat Transfer, 14 (2000) , 278-281.
- Siegel, R. and Howell, J. R. Thermal Radiation Heat Transfer: fourth edition. 2002. Taylor & Francis: New York.
- Marakis, J. G., Application of Narrow and Wide Band Models for Radiative Transfer in Planar Media, Int. J. Heat Mass Transfer, 44 (2001), 131-142.
- Ludwig, D. B., Malkmus, W., Reardon, J. E., and Thomson, J. A. L., Handbook of Infrared Radiation from Combustion Gases. 1973. NASA SP3080.
- Soufiani, A., Hartmann, J. M., and Taine, J., Validity of Band-Model Calculations for CO, and H2O Applied to Radiative Properties and Conductive-Radiative Transfer, JQSRT, 33 (1985), 243-257.
- Rivière, P., Soufiani, A., Updated band model parameters for H2O, CO2 ,CH4 and CO radiation at high temperature. Int J Heat Mass Transf,55(2012), 3349-58.
- Liu F., Smallwood, G. J., and Gülder, Ö. L., Application of the Statistical Narrow-Band Correlated-k Method to Low-Resolution Spectral Intensity and Radiative Heat Transfer Calculations-Effects of the Quadrature Scheme, Int. J. Heat Mass Transfer, 43 (2000), 3119-3135.
- Godson, W.L., The Evaluation of Infra-Red radiation Fluxes Due to Atmospheric Water Vapor, Quart. J. Royal. Meteorol. Soc, 79 (1953), 367-379.
- Liu F., Smallwood, G.J., and Gülder, Ö. L., Application of the Statistical Narrow-Band Correlated-k Method to Non-grey Gas Radiation in CO2-H2O Mixtures: Approximate Treatments of Overlapping Bands. JQSRT, 68 (2001), 401-417.
- Zhou H-C., Cheng Q., Huang Z-F., and He C., The Influence of Anisotropic Scattering on the Radiative Intensity in a Grey, Plane-Parallel Medium Calculated by the DRESOR Method, JQSRT, 104 (2007), 99-115.
- Chu, H., Ren, F., Feng, Y., et al., A comprehensive evaluation of the non gray gas thermal radiation using the line-by-line model in one- and two-dimensional enclosures, Applied Thermal Engineering, 124 (2017), pp. 362-370.