Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Yao-Chuang Han; Yu-Feng Nie; Zhan-Bin Yuan

Applications of Mathematics (2019)

  • Volume: 64, Issue: 1, page 75-100
  • ISSN: 0862-7940

Abstract

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This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm.

How to cite

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Han, Yao-Chuang, Nie, Yu-Feng, and Yuan, Zhan-Bin. "Mathematical and numerical analysis of radiative heat transfer in semi-transparent media." Applications of Mathematics 64.1 (2019): 75-100. <http://eudml.org/doc/294670>.

@article{Han2019,
abstract = {This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm.},
author = {Han, Yao-Chuang, Nie, Yu-Feng, Yuan, Zhan-Bin},
journal = {Applications of Mathematics},
keywords = {radiative heat transfer; existence and uniqueness; collocation-boundary element method; shadow detection; iterative nonlinear solver},
language = {eng},
number = {1},
pages = {75-100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mathematical and numerical analysis of radiative heat transfer in semi-transparent media},
url = {http://eudml.org/doc/294670},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Han, Yao-Chuang
AU - Nie, Yu-Feng
AU - Yuan, Zhan-Bin
TI - Mathematical and numerical analysis of radiative heat transfer in semi-transparent media
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 75
EP - 100
AB - This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm.
LA - eng
KW - radiative heat transfer; existence and uniqueness; collocation-boundary element method; shadow detection; iterative nonlinear solver
UR - http://eudml.org/doc/294670
ER -

References

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