Mathematical and numerical analysis of radiative heat transfer in semi-transparent media
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.
Keywordsradiative heat transfer existence and uniqueness collocation-boundary element method shadow detection iterative nonlinear solver
MSC 201065M38 45K05 80A20 47G10
Unable to display preview. Download preview PDF.
- R. A. Bia lecki, L. Grela: Application of the boundary element method in radiation. Mech. Teor. Stosow. 36 (1998), 347–364.Google Scholar
- A. F. Emery, O. Johansson, M. Lobo, A. Abrous: A comparative study of methods for computing the diffuse radiation viewfactors for complex structures. J. Heat Transfer 113 (1991), 413–422.Google Scholar
- N. A. Qatanani, A. Daraghmeh: Asymptotic error analysis for the heat radiation boundary integral equation. Eur. J. Math. Sci. 2 (2013), 51–61.Google Scholar