Reconstruction of a nonlinear heat transfer law from uncomplete boundary data by means of infrared thermography. (7th October 2016)

• Record Type: Journal Article
• Authors: Clarelli, Fabrizio; Inglese, Gabriele
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-10-07
• Subjects: heat equation -- nonlinear heat transfer -- cooling; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115017
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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).