Temperature Distribution in a Plateheated by a Punctual Radiant Source

This work focuses on the energy transfer process in a system of two bodies. The first one presents a small volume and boundary and possesses a high temperature level due to internal heat generation. The second one has no internal heat generation but is heated by the first body. Since the first body has a high temperature level and a small boundary, it is assumed that its temperature is not affected by the body without internal heat generation. A mathematical model is proposed for a particular case in which there exists an axial symmetry, giving rise to a partial differential equation subjected to nonlinear boundary conditions. An a priori upper bound estimate for the temperature is analytically computed. Some numerical simulations are carried out by means of a finite difference scheme. The results obtained show that most of the usual constant temperature approximations may lead to unrealistic results.