Mathematical Analysis of Environmental System

138 Pages·2014·6.228 MB·English

by  Jun Tanimoto (auth.)

Jun Tanimoto
Mathematical
Analysis of
Environmental
System
Mathematical Analysis of Environmental System

Jun Tanimoto
Mathematical Analysis
of Environmental System
JunTanimoto
KyushuUniversity
Hakata,Japan
TanimotoKyoujuno(DoryokuSureba)DarenidemoWakaruKankyoSystemno
SuuriKaisekiKiso,©2012JunTANIMOTO,Allrightsreserved
OriginalJapaneseeditionpublishedin2012byKyushuUniversityPress
ISBN978-4-431-54621-4 ISBN978-4-431-54622-1(eBook)
DOI10.1007/978-4-431-54622-1
SpringerTokyoHeidelbergNewYorkDordrechtLondon
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Foreword
I am very pleased and proud to announce the launch of the Green Asia Lecture
Book Series. Green Asia (Global Strategy for Green Asia) is one ofthe Programs
for Leading Graduate Schools promoted by the Ministry of Education, Culture,
Sports & Technology in Japan, in which we aim to establish a science and
engineering leadership training program that promotes environmental and energy
innovationtoreach outfromAsia totherestoftheworld.Oneoftheoutstanding
featuresofGreenAsiaasanadvancededucationalprogramisthatalllecturesare
offered in English. Hence, the publication of cutting-edge textbooks is one of the
mostimportant,visibleandtangibleoutputsoftheGreenAsiaProgram.Eachofthe
volumes in the lineup deals with essential theories, fundamentals, practical
applications or up-coming topics, all of which are actually used in the program
lectures. It will be wonderful if our publication project can bring all of the brilliant
contentandapproachesproducedintheGreenAsiaProgramtoaworldwideaudience.
Fukuoka,Japan ProfessorAkiraHarata,Dr.Eng.
DirectorofGreenAsiaEducationCenter&
HeadCoordinatorofAdvancedGraduateProgram
inGlobalStrategyforGreenAsia,KyushuUniversity
Professor,InterdisciplinaryGraduateSchoolof
EngineeringSciences,KyushuUniversity
v

Preface
Formorethan15years,Ihavebeenlecturingaboutenvironmentalengineeringto
master’sdegreestudentsspecializinginengineeringandscience.Probablybecause
the school I work for is an interdisciplinary graduate school, the background the
studentsacquiredduringtheirundergraduateyearsrangeswidely,frommechanical,
civil, and architectural engineering to pure science such as physics and applied
mathematics,andeventoarchitecturaldesign.Onthequestionofwhatagraduate
studentwhostartsstudyingenvironmentalissuesmustlearn,Iwouldliketosayitis
notsowidelydiversebut,rather,isnarrow.Itcomprisesfundamentalknowledgeof
how onemathematically buildsthe so-called physical balance equationson trans-
ferringheat,mass, andmomentum,whichare usuallydealtwithinheatandmass
transfer theory and fluid dynamics, and also how one achieves practical solutions
throughaseriesofnumericalprocedures,whichmaybecruciallyimportant when
heorshe becomes aworkingengineer.Ihavenoticedthat,unfortunately, there is
not a very appropriate book for students at the master’s degree level, while many
specialized books for research fellows including Ph.D. students have been
published. This is because the fundamentals span several fields, as mentioned
above.Therefore,thisbookbringstogetherallthetopicsIbelievethatstudentsat
themaster’slevelshouldknowtostartstudyingenvironmentalsubjects.
ThecourseforwhichIamresponsiblewasrevisedacoupleyearsago.Thenew
lectureseries,entitled“MathematicalAnalysisofEnvironmentalSystem,”isgiven
entirelyinEnglish.Ironically,IhavefounditnecessarytoprepareaJapanesebook
to make it possible for Japanese students to understand and to be able to learn on
theirown eveniftheycan understand noneofwhatIamsayingintheclassroom.
Now,tomygreatpleasure,ithasbeenpossibletopublishanEnglishversion.That
is exactly how this book came about. Readers of the whole text will, I hope,
appreciatetheusefulnessofthisbook.
I sincerely thank my colleagues at the Interdisciplinary Graduate School of
EngineeringSciences(IGSES),KyushuUniversity,fortheirsupport.
Fukuoka,Japan JunTanimoto
vii

Contents
1 EnvironmentalSystemsandAnalysisMethods. . . . . . . . . . . . . . . . . 1
1.1 EnvironmentalSystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 StructureofThisBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 LinearSystemsAnalysisMethods. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Unsteady-StateHeatTransferEquation. . . . . . . . . . . . . . . . . . . . 5
2.2 WhatisDiscretization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 SpaceDiscretizationBasedonControlVolumeMethod. . . . . . . . 10
2.4 SystemStateEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 TimeDiscretization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 StabilityofNumericalSolutions. . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 FluctuationsintheNumericalSolutions. . . . . . . . . . . . . . . . . . . 25
2.8 vonNeumannStabilityAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . 27
2.9 HeatSystemApplications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.10 LinearizationofRadiantHeatTransfer. . . . . . . . . . . . . . . . . . . . 37
2.11 LinearHeatMoistureTransferEquation. . . . . . . . . . . . . . . . . . . 41
2.12 CalculationsofHeatLoadandNaturalRoomTemperature. . . . . 48
2.13 NumericalSimulationofaSingleRoomModel. . . . . . . . . . . . . . 54
2.14 FiniteElementMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.15 EndofChapterExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3 ApplicationsofVectorMatrixOperations. . . . . . . . . . . . . . . . . . . . 89
3.1 LinearMultiRegressionAnalysis. . . . . . . . . . . . . . . . . . . . . . . . 89
3.2 LeastSquareSolution.. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. 91
3.3 ApplicationofLeastSquaresSolution. . . . . . . . . . . . . . . . . . . . . 96
ix