Semidiscrete and Asymptotic Approximations of the Nonstationary Complex Heat Transfer Problem in a System of Grey Square Rods

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