Spectral collocation method for transient conduction-radiation heat transfer

Journal of Thermophysics and Heat Transfer

Volumn 24, Issue 4, 2010, Pages 823-832

  Sun, Ya Song ^a,b   Li, Ben Wen ^a,b  

^a NORTHEASTERN UNIVERSITY   (China)

^b NORTHEASTERN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT RADIATION; RADIATION EFFECTS; RADIATIVE TRANSFER;

CONDUCTION RADIATIONS; DISCRETE ORDINATES METHOD; EXPONENTIAL CONVERGENCE; ISOTROPICALLY SCATTERING; RADIATIVE TRANSFER EQUATIONS; SPECTRAL COLLOCATION; SPECTRAL COLLOCATION METHOD; TWO-DIMENSIONAL RECTANGULAR;

NUMERICAL METHODS;

EID: 78149398518     PISSN: 08878722     EISSN: 15336808     Source Type: Journal    
DOI: 10.2514/1.43400     Document Type: Article

References (46)

1. Viskanta, R., and Grosh, R. J., "Heat Transfer by Simultaneous Conduction and Radiation in an Absorbing Medium", Journal of Heat Transfer, Vol. 84, No. 1, 1962, pp. 63-72.
2. Viskanta, R., and Grosh, R. J., "Effect of Surface Emissivity an Heat Transfer by Simultaneous Conduction and Radiation", International Journal of Heat and Mass Transfer, Vol. 5, No. 8, 1962, pp. 729-734. doi: 10.1016/0017-9310 (62) 90203-X
3. Razzaque, M. M., Howell, J. R., and Klein, D. E., "Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure with Gray Medium Using Finite Elements", Journal of Heat Transfer, Vol. 106, No. 3, 1984, pp. 613-619. doi: 10.1115/1.3246723
4. Sakami, M., Charette, A., and Le Dez, V, "Application of the Discrete Ordinates Method to Combined Conductive and Radiative Heat Transfer in a Two-Dimensional Complex Geometry", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 56, No. 4, 1996, pp. 517-533. doi: 10.1016/0022-4073 (96) 00082-9
5. Liu, L. H., and Tan, J. Y., "Meshless Local Petrov-Galerkin Approach for Coupled Radiative and Conductive Heat Transfer", International Journal of Thermal Sciences, Vol. 46, No. 7, 2007, pp. 672-681. doi: 10.1016/j.ijthermalsci.2006.09.005 (Pubitemid 46670789)
6. Siegel, R., and Howell, J. R., Thermal Radiation Heat Transfer, 4th ed., Taylor & Francis, Washington, D. C., 2002.
7. Modest, M. F, Radiative Heat Transfer, 2nd ed., Academic Press, San Diego, CA, 2003.
8. Barker, C, and Sutton, W. H., "Transient Radiation and Conduction Heat Transfer in a Gray Participating Medium with Semitransparent Boundaries", Developments in Radiative Heat Transfer, Vol. 49, ASME Heat Transfer Div., New York, 1985, pp. 25-36.
9. Sutton, W. H., "A Short Time Solution for Coupled Conduction and Radiation in a Participating Slab Geometry", Journal of Heat Transfer, Vol. 108, No. 2, 1986, pp. 465-466. doi: 10.1115/1.3246949
10. Tsai, J. H., and Lin, J. D., "Transient Combined Conduction and Radiation with Anisotropic Scattering", Journal of Thermophysics and Heat Transfer, Vol. 4, No. 1, 1990, pp. 92-97. doi: 10.2514/3.29171
11. Yi, H. L., Xie, M., and Tan, H. P., "Transient Coupled Heat Transfer in an Anisotropic Scattering Composite Slab with Semitransparent Surfaces", International Journal of Heat and Mass Transfer, Vol. 51, Nos. 25-26, 2008, pp. 5918-5930. doi: 10.1016/j.ijheatmasstransfer.2008.04.054
12. Wu, C. Y, and Ou, N. R., "Transient Two-Dimensional Radiative and Conductive Heat Transfer in a Scattering Medium", International Journal of Heat and Mass Transfer, Vol. 37, No. 17, 1994, pp. 2675-2686. doi: 10.1016/0017-9310 (94) 90384-0
13. Liu, L. H., and Tan, H. P., "Transient Radiation and Conduction in a Two Dimensional Participating Cylinder Subjected to a Pulse Irradiation", International Journal of Thermal Sciences, Vol. 40, No. 10, 2001, pp. 877-889. doi: 10.1016/S1290-0729 (01) 01274-1
14. Talukdar, P., and Mishra, S. C, "Transient Conduction and Radiation Heat Transfer With Heat Generation in a Participating Medium Using the Collapsed Dimension Method", Numerical Heat Transfer, Part A, Applications, Vol. 39, No. 1, 2001, pp. 79-100. doi: 10.1080/104077801458474
