Thermal measurements and inverse techniques

754 Pages·2011·18.671 MB·xiii, 756 p. : ill\754

by  Helcio R B Orlande, et al

THERMAL
MEASUREMENTS
and
INVERSE
TECHNIQUES
H T
EAT RANSFER
A Series of Reference Books and Textbooks
Editor
Afshin J. Ghajar
Regents Professor
School of Mechanical and Aerospace Engineering
Oklahoma State University
Engineering Heat Transfer: Third Edition, William S. Janna
Conjugate Problems in Convective Heat Transfer, Abram S. Dorfman
Thermal Measurements and Inverse Techniques, Helcio R.B. Orlande; Olivier
Fudym; Denis Maillet; Renato M. Cotta
Upcoming titles include:
Introduction to Thermal and Fluid Engineering, Allan D. Kraus, James R. Welty,
and Abdul Aziz
THERMAL
MEASUREMENTS
and
INVERSE
TECHNIQUES
Edited by
Helcio R.B. Orlande
Olivier Fudym
Denis Maillet

Renato M. Cotta
Boca Raton London New York
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Library of Congress Cataloging-in-Publication Data
Thermal measurements and inverse techniques / edited by Helcio R.B. Orlande … [et al.].
p. cm. -- (Heat transfer)
Summary: “The use of inverse problems constitutes a new research paradigm in which groups of
theoretical, computational, and experimental researchers synergistically interact to better understand the
physical phenomena being studied. This book presents a comprehensive research-based survey of modern
inverse techniques and their applications to engineering heat transfer. Written by top-notch contributors,
the text provides a concise, single-source reference on the mathematical modeling, measurements, and
solution of inverse problems in heat transfer. It covers topics such as multiscale modeling, thermophysical
properties, heat flux, and temperature measurements”-- Provided by publisher.
Includes bibliographical references and index.
ISBN 978-1-4398-4555-4 (hardback)
1. Heat--Transmission. 2. Heat equation. 3. Inverse problems (Differential equations) 4. Heat
engineering. I. Orlande, Helcio R. B., 1965- II. Title. III. Series.
TJ260.T4938 2011
621.402’201515357--dc22 2010045340
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
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Contents
Preface........................................................................................................................................... vii
Contributors...................................................................................................................................xi
Part I Modeling and Measurements in Heat Transfer
1. Modeling in Heat Transfer..................................................................................................3
Jean-Luc Battagliaand Denis Maillet
2. Multiscale Modeling Approach to Predict Thermophysical Properties
of Heterogeneous Media....................................................................................................53
ManuelErnaniCruzandCarlos FredericoMatt
3. Temperature Measurements: Thermoelectricity and Microthermocouples.............95
FrançoisLanzetta and Eric Gavignet
4. Temperature Measurements: Resistive Sensors..........................................................143
PauloSeleghim, Jr.
5. Heat Flux Sensors..............................................................................................................171
SauloGüths
6. Radiative Measurements of Temperature....................................................................185
Jean-Claude Krapez
Part II Inverse Heat Transfer Problems
7. Introduction to LinearLeastSquares Estimation and Ill-PosedProblems
for ExperimentalData Processing..................................................................................233
Olivier FudymandJean-Christophe Batsale
8. InverseProblems andRegularization...........................................................................283
HaroldoF. de Campos Velho
9. Nonlinear Estimation Problems......................................................................................315
Benjamin Remy andStéphaneAndre
10. A Surveyof BasicDeterministic,Heuristic, andHybrid Methods
for Single-ObjectiveOptimization and Response Surface Generation..................355
Marcelo J. Colaço and George S. Dulikravich
v
vi Contents
11. AdjointMethods................................................................................................................407
Yvon Jarny andHelcio R. Barreto Orlande
12. Bayesian Approaches fortheSolution of Inverse Problems....................................437
Marina Silva Paez
13. Identification of Low-Order Modelsand Their Use for Solving Inverse
Boundary Problems...........................................................................................................457
ManuelGirault, Daniel Petit, and Etienne Videcoq
14. Karhunen–Loève Decomposition forData, Noise, andModelReduction
in InverseProblems...........................................................................................................507
Elena Palomo del Barrio and Jean-Luc Dauvergne
15. Explicit Formulations forRadiative TransferProblems............................................541
LilianeBassoBarichello
Part III Applications
16. Analysis of Errors in Measurements and Inversion...................................................565
PhilippeLe Masson and Morgan Dal
17. MultisignalLeastSquares:Dispersion,Bias,andRegularization...........................599
Thomas MetzgerandDenisMaillet
18. Thermophysical Properties Identification in theFrequency Domain.....................619
Valério L. Borges, Priscila F.B.Sousa,Ana P.Fernandes, and Gilmar Guimarães
19. FrontFaceThermal Characterization of Materials by aPhotothermal
Pulse Technique.................................................................................................................655
Fabrice Rigollet and ChristopheLe Niliot
20. Estimation of Space VariableThermophysical Properties........................................675
Carolina P.Naveira-Cotta, Renato M. Cotta, and Helcio R. Barreto Orlande
21. InverseThermal Radiation Problems: Estimation of Radiative
Properties of Dispersed Media.......................................................................................709
Luís Mauro Moura
Index............................................................................................................................................739
Preface
Thedesignandoperationofmoderntechnologicalsystemsandthepropercomprehension
of their interaction with nature (e.g., in pollution control and global warming issues)
requirethepermanentprocessingofalargeamountofmeasureddata.Nowadays,progress
inthemathematicalmodelingofcomplexindustrialorenvironmentalsystems,associated
with the continuous increase in memory and calculation power of computers, has made
numericalsimulationsofalmostanyphysicalphenomenapossible.Thesefactsbringabout
the need for an appropriate tool that rigorously bridges the gap between the information
stemmingfrommeasurementsandthatcorrespondingtotheoreticalpredictions,aimingat
the better understanding of physical problems, including real-time applications. Inverse
analysisissuchatool.
Heattransferpermanentlytakespartinourdailylife.Examplescanbefoundinnatural
phenomena, such as the solar heating of Earth, meteorology or thermoregulation of
biological activity, as well as in a wide range of man-made applications, such as the
conversionofenergyinheatengines,thermalcontrolofchemicalreactors,airconditioning,
cooling of electronic equipment, development of micro- and nano-technologies with the
associated thermal challenges, etc. Recent advances in both thermal instrumentation and
heattransfermodelingpermitthecombinationofefficientexperimentalproceduresandof
indirect measurements within the research paradigm of inverse problems. In this para-
digm, the groups of theoretical, computational, and experimental researchers synergistic-
ally interact during the course of the work in order to better understand the physical
phenomena under study. Although initially associated with the estimation of boundary
heat fluxes by using temperature measurements taken inside a heated body, inverse
analyses are nowadays encountered in single- and multi-mode heat transfer problems
dealing with multiscale phenomena. Applications range from the estimation of constant
heattransferparameterstothemappingofspatiallyandtimelyvaryingfunctions,suchas
heat sources, fluxes, and thermophysical properties.
In heat transfer, the classical inverse problem of estimating a boundary heat flux with
temperature measurements taken inside a heat-conducting medium has many practical
applications. For example, the heat load of the surface of a space vehicle reentering the
atmosphere can be estimated through inverse analysis by using temperature measure-

