Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions

193 Pages·2015·4.671 MB·English

by  Kuppalapalle Vajravelu, Swati Mukhopadhyay

Fluid Flow, Heat and Mass Transfer
at Bodies of Different Shapes
Fluid Flow, Heat and
Mass Transfer at Bodies
of Different Shapes
Numerical Solutions
Kuppalapalle Vajravelu
The University of Central Florida, USA
and
Swati Mukhopadhyay
The University of Burdwan, India
AMSTERDAM (cid:129) BOSTON (cid:129) HEIDELBERG (cid:129) LONDON
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Preface
Fluid mechanics is one of the oldest branches of applied mathematics. It is also the
foundationoftheunderstandingofvariousaspectsofscienceandengineering.Awide
varietyofmathematicalproblems,appearinginareas asdiverse asfluidmechanics,
mechanical engineering, chemical engineering, theoretical physics, and aerospace
engineering,havebeensolvedbymeansofanalyticalornumericalmethods.Though
analysisofdifferenttypesoffluidflowandheatormasstransferproblemsareavail-
ableintheopenliterature,therearestillanumberofgapsthataretobefilledup.There
areseveralexcellentbookscoveringdifferentaspectsoffluidflowandheatormass
transfer.Yetonestilllooksforasystematicandsequentialanalysisthathelpsinunder-
standing thisparticular area ofinterest.
Tohelpstudentsandresearchersacquireadeeperunderstandingofthecharacter-
isticsoffluidflowandheatandmasstransfer,thismonographaimstopresent,ingen-
eral,astudyoftransportphenomena.Itiswellknownthatforexternalflows,theshape
oftheobjectinfluencestheflowoveranobject(i.e.,abody)significantly.Asaresult,
itaffectstheheatandmasstransfercharacteristics.Inotherwords,thebookaimsto
helpreadersdeveloptheirunderstandinginthisparticularfieldwithoutspendinghuge
timeinsearchingtheendlessliteratureonthisarea.Tohelpdevelopaclearinsight,we
discussseveralflowfeatures.Bymaintainingtheapplicabilityoftheobtainedresults,
we alsodiscussseveral cases ofphysical problems.
Inselectingspecificproblemstoworkthrough,wehaverestrictedourattentionto
thephenomenaoffluidflowandheatormasstransferassuchproblemsintroducea
widevarietyofmathematicalproblemsofinterest.Hence,inordertoillustratevarious
propertiesandtoolsusefulinanalyzingtheproblems,wehaveselectedrecentresearch
inthe area offluid flow and heat ormass transfer.
WeappreciatethesupportandmotivationoftheeditorGlynJonesandtheeditorial
projectmanagerStevenMathews.WealsoacknowledgetheroleofElsevier(Oxford)
formakingthisbookareality.ThankstoMr.SudiptaGhosh(PhDstudentofDr.Swati
Mukhopadhyay) for his help in drawing some of the figures. We thank Prof. Mike
Taylor for reading the entire manuscript and suggesting some needed changes. The
authorsaregratefultoalltheauthorsofthearticleslistedinthebibliographyofthis
book. The authors are also very much thankful to their coauthors. Finally, we very
much like to acknowledge the encouragement, patience, and support provided by
the membersofourfamilies.
K.Vajravelu
Orlando, Florida
S. Mukhopadhyay
Burdwan,India
2015
Introduction
Air andwater are the mostimportant constituentsof the environment we livein, so
thatalmosteverythingwedoisconnectedtothescienceoffluidmechanics.Forexam-
ple,theflightofbirdsintheairandthemotionoffishinthewatercanbeexplained
from the perspective of fluid mechanics [1]. The designs of airplanes and ships are
basedonthetheoryoffluidmechanics.Fluidmechanicsisoneoftheoldestbranches
ofappliedmathematics,andthefoundationoftheunderstandingofdifferentaspects
of science and engineering [2–5]. From the nineteenth century, the scope of fluid
mechanics has steadily broadened, as the study of hydraulics was associated with
the growth of the fields of civil engineering and naval architecture. In recent times,
thedevelopmentofthedifferentbranchesofengineering,namely,aeronautical,chem-
