Nomenclature

r

radius,mm

angleofasinglethermoelectricleg,degree

halfoftheanglebetweentwolegs,degree

Highperformanceandthermalstressanalysisofasegmentedannularthermoelectricgenerator

SamsonShittua

GuiqiangLia,⁎

Guiqiang.Li@hull.ac.uk

XudongZhaoa,⁎

Xudong.Zhao@hull.ac.uk

XiaoliMaa

YousefGolizadehAkhlaghia

EmmanuelAyodeleb

aSchoolofEngineeringandComputerScience,UniversityofHull,HU67RX,UK

bInstituteofRobotics,AutonomousSystemsandSensing,UniversityofLeeds,LS29JT,UK

⁎Correspondingauthors.

Abstract

Annularthermoelectricgeneratorscaneliminatethethermalcontactresistanceformedduetogeometrymismatchwhenflat-platethermoelectricgeneratorsareusedwithroundshapedheatsourceorheatsink.Therefore,inthisstudy,thenumerical

simulationofasegmentedannularthermoelectricgenerator(SATEG)isinvestigatedusingthree-dimensionalfiniteelementanalysis.Thethermoelectricandmechanicalperformanceofthesegmentedannularthermoelectricgeneratorisstudiedbyconsidering

temperaturedependentthermoelectricmaterialpropertiesandelastoplasticbehaviourofcopperandtheweldinglayer(solder).Theinfluenceofsegmentedpingeometryontheperformanceofthesegmentedannularthermoelectricgeneratorisinvestigated

andcomparison ismadewithnon-segmentedannular thermoelectricgenerators.COMSOL5.3Multiphysicssoftware isused to investigate theeffectsofheatsource temperature, thermoelectric leg lengthand legangleon theelectricalandmechanical

performanceofthesegmentedandnon-segmentedannularthermoelectricgenerators.Resultsshowthatthesegmentedannularthermoelectricgeneratorhasagreaterefficiencycomparedtotheannularthermoelectricgenerator(ATEG)withBismuthtelluride

materialwhenthetemperaturedifferenceisgreaterthan100 K.Inaddition,theefficiencyoftheSATEGisfoundtobe21.7%and82.9%greaterthanthatoftheBismuthtellurideATEGandSkutteruditeATEGrespectivelyat200 Ktemperaturedifference.

Finally,theresultsshowthatincreaseinthermoelectricleglengthcanreducethethermalstressandelectricalperformanceofthesegmentedandnon-segmentedthermoelectricgenerators.Resultsobtainedfromthisstudywouldinfluencethedesignand

optimizationofsegmentedannularthermoelectricgenerators.

Keywords:Segmentedthermoelectricgenerator;Annularthermoelectricgenerator;Finiteelementmethod;Powergeneration;Thermalstress

θ1

θ2

© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

anglebetweenoutercopperandlegs,degree

totallegangle,degree

L

lengthofthermoelectriclegs,mm

nh

hotsegmentn-typematerial

nc

coldsegmentn-typematerial

ph

hotsegmentp-typematerial

pc

coldsegmentp-typematerial

Qin

inputheatflux,W/m2

Qout

outputheatflux,W/m2

RL

loadresistance,

Pout

outputpower,W

specificheatcapacity,J/kg/K

T

temperature,K

E

young’smodulus,GPa

θ3

θ

Ω

CP

z

figureofmerit

Greeksymbols

seebeckcoefficient

efficiency,%

electricalconductivity,S/m

thermalconductivity,W/m/K

density,Kg/m3

electricalresistivity,

Abbreviations

SATEG

segmentedannularthermoelectricgenerator

ATEG

annularthermoelectricgenerator

TEG

thermoelectricgenerator

Bi2Te3

Bismuthtelluride

CoSb3

Cobaltantimony

PbTe

leadtelluride

SiGe

α

η

σ

κ

ρd

ρ

Ωm

silicongermanium

Subscripts

c

coldside

h

hotside

1IntroductionRenewable energy sources have an enormous potential because in principle, they can exceed theworld’s energy demandexponentially. Therefore, a paradigmshift to renewable energy can ensure the simultaneous attainment of the goals of reducing

greenhousegasemissionsandensuringreliable,timelyandcost-efficientdeliveryofenergy[1,2].Oneoftheimportantfactorstoimprovethequalityoflifeofpeopleistheavailabilityofcheapandabundantenergywithlowenvironmentalandecologicalhazards.Solar

energyisoneofthebestenergysourceswithalowimpactontheenvironmentalnegatively[3].About40%offuelenergyiswastedasexhaustgasininternalcombustionenginevehicles,30%isdissipatedintheenginecoolant,5%islostasradiationandfrictionwhile