mentstakenwithinthethermalprotectionshield.Ifatechniquethatsequentiallyestimates
such boundary heat flux is used, inverse analysis may allow for online trajectory correc-
tions in order to reduce the heat load. Therefore, overheating of the structure of the
spacecraft can be avoided, reducing the risk of fatal accidents. Moreover, modern engin-
eering strongly relies on newly developed materials, such as composites, and inverse
analysis can be used for the characterization of the unknown properties of such nonho-
mogeneous materials. The use of nonintrusive measurement techniques with high spatial
resolutions and high measurement frequencies, such as temperature measurements taken
vii
viii Preface
with infrared cameras, allows the characterization of nonhomogeneous materials even at
smallscales,includingcrackordefectdetection.Thelatestresearchinheattransferfollows
a trend toward small scales, at micro- and nano-levels. This requires that physical phe-
nomenabetakenintoconsideration,whichmaybenegligibleand,hence,notaccountedfor
atmacroscales.Bythesametoken,moderntechniquesnowpermitnonintrusivemeasure-
ments to be taken at small space and time scales, thus allowing the observation of such
complex physical phenomena.
All subjects required for the understanding and solution of the physical situations
described above are available in this book, including the modeling of heat transfer prob-
lems,evenatmicro-andnano-scales,modernmeasurementtechniques,andthesolutionof
inverseproblemsbyusingclassicalandnovelapproaches.Thisbookisaimedatengineers,
senior undergraduate students, graduate students, researchers both in academia and
industry, in the broad field of heat transfer. It is assumed, however, that the reader has
basicknowledgeonheattransfer,suchasthatcontainedinanundergraduateheattransfer
course.
This book is intended to be a one-source reference for those involved with different
aspectsofheattransfer,includingthemodelingofphysicalproblems,themeasurementof
primary heat transfer variables, and the estimation of quantities appearing in the formu-
lation (indirect measurements) through the solution of inverse problems. Keeping this
main objective in mind, the book was divided into three parts, namely: Part I—Modeling
and Measurements in Heat Transfer, Part II—Inverse Heat Transfer Problems, and Part
III—Applications. Parts I and II provide a concise theoretical background along with
examplesonmodeling,measurements,andsolutionsofinverseproblemsinheattransfer.
Part III deals with applications of the knowledge built up in Parts I and II to several
practicaltest cases. Each chaptercontainsits own lists of variables andreferences. Hence,
dependingon the reader’sbackgroundand interest, they can bereadindependently.
This book results from the Advanced Schools METTI (Thermal Measurements and
Inverse Techniques) held in 1995, 1999, 2005, and 2009. Started under the auspices of
SFT—French Heat Transfer Society, the last METTI School was co-organized with
ABCM—Brazilian Society of Mechanical Engineering and Sciences, and held in Angra
dos Reis (state of Rio de Janeiro) as one of the activities of the Year of France in Brazil.
However, the book was intended to be self-consistent and didactic, not being at all the
single collection of lecturespreviously given during the METTI schools.
We would like to thank all the contributors for their diligent work that made this book
possible.WeareindebtedtoProfessorAfshinJ.Ghajar,theHeatTransferserieseditorfor