ical,andmechanicalengineering,havegivenadditionalstimulitothestudyoffluid
mechanics.Itnowranksasoneofthemostimportantbasicsubjectsnotonlyinapplied
mathematicsbutalsoinengineering[6].Now,itisasubjectofwidespreadinterestin
almost all fields of engineering as well as in astrophysics, meteorology, physical
chemistry, plasma physics,geophysics, biology, and biomedicine[7–9].
Innature,fluidflowoverbodiesoccursfrequentlyandgivesrisetonumerousphys-
icalphenomena,forexample,dragforceactingontrees,underwaterpipelines,auto-
mobiles,theliftgeneratedbyairplanewings,upwarddraftofrains,dustparticlesin
highwinds,andtransportationofredbloodcellsinbloodflow(see,[6]).Sometimes,
fluidmovesoverastationarybody,forexample,windblowingoverabuilding,ora
bodymovingthroughaquiescentfluidorabusmovingthroughair.Suchmotionsare
referred to as flows over bodies or external flows [10]. The shape of the object has
profound influence on the flow over a body and thus affects significantly the heat
andmasstransfercharacteristics.Flowpastbodiescanbeclassifiedintoincompress-
ibleandcompressibleflows.Compressibilityeffectsareneglectedatvelocitiesbelow
360km/hour,andsuchtypesofflowsareknownasincompressibleflows.Inthisbook,
we are concerned withincompressible fluidflows [11–17].
Becauseoftherecenthighdemandintheneedforunderstandingandanalyzingthe
problemswecomeacrossinscienceandengineering,wefeelthatthereisaneedfora
bookofthiskind.Theunderlyingaimofthisbookistopresenttransportphenomena
that will help students and researchers in the field of fluid mechanics in acquiring
a deeper understanding of the characteristics of flow and heat and mass transfer
(see,e.g.,[18]).Obviously,partofthematerialinthebookcanbeconvenientlyused
asanintroductorycoursematerialforresearchersworkinginboundarylayertheory,
flow,andheatandmasstransfer[19–45].Also,thebookisintendedforgraduatestu-
dentsinmathematics,engineering,andinthemathematicalsciences.Inaddition,the
materialinthebookmaybeofinteresttoresearchersworkinginphysicalchemistry,
soil physics, meteorology, andnanotechnology.
x Introduction
Thebookisdesignedtoaccommodateseveraltopicsofvaryingemphasis,andthe
chapters comprise fairly self-contained material from which one can make various
coherentselections.Thereareseveralunderlyingthemesthatbecomeapparentwhen
oneexaminestheliteratureonthesubject.Wehopetobringoutclearinsightbydis-
cussingseveralflowfeatures.Also,wediscussseveralcasesofphysicalproblemsin
general.
The outline of the book will be as follows. Chapter 1 deals with the numerical
method(s)adoptedintheseworks.InChapters2–4,whichcomprisePartIofthebook,
wepresenttheflowpastsurfacesofdifferenttypes,namely,stretching,shrinking,and
flat surfaces. This first set of chapters provides explanations intended for general
readers and can be directly employed for problems in engineering, applied physics,
and other applied sciences. We keep the discussion broad based so as to provide a
frameworkforresearchers.Inordertomotivatethereaderandprovideagoodunder-
standingofthesubjectmatter,attheendofChapters2–4,weprovidemultipleexam-
ples of problemsthat have been solved numerically.
InPartIIofthebook,Chapters5–6,weshiftthefocustoconcreteexamplesand
problemsrelatedtobluffbodiesinfluidmechanicsandheatandmasstransfer.Here
the governingequationsofthe problems are highlynonlineardifferentialequations.
TheproblemsconsideredinthisPartwillhelpthereaderunderstandproblemsofphys-
icalrelevanceandapplyittotheotherphysicalfieldsofinterest.Wegroupsuchprob-
lems into three chapters: general fluid flow past a cylinder in Chapter 5, fluid flow
over a sphere in Chapter 6, and finally problems related to flow past a wedge in
Chapter7.
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