A time-dependent integral formulation is developed for modeling transient radiative transfer. The development is based on a rigorous analysis of the wave propagation process inside the participating media. The physical significance of the present integral formulation is the consideration of the time-dependent domain of computation, which is different from the domain disturbed by radiation (i.e., the wave front envelope). Numerical computations are performed for the medium that is an absorbing and isotropically scattering one-dimensional plane slab geometry. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary.
Issue Section:
Radiative Transfer
1.
Mitra
, K.
, and Kumar
, S.
, 1999
, “Development and Comparison of Models for Light-Pulse Transport through Scattering-Absorbing Media
,” Appl. Opt.
, 38
, No. 1
, pp. 188
–196
.2.
Crosbie
, A. L.
, and Dougherty
, R. L.
, 1982
, “Two-Dimensional Linearly Anisotropic Scattering in a Semi-Infinite Cylindrical Medium Exposed to a Laser Beam
,” J. Quant. Spectrosc. Radiat. Transf.
, 28
, No. 3
, pp. 233
–263
.3.
Menguc
, M. P.
, and Viskanta
, R.
, 1987
, “Radiation Heat Transfer in Combustion Systems
,” Prog. Energy Combust. Sci.
, 13
, pp. 97
–160
.4.
Weinman
, J. A.
, and Shipley
, S. T.
, 1972
, “Effects of Multiple Scattering on Laser Pulses Transmitted Through Clouds
,” J. Geophys. Res.
, 77
, pp. 7123
–7128
.5.
Yamada, Y., 1995, “Light-Tissue Interaction and Optical Imaging in Biomedicine,” Annual Review of Fluid Mechanics and Heat Transfer, C. L. Tien, ed., 6, Begell House, New York, pp. 1–59.
6.
Majumdar, A., 1998, “Microscale Energy Transport in Solids,” Microscale Energy Transport, C. L. Tien et al., eds., Begell House, New York, pp. 1–93.
7.
Longtin
, J. P.
, and Tien
, C. L.
, 1996
, “Saturable Absorption during High-Intensity Laser Heating of Liquids
,” ASME J. Heat Transfer
118
, pp. 924
–930
.8.
Qiu
, T. Q.
, and Tien
, C. L.
, 1992
, “Short Pulse Laser Heating in Metals
,” Int. J. Heat Mass Transf.
, 35
, pp. 719
–726
.9.
Liu
, F.
, Yoo
, K. M.
, and Alfano
, R. R.
, 1993
, “Ultrafast Laser-Pulse Transmission and Imaging through Biological Tissues
,” Appl. Opt.
, 32
, No. 4
, pp. 554
–558
.10.
Gemert
, M. J. C.
, and Welch
, A. J.
, 1989
, “Clinical Use of Laser-Tissue Interaction
,” IEEE Eng. Med. Biol. Mag.
, 1989
, pp. 10
–13
.11.
Grant
, K. J.
, Piper
, J. A.
, Ramsay
, D. J.
, and Williams
, K. L.
, 1993
, “Pulse Lasers in Particle Detection and Sizing
,” Appl. Opt.
, 32
, No. 4
, pp. 416
–417
.12.
Mitra, K., and Kumar, S., 1997, “Application of Transient Radiative Transfer Equation to Oceanographic Lidar,” ASME HTD-Vol. 353, pp. 359–365.
13.
Balsara
, D. W.
, 1999
, “An Analysis of the Hyperbolic Nature of the Equations of Radiation Hydrodynamics
,” J. Quant. Spectrosc. Radiat. Transf.
, 61
, No. 5
, pp. 617
–627
.14.
Mitra
, K.
, Lai
, M.-S.
, and Kumar
, S.
, 1997
, “Transient Radiation Transport in Participating Media With a Rectangular Enclosure
,” AIAA J. Thermophysics and Heat Transfer
, 11
, No. 3
, pp. 409
–414
.15.
Wu
, C.-Y.
, 1989
, “Hyperbolic Heat Conduction with Surface Radiation and Reflection
,” Int. J. Heat Mass Transf.
, 32
, No. 8
, pp. 1585
–1587
.16.
Frankel
, J. I.
, 1991
, “A Nonlinear Heat Transfer Problem. Solution of Nonlinear, Weakly Singular Volterra Partial Integral Equations of the Second Kind
,” Eng. Anal. Boundary Elem.
, 8
, No. 5
, pp. 231
–238
.17.
Cotta
, R. M.
, 1994
, “Benchmark Results in Computational Heat and Fluid Flow: the Integral Transform Method
,” Int. J. Heat Mass Transf.