15. Mishra, S. C., Talukdar, P., Trimis, D., and Durst, F., "Computational Efficiency Improvements of the Radiative Transfer Problems with or Without Conduction-A Comparison of the Collapsed Dimension Method and the Discrete Transfer Method", International Journal of Heat and Mass Transfer, Vol. 46, No. 16, 2003, pp. 3083-3095. doi: 10.1016/S0017-9310 (03) 00075-9
16. Mishra, S. C., Lankadasu, A., and Beronov, K. N., "Application of the Lattice Boltzmann Method for Solving the Energy Equation of a 2-D Transient Conduction-Radiation Problem", International Journal of Heat and Mass Transfer, Vol. 48, No. 17, 2005, pp. 3648-3659. doi: 10.1016/j. ijheatmasstransfer.2004.10.041 (Pubitemid 40849845)
17. Mondal, B., and Mishra, S. C., "Application of the Lattice Boltzmann Method and the Discrete Ordinates Method for Solving Transient Conduction and Radiation Heat Transfer Problems", Numerical Heat Transfer, Part A, Applications, Vol. 52, No. 8, 2007, pp. 757-775. doi: 10.1080/10407780701347663 (Pubitemid 350021233)
18. Mishra, S. C., and Roy, H. K., "Solving Transient Conduction and Radiation Heat Transfer Problems Using the Lattice Boltzmann Method and the Finite Volume Method", Journal of Computational Physics, Vol. 223, No. 1, 2007, pp. 89-107. doi: 10.1016/j.jcp. 2006.08.021
19. Mondal, B., and Mishra, S. C, "Lattice Boltzmann Method Applied to the Solution of the Energy Equations of the Transient Conduction and Radiation Problems on Nonuniform Lattices", International Journal of Heat and Mass Transfer, Vol. 51, Nos. 1-2, 2008, pp. 68-82. doi: 10.1016/j.ijheatmasstransfer. 2007.04.030 (Pubitemid 350234930)
20. Furmanski, P., and Banaszek, J., "Finite Element Analysis of Concurrent Radiation and Conduction in Participating Media", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 84, No. 4, 2004, pp. 563-573. doi: 10.1016/S0022-4073 (03) 00273-5
21. David, L., Nacer, B., Pascal, B., and Gerard, J., "Transient Radiative and Conductive Heat Transfer in Nongray Semitransparent Two-Dimensional Media with Mixed Boundary Conditions", Heat and Mass Transfer, Vol. 42, No. 4, 2006, pp. 322-337. doi: 10.1007/s00231-005-0023-4 (Pubitemid 41817822)
22. Asllanaj, F., Parent, G., and Jeandel, G., "Transient Radiation and Conduction Heat Transfer in a Gray Absorbing-Emitting Medium Applied on Two-Dimensional Complex-Shaped Domains", Numerical Heat Transfer, Part B, Fundamentals, Vol. 52, No. 2, 2007, pp. 179-200. doi: 10.1080/10407790701227351 (Pubitemid 47011514)
23. Luo, J. F., Chang, S. L., Yang, J. K., Shen, X., and Inoussa, G., "Transient Coupled Heat Transfer in a Rectangular Medium with Black Surfaces", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 109, No. 15, 2008, pp. 2603-2612. doi: 10.1016/j.jqsrt.2008.07.001
24. Gottlieb, D., and Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 1977.
25. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.
26. Peyret, R., Spectral Methods for Incompressible Viscous Flow, Springer-Verlag, New York, 2002.
27. Belgacem, F. B., and Grundmann, M., "Approximation of the Wave and Electromagnetic Diffusion Equations by Spectral Methods", SIAM Journal on Scientific Computing, Vol. 20, No. 1, 1998, pp. 13-32. doi: 10.1137/ S1064827595294344
28. Shan, X. W., and Montgomery, D., "Magnetohydrodynamic Stabilization Through Rotation", Physical Review Letters, Vol. 73, No. 12, 1994, pp. 1624-1627. doi: 10.1103/PhysRevLett.73.1624
29. Chawla, T. C., and Chan, S. H., "Solution of Radiation-Conduction Problems with Collocation Method Using B-Splines as Approximating Functions", International Journal of Heat and Mass Transfer, Vol. 22, No. 12, 1979, pp. 1657-1667. doi: 10.1016/0017-9310 (79) 90082-6
30. Kamiuto, K., "Chebyshev Collocation Method for Solving the Radiative Transfer Equation", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 35, No. 4, 1986, pp. 329-336. doi: 10.1016/0022-4073 (86) 90084-1
31. Zenouzi, M., and Yener, Y., "Simultaneous Radiation and Natural Convection in Vertical Slots", Developments in Radiative Heat Transfer, Vol. 203, ASME Heat Transfer Div., New York, 1992, pp. 179-186.
