Second-order radiative transfer equation and its properties of numerical solution using the finite-element method

Numerical Heat Transfer, Part B: Fundamentals

Volumn 51, Issue 4, 2007, Pages 391-409

  Zhao, J M ^a   Liu, L H ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; HEAT CONDUCTION; INTEGRODIFFERENTIAL EQUATIONS; NUMERICAL METHODS;

CONVECTION DOMINATED EQUATIONS; NONPHYSICAL OSCILLATIONS; SECOND ORDER RADIATIVE TRANSFER EQUATIONS; STABILITY TREATMENT;

RADIATIVE TRANSFER;

EID: 33847660183     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790600964583     Document Type: Article

References (38)

1. H. C. Hottel and E. S. Cohen, Radiant Heat Exchange in a Gas-Filled Enclosure Allowance for Nonuniformity of Gas Temperature, AIChE J., vol. 4, pp. 3-14, 1958.
2. J. R. Howell, Application of Monte Carlo to Heat Transfer Problems, Adv. Heat Transfer, vol. 5, pp. 1-54, 1968.
3. M. F. Modest, Radiative Heat Transfer, McGraw-Hill, New York, 1993.
4. W. A. Fiveland, Discrete-Ordinates Solution of the Radiative Transport Equation for Rectangular Enclosures, ASME J. Heat Transfer, vol. 106, pp. 699-706, 1984.
5. J. C. Chai, H. O. Lee, and S. V. Patankar, Ray Effect and False Scattering in the Discrete Ordinates Method, Numer. Heat Transfer B, vol. 24, pp. 373-389, 1993.
6. J. C. Chai, H. S. Lee, and S. V. Patankar, Improved Treatment of Scattering Using the Discrete Ordinates Method, J. Heat Transfer, vol. 116, pp. 260-263, 1994.
7. F. Liu, H. A. Becker, and A. Pollard, Spatial Differencing Schemes of the Discrete-Ordinates Method, Numer. Heat Transfer B, vol. 30, pp. 23-43, 1996.
8. S. W. Baek and M. Y. Kim, Modification of the Discrete-Ordinates Method in an Axisymmetric Cylindrical Geometry, Numer. Heat Transfer B, vol. 31, pp. 313-326, 1997.
9. J. Con and P. J. Coelho, Parallelization of the Discrete Ordinates Method, Numer. Heat Transfer B, vol. 32, pp. 151-173, 1997.
10. 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.
11. 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.
12. N. Sel and G. Kirbas, The Method of Lines Solution of the Discrete Ordinates Method for Radiative Heat Transfer in Enclosures, Numer. Heat Transfer B, vol. 37, pp. 379-392, 2000.
13. N. Sel and I. Ayranci, The Method of Lines Solution of the Discrete Ordinates Method for Radiative Heal Transfer in Enclosures Containing Scattering Media, Numer. Heat Transfer B, vol. 43, pp. 179-201, 2003.
14. H. S. Li, G. Flamant, and J. D. Lu, Mitigation of Ray Effects in the Discrete Ordinates Method, Numer. Heat Transfer B, vol. 43, pp. 445-466, 2003.
15. G. Krishnamoorthy, R. Rawat, and P. J. Smith, Parallel Computations of Radiative Heat Transfer Using the Discrete Ordinates Method, Numer. Heat Transfer B, vol. 47, pp. 19-38, 2005.
16. G. D. Raithby and E. H. Chui, A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media, ASME J. Heat Transfer, vol. 112, pp. 415-423, 1990.
17. J. C. Chai and H. S. Lee, Finite-Volume Method for Radiation Heat Transfer, J. Thermophys. Heat Transfer, vol. 8, pp. 419-425, 1994.
18. J. C. Chai, H. O. Lee, and S. V. Patankar, Treatment of Irregular Geometries Using a Cartesian Coordinates Finite-Volume Radiation Heat Transfer Procedure, Numer. Heat Transfer B, vol. 26, pp. 225-235, 1994.
