Recostruction of a nonlinear heat transfer law from uncomplete boundary data by means of infrared thermography

Heat exchange between a conducting plate and the environment is described here by means of an unknown nonlinear function F of the temperature u. In this paper we construct a method for recovering F by means of polynomial expansion, perturbation theory and the toolbox of thermal inverse problems. We test our method on two examples: In the first one, we heat the plate (initially at 20 ?C) from one side, read the temperature on the same side and identify the heat exchange law on the opposite side (active thermography); in the second example we measure the temperature of one side of the plate (initially at 1500 ?C) and study the heat exchange while cooling (passive thermography).