25%isreservedforvehiclemobilityandaccessories[4].Recentadvancesinthermoelectricmaterialprocessinghasincreasedthepotentialforalternatorstobereplacedbythermoelectricpowergenerationusingwasteheatrecoveryinautomobiles[5].Athermoelectric

generator isasolidstateheatenginewhichcandeliverelectricalpowertoaloadviaSeebeckeffectprovidingthereisatemperaturedifferencemaintainedacrossitsthermoelements[6].Therefore, theuseofathermoelectricgeneratorcanpotentiallyprovidemore

electricalenergyfromwasteheatandreducetheuseoffossilfuel.Theapplicationofthermoelectricgeneratorwasteheatrecoveryinautomobileshasbeenstudiedbyseveralresearchers[4,5,7,8].Thermoelectricgeneratorshavealsobeenappliedinwearablesensors

[9–12],micropowergeneration[13],wirelesssensornetwork[14],spacepower[15]andbuildings[16].

Thermoelectricdevicesaresmall,lightweightandreliableenergyconvertersthatproducenonoiseorvibrationbecausetheyhavenomovingmechanicalpart[17–19].Notwithstanding,theirlowconversionefficiencyhaslimitedtheirwideapplication[20].To

solvethisproblem,manyresearchershavetriedtwomainmethods;materialoptimizationandgeometryoptimization.Thetwomainfactorsthatinfluencetheefficiencyofathermoelectricgeneratorare;thermoelectricmaterialpropertiesandtemperaturedifferenceacross

thegenerator.Thetemperaturedifference ,betweenthehotside( )andthecoldside( )determinestheupperlimitoftheefficiencythroughtheCarnotefficiency .Whilethethermoelectricmaterialdetermineshowclose,theefficiencycanbetothe

Carnotthroughthethermoelectricfigureofmerit,z,which isdefinedby .Where istheSeebeckcoefficient, is the thermalconductivityand is theelectrical resistivitywhichallvarywith temperature [21].For thermoelectricmaterials,highelectrical

conductivity,lowthermalconductivityandhighSeebeckcoefficientisdesirable[22].Thus,materialswithhighfigureofmeritcanincreasetheefficiencyofthermoelectricgenerators.

Omeretal. [23]developeda theoreticalmodel tooptimize thegeometryof the thermoelectricelement legsandpredict theperformanceof thegenerator.Theyargued thatgeometryoptimization isvery important forhighpowergeneration.Thegeometry

optimizationofthermoelectricgeneratorshavealsobeenappliedsuccessfullytohybridphotovoltaicsystemstoincreasetheiroverallperformance[24–28].Inaddition,heatpipeshavebeenincorporatedintothermoelectricgeneratorstoenhancetheirperformanceand

reducecost[29–32].Thesestudieshaveshowntheimportanceofoptimizingthegeometryofthermoelectricelementsforimprovedperformance.

Researchintosegmentedthermoelectricgenerator(STEG)hasincreasedsignificantlywithinthelastfewyears.Thisisbecauseunderidealconditions,thesegmentationofdifferentmaterialscanenablethecombinationofamaterialwithhighefficiencyathigh

temperaturewithadifferentmaterialwithhighefficiencyat low temperature.Thus,bothmaterialswilloperateonly in theirmostefficient temperature rangeandenhance theoverallperformance [21].Hadjistassouetal. [33]presentedadesignmethodology foran

analyticalmodelusedtostudytheperformanceofasegmentedthermoelectricgenerator.TheirresultsshowedthatthesegmentedTEG(ThermoelectricGenerator)providedapeakefficiencyof5.29%foratemperaturedifferenceof324.6 K.Atwo-pairsegmentedTEG

whichattainedamaximumspecificpowerdensityof42.9 W/kgat498 °CwasfabricatedbyKimetal.[34]andtheresultsobtainedwasingoodagreementwiththeiranalyticalmodel.Zhangetal.[35]utilizedanumericalmethodtostudyasegmentedthermoelectric

generator.Itwasdiscoveredthattheoptimallengthratioformaximumoutputpowerandefficiencyisdependentonthematerialproperties,heattransferconditionsandgeometrystructure.Similarresearchonaninnovativesegmentedthermoelectricgeneratorwascarried

out by the same authors [36–38]. In their study, they considered the effect of tapering and segmented pin configuration in a thermoelectric generator and the general conclusion drawnwas that their innovative TEGperformed better than the singlematerial pin

configurationTEG.Inonecase,theyfoundthattheextendedlegconfigurationincreasedthermoelectricefficiencyby8%[38].

