An upper temperature bound for steady-state conduction heat transfer problems with a linear relationship between temperature and conductivity

摘要

This paper presents an a priori upper bound for the steady-state temperature distribution in a body with a temperature-dependent thermal conductivity. The discussion is carried out assuming linear boundary conditions (Newton law of cooling) and a thermal conductivity linearly dependent on the temperature. Depending on the objectives, the result avoids the necessity of an expensive numerical simulation of a nonlinear heat transfer problem and may be more effective than usual approximations - in which heat sources and thermal conductivities are assumed to be constant.