Solution of the Integrated Radiative Transfer Equation for Gray and Nongray Media

REFERENCES

• D. G. Doornink and R. G. Hering , Transient Radiative Heat Transfer in a Non-Gray Medium , J. Quant. Spectrosc. Radiat. Transfer , vol. 12 , pp. 1161 – 1174 , 1972 . [CSA]
   Google Scholar
• R. Siegel and J. R. Howell , Thermal Radiation Heat Transfer, , 3d ed. , Hemisphere, Taylor & Francis , Washington , DC , 1991 .
   Google Scholar
• M. F. Modest , Radiative Heat Transfer, , 2d ed. , Academic Press, Elsevier Science , San Diego , CA , 2003 .
   Google Scholar
• R. Gardon , Calculation of Temperature Distribution in Glass Plates Undergoing Heat Treatment , J. Am. Ceram. Soc. , vol. 41 , p. 200 , 1958 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• W. Potze , Radiation Heat Transfer in Aximsymmetric Quartz Glass Tubes , J. Quant. Spectrosc. Radiat. Transfer , vol. 84 , pp. 575 – 586 , 2004 . [CSA] [CROSSREF]
   Google Scholar
• A. L. Crosbie and R. Viskanta , The Exact Solution to a Simple Nongray Radiative Transfer Problem , J. Quant. Spectrosc. Radiat. Transfer , vol. 9 , pp. 553 – 568 , 1969 . [CSA] [CROSSREF]
   Google Scholar
• A. L. Crosbie and R. Viskanta , Nongray Radiative Transfer in a Planar Medium Exposed to a Collimated Flux , J. Quant. Spectrosc. Radiat. Transfer , vol. 10 , pp. 465 – 485 , 1970 . [CSA] [CROSSREF]
   Google Scholar
• H.-C. Kung and M. Sibulkin , Radiative Transfer in a Nongray Gas between Parallel Walls , J. Quant. Spectrosc. Radiat. Transfer , vol. 9 , pp. 1447 – 1461 , 1969 . [CSA] [CROSSREF]
   Google Scholar
• D. G. Doornink and R. G. Hering , Simultaneous Radiative and Conductive Heat Transfer in Non-Gray Media , J. Quant. Spectrosc. Radiat. Transfer , vol. 13 , pp. 323 – 332 , 1973 . [CSA] [CROSSREF]
   Google Scholar
• R. Viskanta and M. P. Mengüç , Radiation Heat Transfer in Combustion Systems , Prog. Energy Combustion Sci. , vol. 12 , pp. 97 – 160 , 1987 . [CSA]
   Google Scholar
• S. Chandrasekhar , Radiative Transfer , Dover , New York , 1960 .
   Google Scholar
• W. A. Fiveland , A Discrete Ordinates Method for Predicting Radiative Heat Transfer in Axisymmetric Enclosures , ASME Paper 82-HT-20 , 1982 . [CSA]
   Google Scholar
• J. S. Truelove , Discrete-Ordinate Solutions of the Radiative Transport Equation , ASME J. Heat Transfer , vol. 109 , no. 4 , pp. 1048 – 1051 , 1987 . [CSA]
   Web of Science ®Google Scholar
• R. Koch and R. Becker , Evaluation of Quadrature Schemes for the Discrete Ordinates Method , J. Quant. Spectrosc. Radiat. Transfer , vol. 84 , pp. 423 – 435 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. H. Lee and R. Viskanta , Two-Dimensional Combined Conduction and Radiation Heat Transfer: Comparison of the Discrete Ordinates Method and the Diffusion Approximation Methods , Numer. Heat Transfer A , vol. 39 , pp. 205 – 225 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. D. Raithby , Discussion of the Finite-Volume Method for Radiation, and Its Application Using 3-D Unstructured Meshes , Numer. Heat Transfer B , vol. 35 , pp. 389 – 405 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. D. Raithby and E. H. Chui , A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media , J. Heat Transfer , vol. 112 , no. 2 , pp. 415 – 423 , 1990 . [CSA]
   Web of Science ®Google Scholar
• E. H. Chui and G. D. Raithby , Computation of Radiant Heat Transfer on a Non-Orthogonal Mesh Using the Finite-Volume Method , Numer. Heat Transfer B , vol. 22 , pp. 269 – 288 , 1993 . [CSA]
   Google Scholar
• J. C. Chai and S. V. Patankar , Finite-Volume Method for Radiative Heat Transfer , Adv. Numer. Heat Transfer , vol. 2 , pp. 109 – 138 , 2000 . [CSA]
   Google Scholar
