0
Journal of Heat Transfer | Volume 129 | Issue 8 | TECHNICAL PAPERS
TECHNICAL PAPERS: Radiative Heat Transfer

Discontinuous Finite Element Approach for Transient Radiative Transfer Equation

[+] Author and Article Information
L. H. Liu1

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P.R. Chinalhliu@hit.edu.cn

L. J. Liu

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P.R. China

1

Corresponding author.

J. Heat Transfer 129(8), 1069-1074 (Jan 17, 2007) (6 pages) doi:10.1115/1.2737477 History: Received September 03, 2006; Revised January 17, 2007
Article
References
Figures
Citing Articles

A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.
FIGURES IN THIS ARTICLE
<>
Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

1
Tien, C. L., Majumdar, A., and Gerner, F., 1998, "Microscale Energy Transport", Begell House, New York, Redding, CT, pp. 1–93.
2
Longtin, J. P., and Tien, C. L., 1996, “Saturable Absorption During High Intensity Laser Heating of Liquids,” ASME J. Heat Transfer, 118 (4), pp. 924–930.
3
Qiu, T. Q., and Tien, C. L., 1992, “Short Pulse Laser Heating in Metals,” Int. J. Heat Mass Transfer  [CrossRef], 35 (3), pp. 719–726.
4
Yamada, Y., and Tien, C. L., 1995, “Light-Tissue Interaction and Optical Imaging in Biomediacine,” Annu. Rev. Fluid Mech.  [CrossRef], 6 , pp. 1–59.
5
Liu, F., Yoo, K. M., and Alfano, R. R., 1993, “Ultrafast Laser-Pulse Transmission and Imaging Through Biological Tissues,” Appl. Opt., 32 (4), pp. 554–558.
6
Grant, M. J. C., and Welch, A. J., 1989, “Clinical Use of Laser-Tissue Interaction,” IEEE Eng. Med. Biol. Mag.  [CrossRef], 8 (4), pp. 10–13.
7
Kumar, S., and Mitra, K., 1999, “Microscale Aspects of Thermal Radiation and Laser Applications,” Adv. Heat Transfer, 33 , pp. 187–294.
8
Brewster, M. Q., and Yamada, Y., 1995, “Optical Properties of Thick, Turbid Media From Picosecond Time-Resolved Light Scattering Measurements,” Int. J. Heat Mass Transfer  [CrossRef], 38 (14), pp. 2569–2581.
9
Guo, Z. X., Aber, J., Garetz, B. A., and Kumar, S., 2002, “Monte Carlo Simulation and Experiments of Pulsed Radiative Transfer,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 73 (2–5), pp. 159–168.
10
Lu, X. D., and Hsu, P.-F., 2004, “Reverse Monte Carlo Method for Transient Radiative Transfer in Participating Media,” ASME J. Heat Transfer  [CrossRef], 126 (4), pp. 621–627.
11
Wu, C. Y., and Wu, S. H., 2000, “Integral Equation Formulation for Transient Radiative Transfer in an Anisotropically Scattering Medium,” Int. J. Heat Mass Transfer  [CrossRef], 43 (11), pp. 2009–2020.
12
Wu, C. Y., 2000, “Propagation of Scattered Radiation in a Participating Planar Medium With Pulse Irradiation,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 64 (5), pp. 537–548.
13
Wu, S. H., and Wu, C. Y., 2001, “Time-Resolved Spatial Distribution of Scattered Radiative Energy in A Two-Dimensional Cylindrical Medium With a Large Mean Free Path for Scattering,” Int. J. Heat Mass Transfer  [CrossRef], 44 (14), pp. 2611–2619.
14
Tan, Z. M., and Hsu, P.-F., 2001, “An Integral Formulation of Transient Radiative Transfer,” ASME J. Heat Transfer  [CrossRef], 123 (3), pp. 466–475.
15
Tan, Z. M., Hsu, P.-F., and Chai, J. C., 2002, “Transient Radiative Transfer in Three-Dimensional Homogeneous and Non-Homogeneous Participating Media,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 73 (2–5), pp. 181–194.
16
Chai, J. C., 2003, “One-Dimensional Transient Radiation Heat Transfer Modeling Using a Finite-Volume Method,” Numer. Heat Transfer, Part B, 44 (2), pp. 187–208.
17
Chai, J. C., 2004, “Transient Radiative Transfer Modeling in Irregular Two-Dimensional Geometries,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 84 (3), pp. 281–294.
18
Chai, J. C., Hsu, P.-F., and Lam, Y. C., 2004, “Three-Dimensional Transient Radiative Transfer Modeling Using the Finite-Volume Method,” J. Quant. Spectrosc. Radiat. Transf., 86 (3), pp. 299–313.
19
Sakami, M., Mitra, K., and Hsu, P.-F., 2000, “Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes,” ASME Int. Mechanical Engineering Congress & Exposition, Orlando, Nov, ASME HTD-Vol. 366-1 , pp. 135–143.
20
Sakami, M., Mitra, K., and Hsu, P.-F., 2002, “Analysis of Light Pulse Transport Through Two-Dimensional Scattering and Absorbing Media,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 73 (2–5), pp. 169–179.
21
Cui, X., and Li, B. Q., 2004, “A Discontinuous Finite Element Formulation for Internal Radiation Problems,” Numer. Heat Transfer, Part B  [CrossRef], 46 (3), pp. 223–242.
22
Cui, X., and Li, B. Q., 2004, “A Discontinuous Finite Element Formulation for Multidimensional Radiative Transfer in Absorbing, Emitting, and Scattering Media,” Numer. Heat Transfer, Part B  [CrossRef], 46 (5), pp. 399–428.
23
Cui, X., and Li, B. Q., 2005, “Discontinuous Finite Element Solution of 2-D Radiative Transfer With and Without Axisymmetry,” J. Quant. Spectrosc. Radiat. Transf.  [CrossRef], 96 (3–4), pp. 383–407.
24
Reed, W. H., and Hill, T. R., 1973, “Triangular Mesh Methods for the Neutron Transport Equation,” Los Alamos Scientific Laboratory Technical Report No. LA-UR-73–479, Los Alamos, NM.
25
Chen, Z. X., 2005, "Finite Element Methods and Their Applications", Springer-Verlag, Berlin.
26
Li, B. Q., 2006, "Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer", Springer-Verlag, Berlin.
27
Chai, J. C., Lee, H. S., and Patankar, S. V., 1994, “Improved Treatment of Scattering Using the Discrete Ordinates Method,” ASME J. Heat Transfer, 116 (1), pp. 260–263.

