A least-squares radial point interpolation collocation meshless method based on the discrete ordinates equation is developed for solving the radiative transfer in absorbing, emitting, and scattering media, in which compact support radial basis functions augmented with polynomial basis are employed to construct the trial functions. In addition to the collocation nodes, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three typical examples of radiative transfer in semitransparent media are examined to verify this new solution method. The numerical results are compared with other benchmark approximate solutions in references. By comparison, the results show that the least-squares radial point interpolation collocation meshless method has good accuracy in solving radiative transfer problems within absorbing, emitting, and scattering media.
1.
Hottel
, H. C.
, and Cohen
, E. S.
, 1958, “Radiant Heat Exchange in a Gas-Filled Enclosure: Allowance for Nonuniformity of Gas Temperature
,” AIChE J.
0001-1541, 4
, pp. 3
–14
.2.
Yuen
, W. W.
, and Takara
, E. E.
, 1997, “The Zonal Method, a Practical Solution Method for Radiative Transfer in Non-Isothermal Inhomogeneous Media
,” Annu. Rev. Heat Transfer
1049-0787, 8
, pp. 153
–215
.3.
Yuen
, W. W.
, 2006, “The Multiple Absorption Coefficient Zonal Method (MACZM), an Efficient Computational Approach for the Analysis of Radiative Heat Transfer in Multidimensional Inhomogeneous Nongray Media
,” Numer. Heat Transfer, Part B
1040-7790, 49
, pp. 89
–103
.4.
Yang
, W. J.
, Taniguchi
, H.
, and Kudo
, K.
, 1995, “Radiative Heat Transfer by Monte Carlo Method
,” in Advances in Heat Transfer
, Vol. 27
, Academic Press
, New York
.5.
Farmer
, J. T.
, and Howell
, J. R.
, 1998, “Comparison of Monte Carlo Strategies for Radiative Transfer in Participating Media
,” in Advances in Heat Transfer
, Vol. 31
, Academic Press
, New York
.6.
Fiveland
, W. A.
, 1984, “Discrete-Ordinates Solution of the Radiative Transport Equation for Rectangular Enclosures
,” ASME J. Heat Transfer
0022-1481, 106
, pp. 699
–706
.7.
Truelove
, J. S.
, 1987, “Discrete-Ordinate Solutions of the Radiation Transport Equation
,” ASME J. Heat Transfer
0022-1481, 109
, pp. 1048
–1051
.8.
Raithby
, G. D.
, and Chui
, E. H.
, 1990, “A Finite-Volume Method for Predicting a Radiant Heat Transfer Enclosures With Participating Media
,” ASME J. Heat Transfer
0022-1481, 112
(2
), pp. 415
–423
.9.
Chui
, E. H.
, Raithby
, G. D.
, and Hughes
, P. M. J.
, 1992, “Prediction of Radiative Transfer in Cylindrical Enclosures With the Finite Volume Method
,” J. Thermophys. Heat Transfer
0887-8722, 6
, pp. 605
–611
.10.
Chui
, E. H.
, and Raithby
, G. D.
, 1993, “Computation of Radiation Heat Transfer on a Nonorthogonal Mesh Using the Finite-Volume Method
,” Numer. Heat Transfer, Part B
1040-7790, 23
, pp. 269
–288
.11.
Chai
, J. C.
, Lee
, H. S.
, and Patankar
, S. V.
, 1994, “Finite Volume Method for Radiation Heat Transfer
,” J. Thermophys. Heat Transfer
0887-8722, 8
, pp. 419
–425
.12.
Chai
, J. C.
, Parthasarathy
, H. S.
, Lee
, H. S.
, and Patankar
, S. V.
, 1995, “Finite Volume Method Radiative Heat Transfer Procedure for Irregular Geometries
,” J. Thermophys. Heat Transfer
0887-8722, 9
, pp. 410
–415
.13.
Chai
, J. C.
, Lee
, H. S.
, and Patankar
, S. V.
, 1994, “Treatment of Irregular Geometries Using a Cartesian Coordinates Finite-Volume Radiation Heat Transfer Procedure
,” Numer. Heat Transfer, Part B
1040-7790, 26
, pp. 225
–235
.14.
Chai
, J. C.
, and Patankar
, S. V.
, 2000, “Finite-Volume Method for Radiation Heat Transfer
,” in Advances in Numerical Heat Transfer
, Vol. 2
, Taylor & Francis
, New York
, pp. 109
–141
.15.
Fiveland
, W. A.
, and Jessee
, J. P.
, 1994, “Finite Element Formulation of the Discrete-Ordinates Method For Multidimensional Geometries
,” Journal of Thermophsics and Heat Transfer
, Vol. 7
, pp. 426
–433
.16.
Liu
, L. H.
, 2004, “Finite Element Simulation of Radiative Heat Transfer in Absorbing and Scattering Media
,” J. Thermophys. Heat Transfer
0887-8722, 18
, pp. 555
–557
.17.
Atluri
, S. N.
, and Shen
, S. P.
, 2002, The Meshless Local Petrov-Galerkin (MLPG) Method
, Tech Science Press
, Encino, CA
.18.
Liu
, G. R.
, 2003, Mesh Free Methods
, CRC Press
, Boca Raton, FL
.19.
Liu
, G. R.
, and Gu
, Y. T.
, 2005, An Introduction to Meshfree Methods and Their Programming
, Springer
, New York
.20.
Zhang
, X.
, and Liu
, Y.
, 2004, Meshless Methods
, Tsinghua University Press
, Beijing
.21.
Liu
, L. H.
, 2006, “Meshless Local Petrov-Galerkin Method for Solving Radiative Transfer Equation
,” J. Thermophys. Heat Transfer
0887-8722, 20
, pp. 150
–154
.22.
Liu
, L. H.
, 2006, “Meshless Method for Radiative Heat Transfer in Graded Index Medium
,” Int. J. Heat Mass Transfer
0017-9310, 49
, pp. 219
–229
.23.
Sadat
, H.
, 2006, “On the Use of a Meshless Method for Solving Radiative Transfer With the Discrete Ordinates Formulations
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 101
, pp. 263
–268
.24.
Tan
, J. Y.
, Liu
, L. H.
, and Li
, B. X.
, 2006, “Least-Squares Collocation Meshless Approach for Coupled Radiative and Conductive Heat Transfer
,” Numer. Heat Transfer, Part B
1040-7790, 49
, pp. 179
–195
.25.
Zhang
, X.
, Liu
, X. H.
, Song
, K. Z.
, and Lu
, M. W.
, 2001, “Least-Squares Collocation Meshless Method
,” Int. J. Numer. Methods Eng.
0029-5981, 51
, pp. 1089
–1100
.26.
Modest
, M. F.
, 2003, Radiative Heat Transfer
, 2nd ed., Academic Press
, San Diego
.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
0022-1481, 116
, pp. 260
–263
.28.
Kim
, T. K.
, and Lee
, H.
, 1988, “Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimensional Rectangular Enclosures
,” Int. J. Heat Mass Transfer
0017-9310, 31
, pp. 1711
–1721
.29.
Ratzel
, A. C.
, and Howell
, J. R.
, 1983, “Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation
,” ASME J. Heat Transfer
0022-1481, 105
(2
), pp. 333
–340
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
