The boundary element method is applied to the computation of the radiative heat flux and radiative heat source. Both these quantities are governed by the radiation transfer equations which are integral equations resulting from the balance between emission and absorption. The well-known Hottel’s zoning method is, in fact, a weighted residual approach. Thus, the matrices of a set of discretized integral equations are given by double integrals over boundary and/or volume elements. Inspite the volume integral, the radiation transfer equations can be handled by boundary elements, too. This is so because the volume integration is decomposed into surface and line integrations due to the special form of the integration kernels involved. Thus, the matrix coefficients in the BEM formulation are given by single integrals over boundary elements. The line integrations can be carried out analytically provided that isothermal volume cell approximation is employed. Diagonal matrix coefficients are given by strongly singular integrals, the numerical evaluation of which can be avoided by using the rigid body motion idea. Comparison of the accuracy and efficiency of the zoning and BEM methods is demonstrated in two examples.
For the entire collection see [Zbl 0826.00033].