, 37
, Suppl. 1, pp. 381
–393
.18.
Ramankutty
, M. A.
, and Crosbie
, A. L.
, 1998
, “Modified Discrete-Ordinates Solution of Radiative Transfer in Three-Dimensional Rectangular Enclosures
,” J. Quant. Spectrosc. Radiat. Transf.
, 60
, No. 1
, pp. 103
–134
.19.
Ramankutty
, M. A.
, and Crosbie
, A. L.
, 1997
, “Modified Discrete-Ordinates Solution of Radiative Transfer in Two-Dimensional Rectangular Enclosures
,” J. Quant. Spectrosc. Radiat. Transf.
, 57
, No. 1
, pp. 107
–140
.20.
Roe
, P. L.
, 1986
, “Characteristic-Based Schemes for the Euler Equation
,” Annu. Rev. Fluid Mech.
, 18
, pp. 337
–365
.21.
Harten
, A.
, 1983
, “High Resolution Schemes for Hyperbolic Conservation Laws
,” J. Comput. Phys.
, 49
, pp. 357
–393
.22.
Shu
, C.-W.
, 1988
, “Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes
,” J. Comput. Phys.
, 77
, pp. 439
–471
.23.
Tannehill, J. C., Anderson, D. A., and Pletcher, R. H., 1997, Computational Fluid Mechanics and Heat Transfer, 2nd ed., Taylor & Francis, Washington, DC.
24.
Tan
, Z.
, 1989
, “Radiative Heat Transfer in Multidimensional Emitting, Absorbing, and Anisotropic Scattering Media—Mathematical Formulation and Numerical Method
,” ASME J. Heat Transfer
, 111
, pp. 141
–146
.25.
Tan
, Z.
, and Howell
, J. R.
, 1990
, “A New Numerical Method for Radiation Heat Transfer in Nonhomogeneous Participating Media
,” AIAA J. Thermophysics and Heat Transfer
, 4
, No. 4
, pp. 419
–424
.26.
Hsu
, P.-F.
, Tan
, Z.
, and Howell
, J. R.
, 1993
, “Radiative Transfer by the YIX Method in a Nonhomogeneous, Scattering and Non-Gray Medium
,” AIAA J. Thermophysics and Heat Transfer
, 7
, No. 3
, pp. 487
–495
.27.
Huan
, J.
, and Naraghi
, M. H. N.
, 1991
, “Source Function Approach for Radiative Heat Transfer Analysis
,” AIAA J. Thermophysics and Heat Transfer
, 6
, No. 3
, pp. 568
–571
.28.
Wu, S.-H., Wu, C.-Y., and Hsu, P.-F., 1996, “Solutions of Radiative Transfer in Inhomogeneous Participating Media Using the Quadrature Method,” presented at the ASME 1996 Int. Mechanical Engineering Congress & Exposition, Atlanta, GA, November 1996, ASME HTD-Vol. 332, pp. 101–108.
29.
Penzkofer
, A.
, 1988
, “Passive W-Switching and Mode-Locking for the Generation of Nanosecond to Femtosecond Pulses
,” Applied Physics B
, 46
, pp. 43
–60
.30.
Wu, C.-Y., 1999, private communication.
31.
Pomraning, G. C., 1973, The Equations of Radiation Hydrodynamics, Pergamon Press, New York.
32.
Ozisik, M. N., 1973, Radiative Transfer and Interaction with Conduction and Convection, Wiley, New York.
33.
Modest, M. F. 1993, Radiative Heat Transfer, McGraw-Hill, New York.
34.
Siegel, R., and Howell, J. R., 1992, Thermal Radiative Heat Transfer, 3rd ed., Taylor & Francis, Washington, DC.
35.
Panton, R. L., 1996, Incompressible Flow, 2nd ed., Wiley, New York.
36.
Linz, P., 1985, Analytical and Numerical Methods for Volterra Equation, SIAM.
37.
Wu
, C.-Y.
, 1990
, “Exact Integral Formulation for Radiative Transfer in an Inhomogeneous Scattering Medium
,” AIAA J. Thermophysics and Heat Transfer
, 4
(4
), pp. 425
–431
.38.
Hsu, P.-F., 2000, “Effects of Multiple Scattering and Reflective Boundary on the Transient Radiative Transfer Process,” the 2000 National Heat Transfer Conf., paper NHTC2000-12078, Pittsburgh, PA.
Copyright © 2001
by ASME
You do not currently have access to this content.
