An upper bound estimate for a class of conduction heat transfer problems with nonlinear boundary conditions

This work is concerned with the previous establishment of an upper bound for the solution of a large class of steady-state heat transfer problems, represented by a partial differential equation subjected to nonlinear boundary conditions. Within this class we have the conduction/radiation heat transfer problems in gray bodies. It is presented a general upper bound estimate obtained with the aid of a (conveniently chosen) auxiliary function and of a given (bounded) set. The employed procedure is based on the partial differential inequality div(k grad(T-W))⩾0 and its features.