Heat Transfer Modeling: An Inductive Approach

524 Pages·2015·15.46 MB·English

by  George Sidebotham (auth.)

George Sidebotham
Heat
Transfer
Modeling
An Inductive Approach
Heat Transfer Modeling

George Sidebotham
Heat Transfer Modeling
An Inductive Approach
GeorgeSidebotham
MechanicalEngineeringDepartment
TheCooperUnionfortheAdvancement
ofScienceandArt
NewYork,NY,USA
ISBN978-3-319-14513-6 ISBN978-3-319-14514-3 (eBook)
DOI10.1007/978-3-319-14514-3
LibraryofCongressControlNumber:2015930196
SpringerChamHeidelbergNewYorkDordrechtLondon
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My wife, Judy Wirkula, and our growing
family of dogs have inspired me with their
patient and consistent love, and I dedicate
this work to them.

Preface
TherearemanyexcellenttextbooksonHeatTransfer.Whyanother?
InthecourseofteachingHeatTransfertojuniorlevelChemicalandMechanical
Engineeringstudentsoverseveralyearsanddevelopingreamsofnotes,itbecame
difficultformetoconductclassesinparallelwithatraditionaltextbook.Theorder
oftopicsand general approach Iwanted toemphasizeinmy courses evolved toa
pointthatdeviatedtoomuchfromanytextbookIcouldfind.SoIusedasabbatical
leavetowritemynotesupintheformofatextbook.
Unliketraditionaltexts, Iwantedtofollowtheadagethat“HeatTransfertakes
time” and consider transient problems first, with steady-state applications being
treated as a limiting case. I also wanted to introduce each topic with readily
recognizable applications and build quantitative methods to analyze them as
needed. This perhaps controversial “just in time” approach means that the order
ofdevelopmentdeviatesfromtheacceptednormtosomedegree.Thegoalisthatby
showing a few specific examples in some detail and then drawing general
conclusions, the reader will be in a position to develop his or her own approach
to situations that arise in his or her practice. This approach is considered to be
inductive,incontrasttoadeductiveapproachinwhichgeneralprinciplesaretaught
first. Heattransfer is an invisible, massless, abstract phenomenon and it may help
some students to visualize its nature with a tangible example first. I credit my
mother,areligiouseducator,forteachingmetheinductivemethod.
Only a few problem statements are given in each chapter, some of which are
analyzed indetailaspartofthedevelopmentofthe analysis methodology (witha
suggestiongivenforthereadertoattemptasolutionbeforeproceeding).Theseare
calledworkshops,notproblems,andformthe basisfor how Iteach mycourses. I
use a part of class to lecture and a large part of class time for students to work
togetheronproblemsthatusethoseconceptsrightaway.Myhopeisthatinstructors
thatadoptthistextbookwillwritetheirownproblemstatementsordrawfromthe
manyresourcesavailabletothem.Betteryet,Ihavefoundthatstudentslearnalot
andoftenenjoymakinguptheirownproblemstatements.
Asimple,recognizablesituation,namelyacoolingmugofcoffee,isintroduced
early with an experimental solution and revisited repeatedly. A new modeling
technique is introduced with each iteration, and virtually all traditional first level
heattransferconceptsaretherebydeveloped.Thepatientreaderacquiresatoolbox
vii
viii Preface
that can be applied to a broad range of applications. There naturally arises,
however, a certain redundancy, and some topics are treated in multiple places,
butwithadifferenttwisteachtime. Thischaracteristicofaninductivemethod is
consistentwiththetruththat“learningisaniterativeprocess”.
Allofthosevariationsarecenteredonthescience,theknowingand/orpredicting
howquicklyamugofcoffeecools.However,itisnotengineeringinthesensethat,
other than informing me how long I’ll need to wait (the science), some human
interventionismadetoaddressaneed(theengineering).Ifinditcuriousthat,inthis
modernhightechworld,whenyoubuyacupofcoffee,itisusuallytoohottodrink
when you get it. So you have to wait. Or add a few ice cubes to cool (and dilute)
it.Furthermore,ifyougetdistracted,thecoffeebecomestepid.
Thenitwasbroughttomyattentionthatapairofvisionaryyoungentrepreneurs
(DaveandDave)hadengineeredasolutionandhadbrought“CoffeeJoulies™”to
market. So, with their blessing, I’ve added sections to appropriate chapters that
demonstratetheprinciplesinvolved.Thisexampleprovidesagoodapplicationthat
involves phase change, something that is generally not included prominently in
traditionalheattransfertexts.Atestimonialofminecouldbe“IlikeCoffeeJoulies
so much, I wrote a book about them!”Another common situation is the opposite,
namely if I put a warm beverage in a refrigerator, how long do I wait before it’s
cold?Thisproblem,andanengineeringsolutioncalledtheCooperCoolingprocess
invented by Greg Loibl, a Cooper Union masters student of mine, is treated in
workshops.
Whileaddressingkeytraditionalfundamentalconceptsinheattransferpractice,
