Recent progress in computational thermal radiative transfer

Modest M F. Radiative Heat Transfer. 2nd ed. New York: Academic Press, 2003 Tan H P, Xia X L, Liu L H, et al. Numerical calculation for infrared radiative characteristics and transfer—computational thermal radiation. Harbin: Press of the Harbin Institute of Technology, 2006 Liu L H, Zhao J M, Tan H P. Finite/Spectral Element Methods for Solving Radiative Transfer Equation (in Chinese). Beijing: Science Press, 2008 Tan H P, Lallemand M. Transient radiative-conductive heat transfer in flat glasses submitted to temperature, flux and mixed boundary conditions. Int J Heat Mass Transfer, 1989, 32: 795–810 Tan H P, Maestre B, Lallemand M. Transient and steady-state combined heat transfer in semi-transparent materials subjected to a pulse or a step irradiation. J Heat Trans-T ASME, 1991, 113: 166–173 Tan H P, Ruan L M, Xia X L, et al. Transient coupled radiative and conductive heat transfer in an absorbing, emitting and scattering medium. Int J Heat Mass Transfer, 1999, 42: 2967–2980 Tan H P, Ruan L M, Tong T W. Temperature response in absorbing, isotropic scattering medium caused by laser pulse. Int J Heat Mass Transfer, 2000, 43: 311–320 Tan H P, Luo J F, Xia X L. Transient coupled radiation and conduction in a three-layer composite with semitransparent specular interfaces and surfaces. J Heat Trans-T ASME, 2002, 124: 470–481 Luo J F, Xia X L, Tan H P, et al. Transient coupled heat transfer in three-layer composite with opaque specular surfaces. J Thermophys Heat Tr, 2002, 16: 297–305 Luo J F, Tan H P, Ruan L M, et al. Refractive index effects on heat transfer in multilayer scattering composite. J Thermophys Heat Tr, 2003, 17: 407–419 Tan H P, Luo J F, Ruan L M, et al. Transient coupled heat transfer in a multi-layer composite with opaque specular surfaces and semitransparent specular interfaces. Int J Therm Sci, 2003, 42: 209–222 Tan H P, Luo J F, Xia X L, et al. Transient coupled heat transfer in multi-layer composite with one specular boundary coated. Int J Heat Mass Transfer, 2003, 46: 731–747 Tan H P, Yi H L, Wang P Y, et al. Ray tracing method for transient coupled heat transfer in an anisotropic scattering layer. Int J Heat Mass Transfer, 2004, 47: 4045–4059 Yi H L, Xie M, Tan H P. Transient coupled heat transfer in an anisotropic scattering composite slab with semitransparent surfaces. Int J Heat Mass Transfer, 2008, 51: 5918–5930 Yi H L, Xie M, Tan H P. Ray tracing method for radiative heat transfer within a two-layer anisotropic scattering medium. Numer Heat Tr A-Appl, 2008, 54: 481–506 Tan H P, Yi H L, Luo J F, et al. Transient coupled heat transfer inside a scattering medium with graded refractive index. J Thermophys Heat Tr, 2006, 20: 583–594 Yi H L, Tan H P, Zhang H C, et al. Ray-tracing/nodal-analyzing model for transient thermal behavior of a scattering medium with a variable refractive index. Numer Heat Tr A-Appl, 2006, 49: 607–634 Yi H L, Tan H P. Transient radiative heat transfer in an inhomogeneous participating medium with Fresnel’s surfaces. Sci China Ser E: Tech Sci, 2008, 51: 1110–1124 Reddy J N, Murty V D. Finite element solution of integral equations arising in radiative heat transfer and laminar boundary-layer theory. Numer Heat Tr, 1978, 1: 389–401 Razzaque M M, Klein D E, Howell J R. Finite element solution of radiative heat transfer in two-dimensional rectangular enclosure with gray participating media. J Heat Trans-T ASME, 1983, 105: 933–936 Fiveland W A, Jessee J P. Finite element formulation of the discreteordinates method for multidimensional geometries. J Thermophys Heat Tr, 1994, 8: 426–433 Liu L H. Finite element simulation of radiative heat transfer in absorbing