Abstract

The natural element method (NEM) is extended to solve transient radiative transfer (TRT) in two-dimensional semitransparent media subjected to a collimated short laser irradiation. The least-squares (LS) weighted residuals approach is employed to spatially discretize the transient radiative heat transfer equation. First, for the case of the refractive index matched boundary, LSNEM solutions to TRT are validated by comparison with results reported in the literature. Effects of the incident angle on time-resolved signals of transmittance and reflectance are investigated. Afterward, the accuracy of this algorithm for the case of the refractive index mismatched boundary is studied. Finally, the LSNEM is extended to study the TRT in a two-dimensional semitransparent medium with refractive index discontinuity irradiated by the short pulse laser. The effects of scattering albedo, optical thickness, scattering phase function, and refractive index on transmittance and reflectance signals are investigated. Several interesting trends on the time-resolved signals are observed and analyzed.

© 2014 Optical Society of America

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    [CrossRef]
  2. J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” J. Heat Transfer 124, 1176–1181 (2002).
    [CrossRef]
  3. T. Q. Qiu and C. L. Tien, “Short-pulse laser heating on metals,” Int. J. Heat Mass Transfer 35, 719–726 (1992).
    [CrossRef]
  4. F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Appl. Opt. 32, 554–558 (1993).
    [CrossRef]
  5. M. J. C. Grant and A. J. Welch, “Clinical use of laser-tissue interactions,” IEEE Eng. Med. Biol. Mag. 8, 10–13 (1989).
    [CrossRef]
  6. K. J. Grant, J. A. Piper, D. J. Ramsay, and K. L. Williams, “Pulse lasers in particle detection and sizing,” Appl. Opt. 32, 416–417 (1993).
    [CrossRef]
  7. S. Kumar and K. Mitra, “Microscale aspects of thermal radiation and laser applications,” Adv. Heat Transfer 33, 187–294 (1999).
    [CrossRef]
  8. H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).
  9. Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
    [CrossRef]
  10. X. D. Lu and P. F. Hsu, “Reverse Monte Carlo method for transient radiative transfer in participating media,” J. Heat Transfer 126, 621–627 (2004).
    [CrossRef]
  11. X. D. Lu and P. F. Hsu, “Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media,” J. Quant. Spectrosc. Radiat. Transfer 93, 349–367 (2005).
    [CrossRef]
  12. M. Martinelli, A. Gardner, D. Cuccia, C. Hayakawa, J. Spanier, and V. Venugopalan, “Analysis of single Monte Carlo methods for prediction of reflectance from turbid media,” Opt. Express 19, 19627–19642 (2011).
    [CrossRef]
  13. Z. X. Guo and S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
    [CrossRef]
  14. M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 73, 169–179 (2002).
    [CrossRef]
  15. Z. X. Guo and S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
    [CrossRef]
  16. J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53, 3799–3806 (2010).
    [CrossRef]
  17. Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” J. Heat Transfer 123, 466–475 (2001).
    [CrossRef]
  18. C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transfer 64, 537–548 (2000).
    [CrossRef]
  19. P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40, 539–549 (2001).
    [CrossRef]
  20. J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer. Heat Transfer B 44, 187–208 (2003).
    [CrossRef]
  21. M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer 53, 5682–5691 (2010).
    [CrossRef]
  22. L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
    [CrossRef]
  23. S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
    [CrossRef]
  24. L. H. Liu and L. J. Liu, “Discontinuous finite element approach for transient radiative transfer equation,” J. Heat Transfer 129, 1069–1074 (2007).
    [CrossRef]
  25. L. H. Liu and P. F. Hsu, “Time shift and superposition method for solving transient radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 1297–1308 (2008).
    [CrossRef]
  26. Y. Zhang, H. L. Yi, and H. P. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21, 24532–24549 (2013).
    [CrossRef]
  27. J. Braun and M. Sambridge, “A numerical method for solving partial differential equations on highly irregular evolving grids,” Nature 376, 655–660 (1995).
    [CrossRef]
  28. N. Sukumar, B. Moran, and T. Belytschko, “The natural element method in solid mechanics,” Int. J. Numer. Methods Eng. 43, 839–887 (1998).
    [CrossRef]
  29. Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method for radiative heat transfer in two-dimensional semitransparent medium,” Int. J. Heat Mass Transfer 56, 411–423 (2013).
    [CrossRef]
  30. Y. Zhang, H. L. Yi, and H. P. Tan, “Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces,” Int. J. Heat Mass Transfer 66, 349–354 (2013).
    [CrossRef]
  31. Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries,” Int. J. Therm. Sci. 76, 30–42 (2014).
    [CrossRef]
  32. R. Siegel and C. M. Spuckler, “Variable refractive index effects on radiation in semitransparent scattering multilayered regions,” J. Thermophys. Heat Transfer 7, 624–630 (1993).
    [CrossRef]

