Unique solvability of a steady-state complex heat transfer model

•The unique solvability of a nonlinear complex heat transfer model is proved.•An iterative algorithm for solving such problems is proposed.•Numerical experiments demonstrating the importance of considered model are presented.

The problem of radiative–conductive–convective heat transfer in a three-dimensional domain is studied in the framework of the diffusion (P1P1) steady-state approximation. The unconditional unique solvability of this nonlinear model is proved in the case of Robin-type boundary conditions for the temperature and the mean intensity function. An iterative algorithm for the numerical solution of the model is proposed. Numerical examples demonstrating the importance of the radiative heat transfer at high temperatures are presented.