19. J. Y. Murthy and S. R. Mathur, Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes, J. Thermophys. Heat Transfer, vol. 12, pp. 313-321, 1998.
20. G. D. Raithby, Discussion of the Finite-volume Method for Radiation, and Its Application Using 3D Unstructured Meshes, Numer. Heat Transfer B, vol. 35, pp. 389-405, 1999.
21. J. C. Chai and S. V. Patankar, Finite-Volume Method for Radiation Heat Transfer, Adv. Numer. Heat Transfer, vol. 2, pp. 109-141, 2000.
22. 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.
23. K. Slimi, L. Zili-Ghedira, N. S. Ben, and A. A. Mohamad, A Transient Study of Coupled Natural Convection and Radiation in a Porous Vertical Channel Using the Finite-Volume Method, Numer. Heat Transfer A, vol. 45, pp. 451-478, 2004.
24. M. Lobo and A. F. Emery, Discrete Maximum Principle in Finite-Element Thermal Radiation Analysis, Numer. Heat Transfer B, vol. 24, pp. 209-227, 1993.
25. J. V. Daurelle, R. Occelli, and R. Martin, Finite-Element Modeling of Radiation Heat Transfer Coupled with Conduction in an Adaptive Method, Numer. Heat Transfer B, vol. 25, pp. 61-73, 1994.
26. V. B. Kisslelev, L. Roberti, and G. Perona, An Application of the Finite-Element Method to the Solution of the Radiative Transfer Equation, J. Quant. Spectrosc. Radiat. Transfer, vol. 51, pp. 603-614, 1994.
27. L. H. Liu, Finite Element Simulation of Radiative Heat Transfer in Absorbing and Scattering Media, J. Thermophys. Heat Transfer, vol. 18, pp. 555-557, 2004.
28. X. Cui and B. Q. Li, A Discontinuous Finite-Element Formulation for Internal Radiation Problems, Numer. Heat Transfer B, vol. 46, pp. 223-242, 2004.
29. J. P. Pontaza and J. N. Reddy, Least-Squares Finite Element Formulations for One-Dimensional Radiative Transfer, J. Quant. Spectrosc. Radiat. Transfer, vol. 95, pp. 387-406, 2005.
30. E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport, Wiley, New York, 1984.
31. K. B. Cheong and T. H. Song, Examination of Solution Methods for the Second-Order Discrete Ordinate Formulation, Numer. Heat Transfer B, vol. 27, pp. 155-173, 1995.
32. W. A. Fiveland and J. P. Jessee, Finite Element Formulation of the Discrete-Ordinates Method for Multidimensional Geometries, J. Thermophys. Heat Transfer, vol. 8, pp. 426-433, 1994.
33. W. A. Fiveland and J. P. Jessee, Comparison of Discrete Ordinates Formulations for Radiative Heat Transfer in Multidimensional Geometries, J. Thermophys. Heat Transfer, vol. 9, pp. 47-54, 1995.
34. L. H. Liu, Meshless Local Petrov-Galerkin Method for Solving Radiative Transfer Equation, J. Thermophys. Heat Transfer, vol. 20, pp. 150-154, 2005.
35. J. M. Zhao and L. H. Liu, Least-Squares Spectral Element Method for Radiative Heat Transfer in Semitransparent Media, Numer. Heat Transfer B, vol. 50, pp. 473-489, 2006.
36. A. C. Ratzel and J. R. Howell, Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation, ASME J. Heat Transfer, vol. 105, pp. 333-340, 1983.
37. T. K. Kim and H. Lee, Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimenssional Rectangular Enclosures, Int. J. Heat Mass Transfer, vol. 31, pp. 1711-1721, 1988.
38. M. Y. Kim, S. W. Baek, and J. H. Park, Unstructured Finite-Volume Method for Radiative Heat Transfer in a Complex Two-Dimensional Geometry with Obstacles, Numer. Heat Transfer B, vol. 39, pp. 617-635, 2001.