CRC Press=Taylor & Francis, for his encouragement and support to pursue this book
project. We also appreciate the valuable recommendation by Professor Sadik Kakac, who
carefullyreviewedourbookproposal.ThecooperationofthestaffatCRCPress=Taylor&
Francisisgreatlyappreciated,especiallythatfromJonathanW.Plant,thesenioreditorfor
mechanical,aerospace,nuclear,andenergyengineering,andfromourprojectcoordinator,
Amber Donley. Finally, we would like to express our deepest gratitude for the financial
support provided for the publication of this book by CAPES, an agency of the Brazilian
government for the fostering of science and graduate studies.
Preface ix
1 1
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Contributors
StéphaneAndre Renato M.Cotta
Energy and Theoreticand Applied Energy Department of Mechanical Engineering
Laboratory (LEMTA) Federal University of Rio deJaneiro
University of Nancy and CNRS Rio deJaneiro,Brazil
Vandœuvre-lès-Nancy, France
ManuelErnani Cruz
Liliane BassoBarichello
Department of Mechanical Engineering
Institute of Mathematics
Federal University of Rio deJaneiro
Federal University of Rio Grandedo Sul
Rio deJaneiro,Brazil
Porto Alegre, Brazil
ElenaPalomo del Barrio Morgan Dal
TREFLELaboratory MaterialsEngineeringLaboratoryof
Ecole Nationale Supérieure des Arts et Brittany (LIMATB)
Métiers University of SouthernBrittany
University of Bordeaux Lorient, France
Talence, France
Jean-LucDauvergne
Jean-ChristopheBatsale
TREFLELaboratory
TREFLELaboratory
Ecole Nationale Supérieure des Arts et
Ecole Nationale Supérieure des Arts et
Métiers
Métiers
Talence,France
University of Bordeaux
Talence, France
George S.Dulikravich
Jean-Luc Battaglia Department of Mechanical and Materials
TREFLELaboratory Engineering
Ecole Nationale Supérieure des Arts et FloridaInternationalUniversity
Métiers Miami,Florida
University of Bordeaux
Talence, France
Ana P.Fernandes
School of Mechanical Engineering
ValérioL.Borges
Federal University of Uberlândia
School ofMechanical Engineering
Uberlândia, Brazil
Federal University of Uberlândia
Uberlândia, Brazil
OlivierFudym
Marcelo J.Colaço Research in Albion Particulate Solids,
Department ofMechanical Engineering Energyandthe Environment
Federal University of Rio deJaneiro University of Toulouse
Rio de Janeiro, Brazil Albi, France
xi