• S. H. Kim and K. Y. Huh , Assessment of the Finite-Volume Method and the Discrete Ordinate Method for Radiative Heat Transfer in a Three-Dimensional Rectangular Enclosure , Numer. Heat Transfer B , vol. 35 , pp. 85 – 112 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. C. Chai , One-Dimensional Transient Radiation Heat Transfer Modeling Using a Finite-Volume Method , Numer. Heat Transfer B , vol. 44 , pp. 187 – 208 , 2003 . [CSA]
   Web of Science ®Google Scholar
• L. H. Howell , R. B. Pember , P. Colella , J. P. Jessee , and W. A. Fiveland , A Conservative Adaptive Mesh Algorithm for Unsteady Combined Mode Heat Transfer Using the Discrete Ordinate Method , Numer. Heat Transfer B , vol. 35 , pp. 407 – 430 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• B. van Leer , Towards the Ultimate Conservative Difference Scheme. II. Monotonicity and Conservation Combined in a Second Order Scheme , J. Comput. Phys. , vol. 14 , pp. 361 – 370 , 1974 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. Balsara , Fast and Accurate Discrete Ordinates Methods for Multidimensional Radiative Transfer, Part I. Basic Methods , J. Quant. Spectrosc. Radiat. Transfer , vol. 69 , pp. 671 – 707 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. J. Coelho , Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method , J. Comput. Phys. , vol. 175 , pp. 412 – 437 , 2002 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. A. R. Ismail and C. S. Salinas , Application of Multidimensional Scheme and the Discrete Ordinate Method to Radiative Heat Transfer in a Two-Dimensional Enclosure with Diffusely Emitting and Reflecting Boundary Walls , J. Quant. Spectrosc. Radiat. Transfer , vol. 88 , pp. 407 – 422 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• F. C. Lockwood and N. G. Shah , A New Radiation Solution Method for Incorporation in General Combustion Prediction Procedures , Proc. 18th Symp. (Int.) on Combustion , pp. 1405 – 1414 , The Combustion Institute , Pittsburgh , PA , 1981 .
   Google Scholar
• J. C. Chai , H. S. Lee , and S. V. Patankar , Improved Treatment of Scattering Using the Discrete Ordinates Method , J. Heat Transfer , vol. 116 , p. 260 , 1994 . [CSA]
   Web of Science ®Google Scholar
• H. K. Versteeg , J. C. Henson , and W. Malalasekara , Spatial Discretization Errors in the Heat Flux Integral of the Discrete Transfer Method , Numer. Heat Transfer B , vol. 38 , pp. 333 – 352 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. S. Cumber , Improvements to the Discrete Transfer Method of Calculating Radiative Transfer , Int. J. Heat Mass Transfer , vol. 39 , no. 12 , pp. 2251 – 2258 , 1995 . [CSA] [CROSSREF]
   Google Scholar
• H. Farhat and M. S. Radhouani , Étude tridimensionelle du transfert radiatif dans un milieu semi-transparant diffusant anisotrope par la méthode des transfert discrets modifiée , Rev. Gén. Therm. , vol. 36 , pp. 330 – 344 , 1997 . [CSA]
   Google Scholar
• K. D. Lathrop and B. G. Carlson , Discrete Ordinates Angular Quadrature of Neutron Transport Equation, Tech. Rep. LA-3186 , Los Alamos Scientific Laboratory , Los Alamos , NM , 1965 .
   Google Scholar
• M. F. G. Cremers , M. J. Remie , K. R. A. M. Schreel , and L. P. H. de Goey , Heat Transfer Mechanisms of Laminar Flames of Hydrogen + Oxygen , Combustion & Flame , vol. 139 , no. 1–2 , pp. 39 – 51 , 2004 . [INFOTRIEVE] [CSA]
   Google Scholar
• A. Erdélyi , M. F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, I , p. 134 , McGraw-Hill , New York , 1954 .
   Google Scholar
• I. S. Gradshteyn and I. M. Ryzhik , Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, in Alan Jeffrey (ed.), Table of Integrals, Series, and Products, , 5th ed. , Academic Press , London , translated from Russian by Scripta Technica , 1994 .
   Google Scholar
• H. Bateman and A. Erdélyi , Higher Transcendental Functions, II , pp. 133 – 136 , McGraw-Hill , New York , 1953–1955 .
   Google Scholar