Asymptotic approximations for the stationary radiative-conductive heat transfer problem in the two-dimensional system of plates

Abstract

Abstract Special asymptotic approximations, namely, the first and second homogenized problems are proposed for the boundary value problem describing a stationary radiative-conductive heat transfer in a two-dimensional system of heat-conducting plates of thickness ɛ separated by vacuum layers. The unique solvability of homogenized problems is proved, the comparison theorem is established, and estimates of solutions are obtained. The first homogenized problem has the error estimate of order O ( ε ) $ O(\sqrt{\varepsilon}) $ .