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 fo r the solution of a large class of steady-state heat transfer problems, rep resented by a partial differential equation subjected to nonlinear boundary conditions. Within this class we have the conduction/radiation heat transf er problems in gray bodies. It is presented a general upper bound estimate obtained with the aid of a (conveniently - chosen) auxiliary function and o f a given (bounded) set. The employed procedure is based on the partial dif ferential inequality div (k grad(T-W)) greater than or equal to0 and its fe atures. (C) 2000 Elsevier Science Ltd.