2014 (1)

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries,” Int. J. Therm. Sci. 76, 30–42 (2014).
[CrossRef]

2013 (3)

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method for radiative heat transfer in two-dimensional semitransparent medium,” Int. J. Heat Mass Transfer 56, 411–423 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces,” Int. J. Heat Mass Transfer 66, 349–354 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21, 24532–24549 (2013).
[CrossRef]

2011 (1)

2010 (3)

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53, 3799–3806 (2010).
[CrossRef]

M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer 53, 5682–5691 (2010).
[CrossRef]

L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
[CrossRef]

2008 (1)

L. H. Liu and P. F. Hsu, “Time shift and superposition method for solving transient radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 1297–1308 (2008).
[CrossRef]

2007 (1)

L. H. Liu and L. J. Liu, “Discontinuous finite element approach for transient radiative transfer equation,” J. Heat Transfer 129, 1069–1074 (2007).
[CrossRef]

2006 (1)

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
[CrossRef]

2005 (1)

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media,” J. Quant. Spectrosc. Radiat. Transfer 93, 349–367 (2005).
[CrossRef]

2004 (1)

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo method for transient radiative transfer in participating media,” J. Heat Transfer 126, 621–627 (2004).
[CrossRef]

2003 (1)

J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer. Heat Transfer B 44, 187–208 (2003).
[CrossRef]

2002 (4)

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 73, 169–179 (2002).
[CrossRef]

Z. X. Guo and S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
[CrossRef]

J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” J. Heat Transfer 124, 1176–1181 (2002).
[CrossRef]

2001 (4)

H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).

P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40, 539–549 (2001).
[CrossRef]

Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” J. Heat Transfer 123, 466–475 (2001).
[CrossRef]

Z. X. Guo and S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
[CrossRef]

2000 (1)

C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transfer 64, 537–548 (2000).
[CrossRef]

1999 (1)

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation and laser applications,” Adv. Heat Transfer 33, 187–294 (1999).
[CrossRef]

1998 (1)

N. Sukumar, B. Moran, and T. Belytschko, “The natural element method in solid mechanics,” Int. J. Numer. Methods Eng. 43, 839–887 (1998).
[CrossRef]

1995 (1)

J. Braun and M. Sambridge, “A numerical method for solving partial differential equations on highly irregular evolving grids,” Nature 376, 655–660 (1995).
[CrossRef]

1993 (4)

R. Siegel and C. M. Spuckler, “Variable refractive index effects on radiation in semitransparent scattering multilayered regions,” J. Thermophys. Heat Transfer 7, 624–630 (1993).
[CrossRef]

K. J. Grant, J. A. Piper, D. J. Ramsay, and K. L. Williams, “Pulse lasers in particle detection and sizing,” Appl. Opt. 32, 416–417 (1993).
[CrossRef]

F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Appl. Opt. 32, 554–558 (1993).
[CrossRef]

A. Majumdar, “Microscale heat conduction in dielectric thin films,” J. Heat Transfer 115, 7–16 (1993).
[CrossRef]

1992 (1)

T. Q. Qiu and C. L. Tien, “Short-pulse laser heating on metals,” Int. J. Heat Mass Transfer 35, 719–726 (1992).
[CrossRef]

1989 (1)

M. J. C. Grant and A. J. Welch, “Clinical use of laser-tissue interactions,” IEEE Eng. Med. Biol. Mag. 8, 10–13 (1989).
[CrossRef]

Aber, J.

