1. NURULAFIFAHBINTIMOHDYUSOFF 2013275464 EH1104A FACULTYOFCHEMICALENGINEERING

2. TheLogMeanTemperature DifferenceMethod(LMTD) TheLogarithmicMeanTemperatureDifference(LMTD)is validonlyforheatexchangerwithoneshellpassandone tubepass. Formultiplenumberofshellandtubepassestheflow patterninaheatexchangerisneitherpurelyco-currentnor purelycounter-current. Thetemperaturedifferencebetweenthehotandcoldfluidsvaries alongtheheatexchanger. ItisconvenienttohaveameantemperaturedifferenceTmforuse intherelation. QUAsTm

3. Themeantemperaturedifferenceinaheattransfer processdependsonthedirectionoffluidflowsinvolved intheprocess.Theprimaryandsecondaryfluidinan heatexchangerprocessmay flowinthesamedirection-parallelfloworcocurrent flow intheoppositedirection-countercurrentflowor perpendiculartoeachother-crossflow

5. T2 T1 T2 T1 TLn Co-currentflow ln  T10 1 2 T2 T1 T4 T5 T6 T3 T9 T8 ∆T1 T7 ParallelFlow ∆T2 T1TTT3T7 inin hc T2ThoutTcoutT6T10 A

6. Counter-currentflow T10 1 2 T2 T1 T4 T5 T3 T1 T4 T6 T3 T6 T6 Wall T2 T7 T9 T8 T7 T8 Counter-CurrentFlow T9 T10 T1TT T3T7 inout hc A outin hc

7. LMTDCounter-FlowHX T2T1 ln(T2/T1) QUATLM TLM WhereforCounterFlow: T1Th,1Tc,1Th,iTc,o T2Th,2Tc,2Th,oTc,i Tlm,CF>Tlm,PFFORSAMEU:ACF<APF

8. LMTD-Multi-PassandCross-Flow ApplyacorrectionfactortoobtainLMTD QUATLM TLMFTLM,CF t:TubeSide

9. LMTDParallel-FlowHX T2T1 ln(T2/T1)  QUATLM TLM WhereforParallelFlow: T1Th,1Tc,1Th,iTc,i T2Th,2Tc,2Th,oTc,o

10. Inamulti-passexchanger,inadditiontofrictionallossthehead lossknownasreturnlosshastobetakenintoaccount. Thepressuredropowingtothereturnlossisgivenby- Where, n=thenumberoftubepasses V=linearvelocityofthetubefluid Thetotaltube-sidepressuredropis ∆PT=∆Pt+∆Pr

13. THEEFFECTIVENESS-NTUMETHOD LMTDmethodisusefulfordeterminingtheoverallheat transfercoefficientUbasedonexperimentalvaluesofthe inletandoutlettemperaturesandthefluidflowrates.     Amoreconvenientmethodforpredictingtheoutlet temperaturesistheeffectivenessNTUmethod. ThismethodcanbederivedfromtheLMTDmethod withoutintroducinganyadditionalassumptions. Therefore,theeffectiveness-NTUandLMTDmethodsare equivalent. Anadvantageoftheeffectiveness-NTUmethodisitsability topredicttheoutlettemperatureswithoutresortingtoa numericaliterativesolutionofasystemofnonlinear equations.Theheat-exchangereffectivenessεisdefinedas

14. •Heatexchangereffectiveness, : q qmax  01 •Maximumpossibleheatrate: qmaxCminTh,iTc,i ifCC Chhc or  Cmin WillthefluidcharacterizedbyCminorCmaxexperiencethelargestpossible temperaturechangeintransitthroughtheHX? WhyisCminandnotCmaxusedinthedefinitionofqmax?

15. •NumberofTransferUnits,NTU UA Cmin NTU AdimensionlessparameterwhosemagnitudeinfluencesHXperformance: qwithNTU

16. HeatExchangerRelations    or     or   qmhih,ihi,o   qChTh,iTh,o  qCcTc,oTc,i •PerformanceCalculations: fNTU,Cmin/Cmax Cr RelationsTable11.3orFigs.11.14-11.19 • qmcic,oci,i  qCminTh,iTc,i

17. •DesignCalculations: NTUf,Cmin/Cmax RelationsTable11.4orFigs.11.14-11.19 •Forallheatexchangers, withCr •ForCr=0,asingleNTUrelationappliestoallHXtypes. 1expNTU or NTU1n1

19. References http://www.engineeringtoolbox.com/arithmetic-logarithmic- mean-temperature-d_436.html http://www-old.me.gatech.edu/energy/laura/node5.html http://www.che.ufl.edu/unit-ops-lab/experiments/HE/HE- theory.pdf http://web.iitd.ac.in/~prabal/MEL242/(30-31)-Heat-exchanger- part-2.pdf