J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235229

Fig.1.Diagramofatypicalshell-and-tubeheat

exchanger.

shell-and-tube3

heatexchangerasshowninFig.1istakenasanexampletodemonstratetheapplicationoftheentransydissipationtheoryinheatexchangerdesign,sinceitisthemostcommontypeofheatexchangerappliedinthermalengineering.IntheheatexchangerillustratedinFig.1,thehot uidisinthetube-sidewhilecold uidintheshell-side.2.1.Heattransfercalculation

Undertheusualassumptionssuchasnolongitudinalheatconduction,negligiblepotentialandkineticenergychanges,negligibleheattransferbetweentheexchangeranditssurround-ingsandsoon[22],theenergybalanceequationforheatexchangeriswrittenas

Q¼Àmc

_ÁÀÁÀÁÀÁphTh;iÀTh;o¼mc_pcTc;oÀTc;i(1)

whereQistheheattransferrate,m

_isthemass owrate,cpisthespeci cheatof uidatconstantpressureandassumedtobeaconstant,Trepresentsthetemperature,thesubscriptshandcrefertothehotandcold uid,respectively,thesubscriptsiandorefertotheinletandoutletofheatexchanger,respectively.Theheatexchangereffectivenessisde nedastheratiooftheactualheattransferratetothepossiblemaximumheattransferrate(Qmax)asfollows[23]

¼

QQ(2)

max

Theshellinnerdiameterisexpressedas[24]

DÀ:1p nÀ1Á

s¼1piþ3do

(3)

whereDsistheshellinnerdiameter,nisthenumberofheatexchangetubes,piisthetubepitchfortheequilateraltriangulararrangementoftubes,doistheouterdiameterofheatexchangetube.AschematicdiagramoftubelayoutisdemonstratedinFig.2toexplainEq.(3).The rstterminEq.(3)estimatesthedistancebetweenthecenteroftubebundleandthecirclecenterfortheoutmostheatexchangetubeinthetubebundle,andthesecondtermaccountsforthedistancebetweenthecirclecenterfortheoutmostheatexchangetubeinthetubebundleandtheshellinnerwallasshowninFig.2.AccordingtotheBell-Delawaremethodtheshell-sideheattransfercoef cientcanbeexpressedasfollows[23]

am

0:14

s¼jocp;s

_smAPrs

ss;w

s

À2=3

(4)

wherem

_sistheshell-sidemass owrate,Asisthecross owareaatthecenterlineofshellforonecross owbetweentwobaf es,cp,sisthespeci cheatoftheshell-side uid,msistheshell-side uiddynamicviscosityatbulktemperature,ms,wisthe uiddynamicviscosityatwalltemperature,Prsistheshell-sidePrandtlnumber,joisheattransferfactor.Theheattransferfactorjoisgivenby[23]:

Fig.2.Theschematicdiagramoftubelayout.

jo¼jHjcjljbjsjr

(5)

wherejHistheheattransferfactorforpurecross owofanidealtubebank,jcthecorrectionfactorforbaf ecutandspacing,jlthecorrectionfactorforbaf eleakageeffect,jbthecorrectionfactorforthebundlebypass ow,jsthecorrectionfactorforvariablebaf espacingintheinletandoutletsections,jrthecorrectionfactorforadversetemperaturegradientbuildupinlaminar ow.Thesecorrectionfactorsareverycomplicatedtodetermine,thedetailscanbefoundin[23,24]andarenotlistedhereintosavespace.Forthecasethatthehot uidisinthetube-side,theDittuseBoelterequationgivesrisetothefollowingexpressionofthetube-sideheattransfercoef cient [23]:

0:8

at¼0:023

lrtvtdi

Pr0t

:3

d(6)

i

twherethepartinbracketsindicatesthetube-sideReynoldsnumberdenotedasRet,diistheinnerdiameteroftheheatexchangetube,rtthetube-side uiddensity,vtthetube-side owvelocity,mtthetube-side uiddynamicviscosityatbulktempera-ture,Prtthetube-sidePrandtlnumber.FromEqs.(4)and(5)thetotalheattransfercoef cientbasedontheexternalsurfaceareaoftheheat"

exchangetubeiswrittenas

K1

dd

o¼

o

t

þri

t

odwdoþ

þr1

#À1

i

wi

sþ

(7)

s

wheredwisthewallthicknessoftheheatexchangetube,lwisthewallthermalconductivity,rtandrsstandforthetube-sideandshell-sidefoulingresistances,respectively.2.2.Pressuredropcalculation

Thetotaltube-sidepressuredropincludesthreeparts:pressurelossalongtube,pressurelossinbendaswellasinletandoutletpressurelosses.Ignoringthesecondpartforthesingletubepass,thetotal

tube-sideL pressurem drop

iswrittenas[23,24].

DPt¼

tÀ0:144ftrtv2t

þ1:5

(8)

it;w

whereftisthetube-sidefrictionfactor,Listhetotallengthoftube

passes.Fortheheatexchangerwithmultiplepasses,pressurelossinelbowsshouldalsobetakeninto

account.