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process.Thustheentransydissipationmayserveasa gureof

meritforassessingtheperformanceofheatexchanger.

Muchefforthasalreadydevotedtothestudyofentransydissipationtheory.Wangetal.[10]derivedanentransytransferequationdescribingtheentransytransferprocessesofamulti-componentviscous uidsubjectedtoheattransferbyconductionandconvection,massdiffusionandchemicalreactions.ChenandRen[11]de nedaratiooftemperaturedifferencetoheat uxasthegeneralizedthermalresistanceofconvectiveheattransferprocesses,anddevelopedtheminimumthermalresistancetheoryforconvectiveheattransferoptimization,itwasfoundthattheminimumthermalresistanceprincipleisequivalenttotheentransydissipationextremumprinciple.Chenetal.[12]optimizedtheconvectiveheattransferprocessinatwo-dimensionalfoursquarecavitywiththeentropygenerationminimizationprincipleandentransydissipationextremumprinciple,andtheresultsindicatesthattheformeryieldedthehighestheat-workconversionwhilethelattermadetheconvectiveheattransferef ciencymaximum.Xiaetal.[13]studiedtheoptimumparameterdistributionsintwo- uidheatexchangerbyusingoptimalcontroltheoryunderthe xedheatloadconditionandtakingtheentransydissipationminimi-zationastheoptimizationobjective.Guoetal.[14]foundthatthetotalentransydissipationratereachestheminimumwhenthelocalentransydissipationrateisuniformlydistributedalongtheheatexchanger,whichiscalledtheprincipleofequipartitionofentransydissipation.Liuetal.[15]investigatedtheapplicabilityoftheextremumprinciplesofentropygenerationandentransydissipa-tionforheatexchangeroptimization,andfoundthattheformerisbetterfortheheatexchangeroptimizationwhenitworksintheBraytoncycle,whilethelattergivesbetterresultswhenheat

exchangerisonlyforthepurposeofheatingandcooling.Recently,thein uenceofviscousdissipationheatingontheentransyintwo- uidheatexchangerswasinvestigatedin[16],andtheentransydissipationextremumprinciplewasextendedtotheradiativeheattransferin[17]andtheoptimizationoftransportnetworksin[18].Xuetal.[19,20]derivedtheexpressionsofentransydissipationduetoheatconductionand uidfrictioninheatexchanger.Whentheentransydissipationisappliedtotheperformanceevaluationandoptimizationdesignoftheheatexchanger,itisnecessarytobenon-dimensionalised.In[21],anon-dimensionalisationmethodfortheentransydissipationinheatexchangerwasintroducedandanentransydissipationnumberwhichcanbeusedtoevaluatetheheatexchangerperfor-mancewasde ned.

Inthepresentwork,thenon-dimensionalisationofthetotalentransydissipationincludingentransydissipationcausedbyheatconductionandentransydissipationdueto uidfrictionwillbeenemployedastheobjectivefunctiontooptimizetheshell-and-tubeheatexchanger.Inaddition,themulti-objectiveoptimizationdesignofshell-and-tubeheatexchangerwhichtakestheentransydissipationnumberduetoheatconductionandthenon-dimensionalisationoftheentransydissipationcausedby uidfric-tionastwoobjectivefunctionswillbedemonstrated,andthetwooptimizationdesignapproacheswillbecomparedwitheachother.2.Thermalcalculationofshell-and-tubeheatexchangerInthepresentsection,thebasiccalculationsofheattransferandpressuredropintheshell-and-tubeheatexchangerarepresented.Inthefollowingdiscussiontheoptimizationdesignof

the