Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 52, 2007 - Issue 8
396
Views
51
CrossRef citations to date
0
Altmetric
Original Articles

Application of the Lattice Boltzmann Method and the Discrete Ordinates Method for Solving Transient Conduction and Radiation Heat Transfer Problems

&
Pages 757-775 | Received 12 Jan 2007, Accepted 16 Feb 2007, Published online: 25 Oct 2007

REFERENCES

  • S. Chen and G. D. Doolen , Lattice Boltzmann Method for Fluid Flows , Annu. Rev. Fluid Mech. , vol. 30 , pp. 329 – 364 , 1998 .
  • 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 .
  • D. A. Wolf-Gladrow , Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , Springer-Verlag , Berlin-Heidelberg , 2000 .
  • S. Succi , The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , Oxford University Press , New York , 2001 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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.
  • W. A. Fiveland , Three-Dimensional Radiative Heat-Transfer Solutions by the Discrete-Ordinates Method , J. Thermophys. Heat Transfer , vol. 2 , pp. 309 – 316 , 1988 .
  • 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 .
  • 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 .
  • 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 .
  • R. Siegel and J. Howell , Thermal Radiation Heat Transfer, ed. , 4th , Taylor & Francis , New York , 2002 .
  • M. F. Modest , Radiative Heat Transfer, , 2nd ed. , Academic Press , New York , 2003 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .
  • 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 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.