and scattering media. J Thermophys Heat Tr. 2004, 18: 555–557 Zhang L, Liu L H, Zhao J M. Upwind finite element method for solving radiative heat transfer in semitransparent media. Proc CSEE, 2007, 27: 73–77 Liu L H. Least-squares finite element method for radiative heat transfer in graded index medium. J Quant Spectrosc Ra, 2007, 103: 536–544 Zhao J M, Liu L H. Second order radiative transfer equation and its properties of numerical solution using finite element method. Numer Heat Tr B-Fund, 2007, 51: 391–409 Coelho P J. A hybrid finite volume/finite element discretization method for the solution of the solution of the radiative heat transfer equation. J Quant Spectrosc Ra, 2005, 93: 89–101 An W, Ruan L M, Tan H P, et al. Least-squares finite element analysis for transient radiative transfer in absorbing and scattering media. J Heat Trans-T ASME, 2006, 128: 499–503 Liu L H. Finite Element solution of radiative transfer across a slab with variable spatial refractive Index. Int J Heat Mass Transfer, 2005, 48: 2260–2265 Liu L H, Zhang L, Tan H P. Finite element method for radiation heat transfer in multi-dimensional graded index medium. J Quant Spectrosc Ra, 2006, 97: 436–445 Li B W, Sun Y S, Zhang D W. Chebyshev collocation spectral methods for coupled radiation and conduction in a concentric spherical participating medium. J Heat Trans-T ASME, 2009, 131: 062701 Li B W, Sun Y S, Yu Y. Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer. Int J Heat Mass Transfer, 2008, 51: 5887–5894 Sun Y S, Li B W. Chebyshev collocation spectral method for onedimensional radiative heat transfer in graded index media. Int J Therm Sci, 2009, 48: 691–698 Zhao J M, Liu L H. Least-squares spectral element method for radiative heat transfer in semitransparent media. Numer Heat Tr B-Fund, 2006, 50: 473–489 Zhao J M, Liu L H. Spectral element approach for coupled radiative and conductive heat transfer in semitransparent medium. J Heat Trans-T ASME, 2007, 129: 1417–1424 Zhao J M, Liu L H. Spectral element method with adaptive artificial diffusion for solving radiative transfer equation. Numer Heat Tr B-Fund, 2008, 53: 536–554 Zhao J M, Liu L H. Solution of radiative heat transfer in graded index media by least square spectral element method. Int J Heat Mass Tran, 2007, 50: 2634–2642 Cui X, Li B Q. Discontinuous finite element solution of 2-D radiative transfer with and without axisymmetry. J Quant Spectrosc Ra, 2005, 96: 383–407 Cui X, Li B Q. A discontinuous finite-element formulation for internal radiation problems. Numer Heat Tr B-Fund, 2004, 46: 223–242 Liu L H, Liu L J. Discontinuous finite element method for radiative heat transfer in semitransparent graded index medium. J Quant Spectrosc Ra, 2007, 105: 377–387 Zhao J M, Liu L H. Discontinuous spectral element method for solving radiative heat transfer in multidimensional semitransparent media. J Quant Spectrosc Ra, 2007, 107: 1–16 Liu L H, Liu L J. Discontinuous finite element approach for transient radiative transfer equation. J Heat Trans-T ASME, 2007, 129: 1069–1074 Liu L H, Hsu P F. Analysis of transient radiative transfer in semitransparent graded index medium. J Quant Spectrosc Ra, 2007, 105: 357–376 Liu L H, Hsu P F. Time shift and superposition method for solving transient radiative transfer equation. J Quant Spectrosc Ra, 2008, 109: 1297–1308 Zhao J M, Liu L H. Discontinuous spectral element approach for solving transient radiative transfer equations. J Thermophys Heat Tr, 2008, 22: 20–28 Liu G R. Mesh Free Methods. Boca Raton: CRC Press, 2003 Zhang X, Liu Y. Meshless Method (in Chinese). Beijing: Science Press, 2004 Liu G R, Gu Y T. An Introduction to Meshfree Methods and Their Programming. New York: Springer, 2005 Liu L H. Meshless local Petrov-Galerkin method for solving radiative transfer equation. J Thermophys Heat Tr, 2006, 20: 150–154 Liu L H. Meshless method for radiative heat transfer in graded index medium. Int J Heat Mass Transfer, 2006, 49: 219–229 Liu L H, Tan J Y. Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium. J Quant Spectrosc Ra, 2006, 101: 237–248 Liu L H, Tan J Y. Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media. J Quant Spectrosc Ra, 2007, 103: 536–544 Tan J Y, Liu L H, Li B X. Least-squares collocation meshless approach for coupled Radiative and conductive heat transfer. Numer Heat Tr B-Fund, 2006, 49: 179–195 Tan J Y, Liu L H, Li B X. Least-squares radial point interpolation collocation meshless approach for radiative transfer. J Heat Trans-T ASME, 2007, 129: 669–673 Liu L H, Tan J Y. Meshless local Petrov-Galerkin approach for coupled radiative and conductive heat transfer. Int J Therm Sci, 2007, 46: 672–681 Born M, Wolf E. Principles of Optics. Cambridge: Cambridge University Press, 1999 Qiao Y T. Graded Index Optics. Beijing: Science Press, 1991 Liu L H, Tan H P. Numerical Simulation of Thermal Radiative Transfer in Graded Index Medium (in Chinese). Beijing: Science Press, 2006 Ben A P, Le Dez V. Thermal field inside an absorbing-emitting semitransparent slab at radiative equilibrium with variable spatial refractive index. J Quant Spectrosc Ra, 2000, 65: 595–608 Ben A P, Le Dez V. Thermal emission of a semitransparent slab with variable spatial refractive index. J Quant Spectrosc Ra, 2000, 67: 185–198 Huang Y, Xia X L, Tan H P. Radiative intensity solution and thermal emission analysis of a semitransparent medium layer with a sinusoidal refractive index. J Quant Spectrosc Ra, 2002, 74: 217–233 Huang Y, Xia X L, Tan H P. Temperature field of radiative equilibrium in a semitransparent slab with a linear refractive index and gray walls. J Quant Spectrosc Ra, 2002, 74: 249–261 Xia X L, Huang Y, Tan H P. Thermal emission and volumetric absorption of a graded index semitransparent medium layer. J Quant Spectrosc Ra, 2002, 74: 235–248 Liu L H. Discrete curved ray-tracing method for Radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index. J Quant Spectrosc Ra, 2004, 83: 223–228 Liu L H, Zhang H C, Tan H P. Monte Carlo discrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index. J Quant Spectrosc Ra, 2004, 84: 357–362 Liu L H, Tan H P. Transient temperature response in semitransparent variable refractive index medium subjected to a pulse irradiation. J Quant Spectrosc Ra, 2004, 83: 333–344 Liu L H. Finite volume method for radiation heat transfer in graded index medium. J Thermophys Heat Tr, 2006, 20: 59–66 Liu L H, Xu X, Chen Y L, et al. Fluctuating characteristics of radiative source term in hydrogen turbulent jet diffusion flame. J Quant Spectrosc Ra, 2004, 87: 193–201 Liu L H, Xu X, Chen Y L. On the shape of presumed probability density function for the modeling of turbulence radiation interaction. J Quant Spectrosc Ra, 2004, 87: 311–323 Liu L H, Li B X. Inverse radiation problem of axisymmetric turbulent sooting free flame. J Quant Spectrosc Ra, 2002, 75: 481–491 Liu L H, Man G L. Reconstruction of time-averaged temperature of non-axisymmetric turbulent unconfined sooting flame by inverse radiation analysis. J Quant Spectrosc Ra, 2003, 78: 139–149 Liu L H, Tan H P, Yu Q Z. Simultaneous identification of temperature profile and wall emissivities in one-dimensional semitransparent medium by inverse radiation analysis. Numer Heat Tr A-Appl, 1999, 36: 511–525 Liu L H, Tan H P, Yu Q Z. Inverse radiation problem of sources and emissivities in one-dimensional semitransparent media. Int J Heat Mass Transfer, 2001, 44: 63–72 Liu L H, Tan H P, Yu Q Z. Inverse radiation problem of temperature field in three-dimensional rectangular furnaces. Int Commun Heat Mass, 1999, 26: 239–248 Liu L H, Tan H P. Inverse radiation problem in three dimensional complicated geometric systems with opaque boundaries. J Quant Spectrosc Ra, 2001, 68: 559–573 Wang F, Liu D, Cen K F, et al. Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method. J Quant Spectrosc Ra, 2008, 109: 2171–2181 Liu L H, Zhao L, Li B X. A concept of equivalent absorption and emission coefficients for gray analysis of radiative heat transfer. J Quant Spectrosc Ra, 2005, 90: 253–258 An W, Ruan L M, Qi H, et al. Finite element method for radiative heat transfer in absorbing and anisotropic scattering media. J Quant Spectrosc Ra, 2005, 96: 409–422 An W, Ruan L M, Tan H P, et al. Finite element simulation for short pulse light radiative transfer in homogeneous and non-homogeneous media. J Heat Trans-T ASME, 2007, 129: 352–362 Ruan L M, An W, Tan H P, et al. Least-squares finite element method for multidimensional radiative heat transfer. Numer Heat Tr A-Appl, 2007, 51: 657–677 An W, Ruan L M, Qi H. Inverse radiation problem in one-dimensional slab by time-resolved reflected and transmitted signals. J Quant Spectrosc Ra, 2007, 105: 221–235 Liu L H, Li B X, Tan H P. Genetic Algorithm for inverse radiative problem in one-dimensional semitransparent medium (in Chinese). J Northeastern Univ, 2001, 22(S2): 198–201 Qi H, Ruan L M, Zhang H C, et al. Inverse radiation analysis in a one-dimensional participating slab by the stochastic particle swarm optimizer algorithm. Int J Therm Sci, 2007, 46: 649–661 Qi H, Ruan L M, Shi M, et al. Application of multi-phase particle swarm optimization technique to inverse radiation problem. J Quant Spectrosc Ra, 2008, 109: 476–490 Qi H, Ruan L M, Wang S G, et al. Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution. Chin Opt Lett, 2008, 6: 346–349 Zhou H C, Yuan P, Sheng F, et al. Simultaneous estimation of the profiles of the temperature and the scattering albedo in an absorbing, emitting, and isotropically scattering medium by inverse analysis. Int J Heat Mass Transfer, 2000, 43: 4361–4364 Zhou H C, Hou Y B, Chen D L, et al. An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements. J Quant Spectrosc Ra, 2002, 74: 605–620 Zhou H C, Han S D, Lou C, et al. A new model of radiative image formation used in visualization of 3-D temperature distributions in large-scale furnaces. Numer Heat Tr B-Fund, 2002, 42: 243–258 Zhou H C, Han S D, Sheng F, et al. Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies. J Quant Spectrosc Ra, 2002, 72: 361–383 Lou C, Zhou H C. Assessment of regularization reconstruction of three-dimensional temperature distributions in large-scale furnaces. Numer Heat Tr B-Fund, 2008, 53: 555–567 Lou C, Zhou H C, Yu P F, et al. Measurements of the flame emissivity and radiative properties of particulate medium in pulverized-coalfired boiler furnaces by image processing of visible radiation. Proceedings of the Combustion Institute, 2007, 31: 2771–2778 Lou C, Zhou H C. Decoupled reconstruction method for simultaneous estimation of temperatures and radiative properties in a 1-D, gray, participating medium. Numer Heat Tr B-Fund, 2007, 51: 275–292. Daun K J, Howell J R. Inverse design methods for radiative transfer systems. J Quant Spectrosc Ra, 2005, 93: 43–60 Daun K J, Morton D P, Howell J R. Geometric optimization of radiant enclosures containing specular surfaces. J Heat Trans-T ASME, 2003, 125: 845–851 Tan J Y, Liu L H. Inverse geometry design of radiating enclosure filled with participating media using meshless method. Numer Heat Tr A-Appl, 2009, 56: 132–152