Solution of Radiative Transfer Equation in Two-Dimensional Media with Real Gas through Zone Method and Box Model

Document Type : Research Article

Authors

Abstract

According to high dependence of spectral behavior of gases to temperature, pressure, wave length and concentration, it is needed that such properties be explained by simpler mathematical models. Moreover, appropriate numerical methods should be used to solve the radiative transfer equation for radiation intensity in the media, heat flux divergence and temperature field. Solution of the radiative transfer equation has been made by several researchers for gray gas in one-dimensional case. In this article, the radiative transfer equation is solved for two-dimensional case (long rectangular section) considering the spectral behavior of media (CO2 , H2O gases) through combining the box model and zone method. Because of the nongray behavior of the industrial gases, solving this equation can improve the gray gases assumptions in the model.

Keywords


[1] حسینی، رضا وزیری ، مهرداد ; بیدی، مختار ”توزیع دمای یک گاز غیر خاکستری بین دو صفحه موازی با استفاده از مدل باند پهن نمایی ” استقلال سال 24 ، ش 1 ،جلد دوم، ص. 299 تا 313
[2] K. Kudo, A. Kuroda, T. Fujikane, Sh. Saido, M. Oguma: “Development of a method to estimate profiles of equivalent absorption coefficient for gray analysis,” Journal of Quantitative Spectroscopy & Radiative Transfer, 73 pp 385–395, 2002.
[3] F. Liu, O. L. Gulder and G. J. Smallwood “Non-grey gas radiative transfer analyses using the statistical narrow-band model,” Int. J. Heat Mass Transfer, Vol. 41, No. 14, pp. 2227-2236,1998.
[4] J. Strohle, P. J. Coelho: “On the application of the exponential wide band model to the calculation of radiative heat transfer in one- and two-dimensional enclosures,” International Journal of Heat and Mass Transfer 45 , pp 2129–2139, 2002.
[5] D.N Trivic, “Modeling of 3D non-gray gases radiation by coupling the method with weighted sum of gray gases model”,
International Journal of Heat and Mass Transfer 47 , p.p 1367-1382, 2004.
[6] P.J. Coelho, “Numerical simulation of radiative from non-gray gases in three dimensional enclosure”, Journal of Quantitative Spectroscopy &Radiative Transfer 74 , p.p 307–328, 2002.
[7] F. Liu, H. A. Becker, Y. Bindar: “A comparative study of radiative heat transfer modeling in gas-fired furnaces using the simple grey gas and the weighted-sum-of-grey-gases models,” International Journal of Heat and Mass Transfer 41 , p.p 3357-3371, 1998.
[8] P.J.Coelho, J.M.Gonçalves , M.G Carvalho. “Modeling of radative heat transfer in enclosures with obstacles”. Int J. Heat Mass Transfer, Vol. 41, Nos 4-5, pp. 745-756, 1998.
[9] A.T Modak “ radiation from products of combustion” fire research; 1:3 pp 39-61, 1978/1979.
[10] M.K Deninson,Webb “an absorption-line blackbody distribution function for efficient calculation of total gas radiative transfer” , Journal of Quantitative Spectroscopy &Radiative Transfer;50: pp 499-510, 1993.
[11] M.K Deninson,Webb “Development and application of an absorption-line blackbody distribution function for CO2” .int Journal of Heat Mass Transfer:38:18 p.p 13-21, 1995.
[12] C. E Siewert, and P. F. Zweifel: “An Exact Solution of Equation of Radiative Transfer for Local Thermodynamic Equilibrium in Non-Gray Case: Picket Fence Approximation,” Ann. Phys, vol. 36, pp 61-85, 1966.
[13] M.F Modest “Radiative Equilibrium in Rectangular Enclosure Bounded by Gray Non-Isothermal Walls,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 15, pp 445-461, 1975.
[14] M.F Modest “ A Simple Differential Approximation for Radiative Transfer in Non- Gray Gases,” ASME Journal of Heat and Mass Transfer, vol. 101, pp 735-7, 1979.
[15] M.F Modest, K. K. Sikka “The Application of Stepwise-Gray P-1 Approximation to Molecular Gas-Particulate Mixtures,” in Fundamentals of Radiation Heat Transfer, vol. HTD-160, ASME, pp 97-103, 1991.
[16] H. C. Hotel, E. S. Cohen: “ Radiant Heat Exchange in Gas-Filled Enclosure: Allowance for No uniformity of Gas Temperature,” AIChE Journal, vol. 4, pp. 3-14, 1958
[17] M. F Modest, “Radiative Heat Transfer,” McGraw-Hill, New York, 1993.
[18] V. Goutiere, F. Liu, A. Charette: “An Assessment of Real-Gas Modeling in 2D Enclosures,” Journal of Quantitative Spectroscopy & Radiative Transfer 64, p.p 299-326,2000.