Transient temperature and elastic response of a space-based mirror in the radiation-conduction environment

Abstract

The problem of the one-dimensional heat equation with radiation boundary conditions is studied. Steady state and transient solutions for a space-based mirror are obtained under a broad class of boundary specification. Associated elastic stress and displacement are investigated. Time-varying heat flux at the boundary is also considered. The method requires solving equations of the type tan ⁡ λ = ( B i 1 + B i 2 ) λ / ( λ 2 − B i 1 B i 2 ) \tan \lambda =\left (Bi_1+Bi_2\right )\lambda /\!\left (\lambda ^2-Bi_1Bi_2\right ) for the eigenvalues λ \lambda , for which complete asymptotic solutions are given. Selected transient response results for temperature and stresses are presented.