theemphasisisonsimplifiedmodelingphilosophies,whichcarryintoallwalksof
life. If it is determined that simplified analytical solutions are considered to be
insufficient to address a specific need, basic numerical methods are preferred to
complex analytical solutions. The goal is to develop the art of using theory as a
designtool.Theoryfortheory’ssakecanobfuscatesoundengineeringjudgment.
Thepracticingengineermustnavigateadiversearrayofsometimesinconsistent
and/orconflictingnomenclatureanddefinitions,soagoodfoundationinEngineer-
ingThermodynamicsisconsideredaprerequisitetothistextbook.Intheso-called
thermalapplications,termslikeenergy,heat,work,andtemperaturehavespecific
meanings. Heat transfer is defined as the transport of energy across a system
boundary driven by a spatial temperature gradient. Heat is a transported form of
energy and is always associated with a boundary that has a surface area. Other
forms ofenergy(internal, kinetic, and potential)are “storable”and are associated
witharegionofspacethathasavolume.Temperatureisnotaformofenergyandis
difficult to succinctly define, yet everybody knows what it is (or thinks they do),
some sort of measure of hotness or coldness. Work is another transported energy
form and is associated with a force acting through distance, or in the case of
“electrical work” of electrons moving across the boundary against an electrical
potentialdifference.
The word “heat” in common usage frequently means something different than
thatformaltechnicaldefinition.Mywifeoftensays,“There’snoheatinthishouse.”
Iknowwhatshemeans,andIknowtorespond,“I’llturnupthethermostat.Inthe
Preface ix
meantime, put on a sweater.” An hour later, the house is toasty. But in my head,
I might say “You’re right. There is technically no heat in this house. But the air
temperature is sufficiently low relative to your body temperature that the rate at
whichyouarelosingheatisuncomfortabletoyou.Turningupthethermostatwill
send a signal for a fuel valve to open and a spark to ignite a flame in the boiler,
where chemical energy will be converted to thermal energy. Then heat will be
transferredfromthehotgasestothewaterintheboiler,whichwillcreatesteamthat
willflowintotheradiators(whichshouldbecalledconvector/radiators)throughout
the house. Then heat will be transferred to the air in the room, raising its internal
energy,andtherebytheairtemperaturetothenewsetpoint.”Iguessit’seasierto
justsay“There’snoheatinthishouse.”
Modeling involves the creation of a simplified view of a complex system.
In general, mathematical modeling (of anything, not just heat) involves two main
steps:modeldevelopmentanditssubsequentsolution.Theyarenotalwayspurely
sequential, andfeedback fromonetothe otherandaniterative solutionis usually
required for a good engineering solution. Modeling becomes a design tool when
thatsolutionleadstoadecisionthataddressestheoriginalproblemstatement,such
as “what material and what dimensions should that heat sink be to keep the
motherboardfromoverheating?”
Model development involves a derivation of governing equations from the
application of fundamental laws of nature to a defined system, a specific limited
portionoftheuniverse.Theartofthisstageofmodelingistochooseclearsystem
boundariesandtomakesimplifyingassumptionsthateasethesubsequentsolution,
while still capturing the “controlling physics.” Frequently, complex systems are
controlledbyasimplebalance betweentwoorthree“things.”Adetermination of
theextenttowhichthatmodelcapturesrealityiscontext-specificandamajorpart
ofengineeringdecision-making.Creationofthemodelisnottheend,itisthestart.
Theinput isa wordproblemstatement, andthe outputisamathematical problem
statement.
Thenextstepistosolvethemathematicalproblem.Thisstepcanbetrivial,easy,
hard,orimpossible,andtheremaybemultipleapproaches.Itisgooddesigntoinvoke
afeedbackresponse,areturntothemodeldevelopmentwithaneyetowardeither
making additional simplifications or relaxing others, and ultimately arrive at a
solutionthatisdeemedadequatetoaddresstheoriginalwordstatement.Itiscommon
tolosesightoftheoriginalproblemstatementonceadetailedanalysisisinitiated.
Theapproachofthisbookistostartwithawordproblemstatement(oftenwith
specific parameter values) andto develop A modeling strategy indetail. Not THE
modelingstrategy.Apatientandresourcefulreaderwilldevelopalternativemodels
tothesameinitialproblemstatement,solvethose,andthencompare(qualitatively
andquantitatively)totheexamplesgiveninthistext.
Oncetheyareimplemented(andgenerallynotbefore),modelscanbetestedand
thendefinedasbeingsimple,simplistic,orcomplex.Thetestingcriteriondepends
onthe problem athandandmay involve comparison withexperiment, parametric
study (observe the effect of various parameters), or testing assumptions after the
fact.Generally,asimplemodelismostdesirable.Itdoesthejobwiththeleasteffort