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

Volumn 52, Issue 8, 2007, Pages 757-775

  Mondal, Bittagopal ^a   Mishra, Subhash C ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; COMPUTATIONAL GEOMETRY; NUMERICAL METHODS; PROBLEM SOLVING;

BOUNDARY EMISSIVITY; DISCRETE ORDINATES METHOD (DOM); FINITE-DIFFERENCE METHOD (FDM);

HEAT RADIATION;

EID: 35648956288     PISSN: 10407782     EISSN: 15210634     Source Type: Journal    
DOI: 10.1080/10407780701347663     Document Type: Article

References (35)

1. S. Chen and G. D. Doolen, Lattice Boltzmann Method for Fluid Flows, Annu. Rev. Fluid Mech., vol. 30, pp. 329-364, 1998.
2. X. He, S. Chen, and G. D. Doolen, A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit, J. Comput. Phys., vol. 146, pp. 282-300, 1998.
3. D. A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction, Springer-Verlag, Berlin-Heidelberg, 2000.
4. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York, 2001.
5. Z. L. Yang, T. N. Dinh, R. R. Nourgaliev, and B. R. Sehgal, Numerical Investigation of Bubble Growth and Detachment by the Lattice Boltzmann Method, Int. J. Heat Mass Transfer, vol. 44, pp. 195-206, 2001.
6. R. R. Nourgaliev, T. N. Dinh, T. G. Theofanous, and D. Joseph, The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications, Int. J. Multipase Flow, vol. 29, pp. 117-169, 2003.
7. J. R. Ho, C.-P. Kuo, W.-S. Jiaung, and C.-J. Twu, Lattice Boltzmann Scheme for Hyperbolic Heat Conduction Equation, Numer. Heat Transfer B, vol. 41, pp. 591-607, 2002.
8. J. R. Ho, C.-P. Kuo, and W. S. Jiaung, Study of Heat Transfer in Multilayered Structure within the Framework of Dual-Phase-Lag Heat Conduction Model Using Lattice Boltzmann Method, Int. J. Heat Mass Transfer, vol. 46, pp. 55-69, 2003.
9. W.-S. Jiaung, J. R. Ho, and C.-P. Kuo, Lattice Boltzmann Method for Heat Conduction Problem with Phase Change, Numer. Heat Transfer B, vol. 39, pp. 167-187, 2001.
10. S. Srinivasan, R. S. Miller, and E. Marotta, Parallel Computation of the Boltzmann Transport Equation for Microscale Heat Transfer in Multilayered Thin Films, Numer. Heat Transfer B, vol. 46, pp. 31-58, 2004.
11. Z. Guo and T. S. Zhao, Lattice Boltzmann Simulation of Natural Convection with Temperature-Dependent Viscosity in a Porous Cavity, Prog. Comput. Fluid Dynam., vol. 5, pp. 110-117, 2005.
12. M. Jamia, A. Mezrhaba, M. Bouzidib, and P. Lallemand, Lattice-Boltzmann Computation of Natural Convection in a Partitioned Enclosure with Inclined Partitions Attached to Its Hot Wall, Physica A, vol. 368, pp. 481-494, 2006.
13. C. van Treecka, E. Ranka, M. Krafczykb, J. Tölkeb, and B. Nachtwey, Extension of a Hybrid Thermal LBE Scheme for Large-Eddy Simulations of Turbulent Convective Flows, Comput. Fluids, vol. 35, pp. 863-871, 2006.
14. D. Chatterjee and S. Chakraborty, An Enthalpy-Based Lattice Boltzmann Model for Diffusion Dominated Solid-Liquid Phase Transformation, Phys. Lett. A, vol. 341, pp. 320-330, 2005.
15. S. C. Mishra and A. Lankadasu, Analysis of Transient Conduction and Radiation Heat Transfer Using the Lattice Boltzmann Method and the Discrete Transfer Method, Numer. Heat Transfer A, vol. 47, pp. 935-954, 2005.
16. S. C. Mishra, A. Lankadasu, and K. Beronov, Application of the Lattice Boltzmann Method for Solving the Energy Equation of a 2-D Transient Conduction-Radiation Problem, Int. J. Heat Mass Transfer, vol. 48, pp. 3648-3659, 2005.
