Inclusion of radiative heat transfer in the ceramic filling of a combination element of a fire wall

An analytical solution (in series) for the equation of diffusion of external radiation over the two-dimensional rectangular region of a weakly absorbing and strongly scattering ceramic filling of a combination element of heat shielding is obtained under different conditions of reflection at the remaining boundaries of the calculation region. The results obtained by solving a set of diffusion and energy equations are given for two types of materials with different optical properties using $\mathrm{ZrO}_2$ and $\mathrm{SiO}_2$ as an example. The results are presented as a function of the hemispherical reflectivity of the metal–ceramic interface.