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
[CrossRef]

Alfano, R. R.

Baek, S. W.

M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer 53, 5682–5691 (2010).
[CrossRef]

Belytschko, T.

N. Sukumar, B. Moran, and T. Belytschko, “The natural element method in solid mechanics,” Int. J. Numer. Methods Eng. 43, 839–887 (1998).
[CrossRef]

Braun, J.

J. Braun and M. Sambridge, “A numerical method for solving partial differential equations on highly irregular evolving grids,” Nature 376, 655–660 (1995).
[CrossRef]

Chai, J. C.

J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer. Heat Transfer B 44, 187–208 (2003).
[CrossRef]

Chugh, P.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
[CrossRef]

Costa, M.

H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).

Cuccia, D.

Gardner, A.

Garetz, B. A.

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
[CrossRef]

Grant, K. J.

Grant, M. J. C.

M. J. C. Grant and A. J. Welch, “Clinical use of laser-tissue interactions,” IEEE Eng. Med. Biol. Mag. 8, 10–13 (1989).
[CrossRef]

Guo, Z.

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
[CrossRef]

Guo, Z. X.

Z. X. Guo and S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

Z. X. Guo and S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
[CrossRef]

Hayakawa, C.

Hsu, P. F.

L. H. Liu and P. F. Hsu, “Time shift and superposition method for solving transient radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 1297–1308 (2008).
[CrossRef]

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media,” J. Quant. Spectrosc. Radiat. Transfer 93, 349–367 (2005).
[CrossRef]

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo method for transient radiative transfer in participating media,” J. Heat Transfer 126, 621–627 (2004).
[CrossRef]

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 73, 169–179 (2002).
[CrossRef]

Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” J. Heat Transfer 123, 466–475 (2001).
[CrossRef]

P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40, 539–549 (2001).
[CrossRef]

Kim, M. Y.

M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer 53, 5682–5691 (2010).
[CrossRef]

Kumar, P.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
[CrossRef]

Kumar, S.

Z. X. Guo and S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 73, 159–168 (2002).
[CrossRef]

Z. X. Guo and S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
[CrossRef]

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation and laser applications,” Adv. Heat Transfer 33, 187–294 (1999).
[CrossRef]

Liu, F.

Liu, L. H.

L. H. Liu and P. F. Hsu, “Time shift and superposition method for solving transient radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 1297–1308 (2008).
[CrossRef]

L. H. Liu and L. J. Liu, “Discontinuous finite element approach for transient radiative transfer equation,” J. Heat Transfer 129, 1069–1074 (2007).
[CrossRef]

Liu, L. J.

L. H. Liu and L. J. Liu, “Discontinuous finite element approach for transient radiative transfer equation,” J. Heat Transfer 129, 1069–1074 (2007).
[CrossRef]

Lu, X. D.

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media,” J. Quant. Spectrosc. Radiat. Transfer 93, 349–367 (2005).
[CrossRef]

X. D. Lu and P. F. Hsu, “Reverse Monte Carlo method for transient radiative transfer in participating media,” J. Heat Transfer 126, 621–627 (2004).
[CrossRef]

Majumdar, A.

A. Majumdar, “Microscale heat conduction in dielectric thin films,” J. Heat Transfer 115, 7–16 (1993).
[CrossRef]

Martinelli, M.

Mathur, S. R.

J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” J. Heat Transfer 124, 1176–1181 (2002).
[CrossRef]

Menon, S.

M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer 53, 5682–5691 (2010).
[CrossRef]

Mishra, S. C.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
[CrossRef]

Mitra, K.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49, 1820–1832 (2006).
[CrossRef]

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 73, 169–179 (2002).
[CrossRef]

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation and laser applications,” Adv. Heat Transfer 33, 187–294 (1999).
[CrossRef]

Moran, B.