Figures

Grahic Jump Location
+Element boundary, its unit outward normal vectors, and the neighboring elements
View Large  |  Save Figure  |  Download Slide (.ppt)
Element boundary, its unit outward normal vectors, and the neighboring elements
Figure 1

Element boundary, its unit outward normal vectors, and the neighboring elements

Grahic Jump Location
+Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements
View Large  |  Save Figure  |  Download Slide (.ppt)
Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements
Figure 2

Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements

Grahic Jump Location
+Dimensionless incident radiation distributions at different dimensionless times
View Large  |  Save Figure  |  Download Slide (.ppt)
Dimensionless incident radiation distributions at different dimensionless times
Figure 3

Dimensionless incident radiation distributions at different dimensionless times

Grahic Jump Location
+Dimensionless radiation heat flux distributions at different dimensionless times
View Large  |  Save Figure  |  Download Slide (.ppt)
Dimensionless radiation heat flux distributions at different dimensionless times
Figure 4

Dimensionless radiation heat flux distributions at different dimensionless times

Grahic Jump Location
+Effects of dimensionless time step on the solution accuracy for incident radiation
View Large  |  Save Figure  |  Download Slide (.ppt)
Effects of dimensionless time step on the solution accuracy for incident radiation
Figure 5

Effects of dimensionless time step on the solution accuracy for incident radiation

Grahic Jump Location
+Dimensionless incident radiation distributions in medium with collimated irradiation at boundary
View Large  |  Save Figure  |  Download Slide (.ppt)
Dimensionless incident radiation distributions in medium with collimated irradiation at boundary
Figure 6

Dimensionless incident radiation distributions in medium with collimated irradiation at boundary

Grahic Jump Location
+Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary
View Large  |  Save Figure  |  Download Slide (.ppt)
Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary
Figure 7

Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary

Grahic Jump Location
+Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)
Figure 8

Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)

Grahic Jump Location
+Relationship of node, boundary, and upwind radiative intensity in triangular elements
View Large  |  Save Figure  |  Download Slide (.ppt)
Relationship of node, boundary, and upwind radiative intensity in triangular elements
Figure 9

Relationship of node, boundary, and upwind radiative intensity in triangular elements

Grahic Jump Location
+Transient evolution of dimensionless radiative heat fluxes on the bottom wall
View Large  |  Save Figure  |  Download Slide (.ppt)
Transient evolution of dimensionless radiative heat fluxes on the bottom wall
Figure 10

Transient evolution of dimensionless radiative heat fluxes on the bottom wall

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Short-Pulse Collimated Radiation in a Participating Medium Bounded by Diffusely Reflecting Boundaries
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Compare the Results of Comsol Multiphysics Software and Matlab Pdetool in Finite Element Analysis of the Diffusiion Equation
International Conference on Computer Engineering and Technology, 3rd (ICCET 2011)
Basic Finite Element Equations
Design of Plate and Shell Structures> Chapter 16
Modeling Grain Boundary Scattering in Nanocomposites
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)
Study on Load Position Switching of Radial Scattering Dispenser
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In