Applications of Mathematics, Vol. 64, No. 1, pp. 75-100, 2019


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

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

Received October 22, 2017.   Published online January 8, 2019.

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.
Keywords:  radiative heat transfer; existence and uniqueness; collocation-boundary element method; shadow detection; iterative nonlinear solver
Classification MSC:  65M38, 45K05, 80A20, 47G10
DOI:  10.21136/AM.2019.0276-17


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Affiliations:   Yao-Chuang Han, Yu-Feng Nie, Zhan-Bin Yuan, Department of Applied Mathematics, Northwestern Polytechnical University, Xian, Shaanxi, China, 710129, e-mail: hychuang2013@mail.nwpu.edu.cn, yfnie@mail.nwpu.edu.cn, yzzzb@nwpu.edu.cn


 
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