32. Kuo, D. C., Morales, J. C., and Ball, K. S., "Combined Natural Convection and Volumetric Radiation in a Horizontal Annulus: Spectral and Finite Volume Predictions", Journal of Heat Transfer, Vol. 121, No. 3, 1999, pp. 610-615. doi: 10.1115/1.2826023
33. De Oliveira, J. V. P., Cardona, A. V., Vilhena, M. T., and Barros, R. C., "A Semi-Analytical Numerical Method for Time-Dependent Radiative Transfer Problems in Slab Geometry with Coherent Isotropic Scattering", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 73, No. 1, 2002, pp. 55-62. doi: 10.1016/S0022-4073 (01) 00169-8
34. Lara, F. E., and Rieutord, M., "The Dynamics of a Fully Radiative Rapidly Rotating Star Enclosed Within a Spherical Box", Astronomy and Astrophysics, Vol. 470, No. 3, 2007, pp. 1013-1022. doi: 10.1051/0004-6361: 20077263 (Pubitemid 47219669)
35. Modest, M. F, and Yang, J., "Elliptic PDE Formulation and Boundary Conditions of the Spherical Harmonics Method of Arbitrary Order for General Three-Dimensional Geometries", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 109, No. 9, 2008, pp. 1641-1666. doi: 10.1016/j.jqsrt.2007.12.018
36. Li, B. W., Sun, Y. S., and Yu, Y, "Iterative and Direct Chebyshev Collocation Spectral Methods for One-Dimensional Radiative Heat Transfer", International Journal of Heat and Mass Transfer, Vol. 51, Nos. 25-26, 2008, pp. 5887-5894. doi: 10.1016/j.ijheatmasstransfer.2008.04.048
37. Sun, Y. S., and Li, B. W., "Chebyshev Collocation Spectral Method for One-Dimensional Radiative Heat Transfer in Graded Index Media", International Journal of Thermal Sciences, Vol. 48, No. 4, 2009, pp. 691-698. doi: 10.1016/j.ijthermalsci.2008.07.003
38. Li, B. W., Sun, Y. S., and Zhang, D. W, "Chebyshev Collocation Spectral Methods for Coupled Radiation and Conduction in a Concentric Spherical Participating Medium", Journal of Heat Transfer, Vol. 131, No. 6, 2009, Paper 062701. doi: 10.1115/1.3090617
39. Sun, Y. S., and Li, B. W, "Chebyshev Collocation Spectral Approach for Combined Radiation and Conduction Heat Transfer in One-Dimensional Semitransparent Medium with Graded Index", International Journal of Heat and Mass Transfer, Vol. 53, Nos. 7-8, 2010, pp. 1491-1497. doi: 10.1016/j.ijheatmasstransfer.2009.11.047
40. Sun, Y. S., and Li, B. W., "Spectral Collocation Method for Transient Combined Radiation and Conduction in an Anisotropic Scattering Slab with Graded Index", Journal of Heat Transfer, Vol. 132, No. 5, 2010, Paper 052701. doi: 10.1115/1.4000444
41. Li, B. W., Tian, S., Sun, Y. S., and Hu, Z. M., "Schur-Decomposition for 3D Matrix Equations and Its Application in Solving Radiative Discrete Ordinates Equations Discretized by Chebyshev Collocation Spectral Method", Journal of Computational Physics, Vol. 229, No. 4, 2010, pp. 1198-1212. doi: 10.1016/j.jcp. 2009.10.025
42. Boyd, J. P., Chebyshev and Fourier Spectral Methods, 2nd ed., Dover, New York, 2001.
43. Li, B. W., Chen, H. G., Zhou, J. H., Cao, X. Y., and Cen, K. F., "The Spherical Surface Symmetrical Equal Dividing Angular Quadrature Scheme for Discrete Ordinates Method", Journal of Heat Transfer, Vol. 124, No. 3, 2002, pp. 482-490. doi: 10.1115/1.1459731 (Pubitemid 34641773)
44. Yuen, W. W., and Takara, E. E., "Analysis of Combined Conductive-Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure with a Gray Medium", Journal of Heat Transfer, Vol. 110, No. 2, 1988, pp. 468-474. doi: 10.1115/1.3250509
45. Mahanta, P., and Mishra, S. C., "Collapsed Dimension Method Applied to Radiative Transfer Problems in Complex Enclosures with Participating Medium", Numerical Heat Transfer, Part B, Fundamentals, Vol. 42, No. 4, 2002, pp. 367-388. doi: 10.1080/10407790190053996 (Pubitemid 35263859)
46. Talukdar, P., and Mishra, S. C., "Analysis of Conduction-Radiation Problem in Absorbing, Emitting and Anisotropically Scattering Media Using the Collapsed Dimension Method", International Journal of Heat and Mass Transfer, Vol. 45, No. 10, 2002, pp. 2159-2168. doi: 10.1016/S0017-9310 (01) 00305-2