An upper temperature bound for steady-state conduction heat transfer problems with a linear relationship between temperature and conductivity
Rogério M. Saldanha Da Gama, Wendel Fonseca Da Silva, Eduardo D. Corrêa and Maria Laura Martins-Costa
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.
Keywords: Nonlinear heat transfer; temperature-dependent thermal conductivity; upper bound estimate; Kirchhoff transformation