N. Sukumar, B. Moran, and T. Belytschko, “The natural element method in solid mechanics,” Int. J. Numer. Methods Eng. 43, 839–887 (1998).
[CrossRef]

Murthy, J. Y.

J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” J. Heat Transfer 124, 1176–1181 (2002).
[CrossRef]

Oliva, A.

H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).

Piper, J. A.

Qi, H.

L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
[CrossRef]

Qiu, T. Q.

T. Q. Qiu and C. L. Tien, “Short-pulse laser heating on metals,” Int. J. Heat Mass Transfer 35, 719–726 (1992).
[CrossRef]

Ramsay, D. J.

Ruan, L. M.

L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
[CrossRef]

Sakami, M.

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 73, 169–179 (2002).
[CrossRef]

Sambridge, M.

J. Braun and M. Sambridge, “A numerical method for solving partial differential equations on highly irregular evolving grids,” Nature 376, 655–660 (1995).
[CrossRef]

Schweiger, H.

H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).

Segarra, C. D. P.

H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transfer B 35, 113–136 (2001).

Siegel, R.

R. Siegel and C. M. Spuckler, “Variable refractive index effects on radiation in semitransparent scattering multilayered regions,” J. Thermophys. Heat Transfer 7, 624–630 (1993).
[CrossRef]

Spanier, J.

Spuckler, C. M.

R. Siegel and C. M. Spuckler, “Variable refractive index effects on radiation in semitransparent scattering multilayered regions,” J. Thermophys. Heat Transfer 7, 624–630 (1993).
[CrossRef]

Sukumar, N.

N. Sukumar, B. Moran, and T. Belytschko, “The natural element method in solid mechanics,” Int. J. Numer. Methods Eng. 43, 839–887 (1998).
[CrossRef]

Tan, H. P.

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries,” Int. J. Therm. Sci. 76, 30–42 (2014).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21, 24532–24549 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces,” Int. J. Heat Mass Transfer 66, 349–354 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method for radiative heat transfer in two-dimensional semitransparent medium,” Int. J. Heat Mass Transfer 56, 411–423 (2013).
[CrossRef]

Tan, Z. M.

Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” J. Heat Transfer 123, 466–475 (2001).
[CrossRef]

Tien, C. L.

T. Q. Qiu and C. L. Tien, “Short-pulse laser heating on metals,” Int. J. Heat Mass Transfer 35, 719–726 (1992).
[CrossRef]

Venugopalan, V.

Wang, D. L.

L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
[CrossRef]

Wang, J. M.

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53, 3799–3806 (2010).
[CrossRef]

Wang, S. G.

L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transfer 111, 2405–2414 (2010).
[CrossRef]

Welch, A. J.

M. J. C. Grant and A. J. Welch, “Clinical use of laser-tissue interactions,” IEEE Eng. Med. Biol. Mag. 8, 10–13 (1989).
[CrossRef]

Williams, K. L.

Wu, C. Y.

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53, 3799–3806 (2010).
[CrossRef]

C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transfer 64, 537–548 (2000).
[CrossRef]

Yi, H. L.

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries,” Int. J. Therm. Sci. 76, 30–42 (2014).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method for radiative heat transfer in two-dimensional semitransparent medium,” Int. J. Heat Mass Transfer 56, 411–423 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces,” Int. J. Heat Mass Transfer 66, 349–354 (2013).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21, 24532–24549 (2013).
[CrossRef]

Yoo, K. M.

Zhang, Y.

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries,” Int. J. Therm. Sci. 76, 30–42 (2014).
[CrossRef]

Y. Zhang, H. L. Yi, and H. P. Tan, “Natural element method for radiative heat transfer in two-dimensional semitransparent medium,” Int. J. Heat Mass Transfer 56, 411–423 (2013).
[CrossRef]

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