17. R. Raj, A. Prasad, P. R. Parida, and S. C. Mishra, Analysis of Solidification of a Semitransparent Planar Layer Using the Lattice Boltzmann Method and the Discrete Transfer Method, Numer. Heat Transfer A, vol. 49, pp. 279-299, 2006.
18. N. Gupta, G. R. Chaitanya, and S. C. Mishra, Lattice Boltzmann Method Applied to Variable Thermal Conductivity Conduction and Radiation Problems, J. Thermophys. Heat Transfer, vol. 20, pp. 895-902, 2006.
19. S. C. Mishra and H. K. Roy, Solving Transient Conduction-Radiation Problems Using the Lattice Boltzmann Method and the Finite Volume Method, J. Comput. Phys., vol. 223, pp. 89-107, 2007.
20. W. A. Fiveland, Three-Dimensional Radiative Heat-Transfer Solutions by the Discrete-Ordinates Method, J. Thermophys. Heat Transfer, vol. 2, pp. 309-316, 1988.
21. I.-K. Kim and W.-S. Kim, Hybrid Spatial Differencing Scheme for Discrete Ordinates Method in 2D Rectangular Enclosures, Int. J. Heat Mass Transfer, vol. 44, pp. 575-586, 2001.
22. N. Selcuk 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.
23. 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.
24. R. Siegel and J. Howell, Thermal Radiation Heat Transfer, 4th ed., Taylor & Francis, New York, 2002.
25. M. F. Modest, Radiative Heat Transfer, 2nd ed., Academic Press, New York, 2003.
26. H.-S. Li, G. Flamant, and J.-D. Lu, A New Discrete Ordinate Algorithm for Computing Radiative Transfer in One-Dimensional Atmospheres, J. Quant. Spectrosc. Radiat. Transfer, vol. 83, pp. 407-421, 2004.
27. K. A. R. Ismail and C. T. S. Salinas, Gray Radiative Conductive 2D Modeling Using Discrete Ordinates Method with Multidimensional Spatial Scheme and Non-Uniform Grid, Int. J. Thermal Sci., vol. 45, pp. 706-715, 2006.
28. S. C. Mishra, H. K. Roy, and N. Mishra, Discrete Ordinate Method with a New and a Simple Quadrature Scheme, J. Quant. Spectrosc. Radiat. Transfer, vol. 101, pp. 249-262, 2006.
29. C. Barker and W. H. Sutton, The Transient Radiation and Conduction Heat Transfer in a Gray Participating Medium with Semi-Transparent Boundaries, in Radiation Heat Transfer, ASME HTD-49, pp. 25-36, 1985.
30. W. H. Sutton, A Short Time Solution for Coupled Conduction and Radiation in a Participating Slab Geometry, J. Heat Transfer, vol. 108, pp. 465-466, 1986.
31. J. H. Tsai and J. D. Lin, Transient Combined Conduction and Radiation with Anisotropic Scattering, J. Thermophys. Heat Transfer, vol. 4, pp. 92-97, 1990.
32. P. Talukdar and S. C. Mishra, Analysis of Conduction and Radiation Heat Transfer with Heat Generation in Participating Medium Using the Collapsed Dimension Method, Numer. Heat Transfer A, vol. 39, pp. 79-100, 2001.
33. C. Y. Wu and N. R. Ou, Transient Two-Dimensional Radiative and Conductive Heat Transfer in a Scattering Medium, Int. J. Heat Mass Transfer, vol. 37, pp. 2675-2686, 1994.
34. W. W. Yuen and E. E. Takara, Analysis of Combined Conductive-Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure with a Gray Medium, J. Heat Transfer, vol. 110, pp. 468-474, 1988.
35. S. C. Mishra, P. Talukdar, D. Trimis, and F. Durst, Computational Efficiency Improvements of the Radiative Transfer Problems with or without Conduction - a Comparison of the Collapsed Dimension Method and the Discrete Transfer Method, Int. J. Heat Mass Transfer, vol. 46, pp. 3083-3095, 2003.