### Summary

The problem addressed in the paper is the coupling between heat radiation and convection in participating media. While convection is modelled by finite volumes, heat radiation is solved using the boundary element method (BEM). The latter is a technique of solving the integral equations of radiation using weighted residuals.

BEM can be seen as an alternative approach to the well established zoning method or FEM, its higher order generalization. When compared with these approaches, BEM offers substantial computing time economy due to the reduction of the integration dimension and lack of volume integrals.

Coupling convection solution with heat radiation is accomplished in an iterative way. First the initial temperatures of the medium is computed by the convection solver for given walls temperature assuming no interaction with radiation. Using this temperature field the radiative heat fluxes and sources are computed and their values substituted to the corrected energy convection equation. The procedure is repeated until a required accuracy is reached. Mild underrelaxaction of the heat sources improves the convergence.

BEM radiation procedure requires numerical integration over all discrete surface elements, and ray tracing of the Gaussian rays connecting the collocation point and the nodes of the Gaussian quadrature. The latter is the most time consuming operation. Numerical tests have shown that standard ray tracing on convection meshes leads to prohibitively long computing time. To accelerate the procedure the ray tracing is performed on a much coarser structural grid. This is an acceptable approximation as heat radiation volumetric grid does not need to capture small scale phenomena which is in contrast with the convection grid where the resolution of the resulting fields depends strongly on the mesh density. This assumption accelerates the ray tracing by at least two orders of magnitude. The transition between the radiative and convection nodes is accomplished using the radial basis function network concept.

Several industrial problems have been solved using this model. Commercial CFD code Fluent has been used to solve the convection equations. The interaction between the in-house radiative code BERTA and Fluent was maintained by modifying source term of energy balance equation within latter. The coupling was programmed at a level of a script.

The results have been compared with some available benchmark solutions and with the radiative transfer solvers (Discrete Ordinates and Discrete Transfer) installed in the CFD code. Very good agreement has been observed.

The ray tracing concept has been extended to cylindrical coordinates systems to solve axisymmetric problems. The technique has been also used to model the interaction of radiation and conduction in semitransparent, non gray media.

Numerical results of both some benchmark solutions and industrial problems are shown in the paper.