The Nonstationary Radiative–Conductive Heat Transfer Problem in a Periodic System of Grey Heat Shields. Semidiscrete and Asymptotic Approximations

Abstract

We consider semidisctete and asymptotic approximations to a solution to the nonstationary nonlinear initial-boundary value problem describing the radiative-conductive heat transfer in a periodic system consisiting on n grey parallel plate heat shields of widh $\varepsilon = 1/n$, separated by vacuum inerlayers. We study properties of special semidiscrete and homogenized problems whose approximate the solution to the problem under consideration. We establish the unique solvability of the problems and deduce an a’priori estimates for the solutions. We obtain error estimates of the order $O(\sqrt{\varepsilon })$ and $O(\varepsilon )$ for semidiscrete approximations and error estimates of order $O(\sqrt{\varepsilon })$ and $O(\varepsilon ^{3/4})$ for asymptotic approximations.