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Article | REF: BE8265 V2

Inverse problems in heat diffusion : Diffusive models, measurements, sensitivities

Authors: Denis MAILLET, Yvon JARNY, Daniel PETIT

Publication date: June 10, 2018

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ABSTRACT

The task of constructing an appropriate model, here the solution of one of the forms of the heat equation, is tackled in the framework of inverse problems in heat diffusion. Several examples are used to introduce the notions of input, output and structural parameters of a model. The physical principles of the techniques of temperature measurement, with or without contact, are detailed together with the corresponding calibration laws, taking into account the notions of measurement noise and of sampling of the sensor signal. The sensitivity of the model output to its structural parameters or to its parameterized input is the basis of the inverse approach.

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AUTHORS

  • Denis MAILLET: Professor Emeritus, University of Lorraine (UL) - Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée (LEMTA) – CNRS and UL

  • Yvon JARNY: Professor Emeritus, University of Nantes - Laboratoire de Thermique et Énergie de Nantes (LTeN) – UMR CNRS 6607 Nantes

  • Daniel PETIT: Professor Emeritus, École Nationale Supérieure de Mécanique et d'Aérotechnique (ISAE-ENSMA) - Institut P' UPR CNRS 3346 Département Fluides, Thermique, Combustion – Poitiers

 INTRODUCTION

This article is the first in a series of three ([BE 8 265], [BE 8 266] and [BE 8 267] ). It is intended to introduce the notion of a model, relative to the solution of a so-called "direct" problem, in thermal conduction where the heat equation is used to deduce temperatures from a source, an exciting heat flux, for example. By taking temperature measurements into account, this model can then be used to feed the so-called "inverse" approach, aimed, for example, at tracing the heat flow. The different types of model, and the quantities used, are first presented, opting for an approach widely used in system dynamics, and which links input(s) and output(s). The instrumentation techniques currently available to measure temperature are then reviewed, with emphasis on the measurement principle, the calibration law and the stochastic characteristics of noise on the signal. Finally, the notion of sensitivity, which derives directly from the model adopted, is discussed: it is an essential tool for ensuring the success of subsequent inversion.

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KEYWORDS

temperature   |   thermal conduction   |   heat equation   |   inverse problems   |   sensitivity

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