Justification of Discrete and Asymptotic Approximations for the Complex Heat Transfer Problem

We justify discrete and asymptotic approximations for the radiative-conductive heat transfer problem in a system of heat-conductive rods with square cross-section separated by vacuum layers placed box. obtain error estimates order $$ O\left(\sqrt{\varepsilon }/\lambda \right) O\left(\sqrt{\varepsilon}\right), where ε is length rod side, λ conductivity.