An a priori upper bound estimate for conduction heat transfer problems with temperature-dependent thermal conductivity

This article presents an a priori upper bound estimate for the steady-state temperature distribution in a body with any temperature-dependent thermal conductivity, generalizing a previous result (Gama et al., 2013) [1]. The discussion is carried out assuming a large class of nonlinear boundary conditions (for instance representing thermal radiant interchange). These estimates consist of a powerful tool that may avoid an expensive numerical simulation of a nonlinear heat transfer problem, whenever it suffices to know the highest temperature. In these cases the methodology proposed in this work is more effective than the usual approximations that assume thermal conductivities and heat sources as constants.