Morerecently,anattemptwasmadebyLiuetal.[39]todesignasolarthermoelectricgeneratorwhichhadacombinationofsegmentedmaterialsandasymmetricallegs.Athree-dimensionalanalysismethodwasemployedandCOMSOLMultiphysicssoftware

wasusedforthisanalysis.Itwasfoundthatincomparisonwithtwodifferentnon-segmenteddesigns,thesegmenteddesignincreasedoutputpowerby14.9%and16.6%respectivelyatanoptimizedleglengthratio.Anoptimizeddesignforasegmentedthermoelectric

generatorwasalsopresentedbyGeetal.[40].BismuthtellurideandSkutteruditewereusedasthecoldandhotsidematerialsrespectively.TheirresultsshowedthattheoutputpowerandconversionefficiencyofthesegmentedTEGweregreaterthanthoseofthe

SkutteruditeTEGwithoutsegmentation.Ouyangetal.[41]performeda3DfiniteelementanalysisonasegmentedthermoelectricgeneratorusingANSYSsimulationsoftwareandtheyfoundthatthesegmentationofthermoelectricmaterialswithhighfigureofmeritcan

offer<1$/Wcost-performanceratio.

ΔT Th Tc

α κ ρ

Heatfromroundshapedheatsourcesorheatsinkscanbeeffectivelyutilizedbyathermoelectricgeneratorwithannularshapedlegs.Theconventionalflatplateconfigurationofthermoelectricgeneratorsissuitableforapplicationswheretheflowofheatis

perpendiculartotheceramicplates.Thus,suchaconfigurationwillbeunsuitableforsystemsinwhichtheheatflowisinaradialdirectionorforcylindricalheatsources.Tosolvethisproblem,Minetal.[42]developedanovelring-structuredthermoelectricmoduleto

overcomethedrawbacksoftheflatplatemodulesandtheyobtainedanelectricoutputpowerof30mWwhenatemperaturedifferenceof70 Kwasapplied.Subsequently,Bauknechtetal.[43]usedcomputationalfluiddynamics(CFD)tooptimizetheperformanceofan

annularthermoelectricgenerator(ATEG).Withinthelastfouryears,therehasbeenasignificantincreaseintheresearchintoannularthermoelectricgenerators.Shenetal.[44]performedatheoreticalinvestigationonanannularthermoelectricgenerator.Theyusedan

annularshapedparametertocharacterizetheperformanceofthedeviceandtheresultsobtainedshowedthattheinfluenceoftheshapedparameterwasseriouslyaffectedbytheexternalload.Kaushiketal.[45]developedanexoreversiblethermodynamicmodelforan

annularthermoelectricgeneratorconsideringJouleheating,FourierheatandThomsoneffectusingenergyandexergyanalysis.TheyobservedthattheATEG’soutputpower,energyandexergyefficiencywereactuallylowerthanthoseoftheflatplatethermoelectric

generator.Ayearlater,thesameauthors[46]performedanenergyandexergyanalysisonasolarheatpipeannularthermoelectricgenerator.Thistimehowever,theyfoundthattheoutputpowerandoverallexergyefficiencyofthesolarannularthermoelectricgenerator

were0.52%and0.40%greaterthanthoseofthesolarflatplatethermoelectricgeneratorrespectively.Shenetal.[47]performedatheoreticalanalysistostudytheperformanceofannularthermoelectriccouplesunderaconstantheatflux.Intheirstudy,theyusedfinite

elementmethodtoinvestigatethetemperaturedependencyofthermoelectricmaterialsandThomsoneffect.Theirresultsindicatedthattheleveloftheinputheatfluxmustbecontrolledtoprotectthedevicefromdamage.Similarly,Asaadietal.[48]studiedthethermal

andelectricalperformanceofanATEGunderpulsedheatfluxusingfiniteelementmethod.TheyconcludedthattransientpulsedheatingenhancedtheoutputpowerandefficiencyoftheATEGcomparedtoconstantsteadystateheating.

Zhangetal.[49]investigatedtheinfluenceofthermoelectricleggeometryconfigurationandcontactresistanceontheperformanceofanATEG.Theyfoundthatthemaximumoutputpowerperunitmassisattainedwhentheleggeometryparameterm = −1whilethevalueofmhadno influenceon theefficiencyof the idealATEGmodel.Thesameauthorsalso investigated theeffectsof internalandexternal interface layerson theperformanceofanannular thermoelectricgeneratorusingaphenomenologicalmodel [50].A

significantreductionintheperformanceoftheATEGwasobservedwhentheinfluenceofinterfacelayerswasconsidered.Fanetal.[51]carriedoutathreedimensionalnumericalstudyonanATEGanditwasobservedthatincreasingthethermocoupleleglengthscould

reducethermoelectricperformancebutimprovemechanicalreliability.Consideringsegmentedannularthermoelectricgenerator(SATEG),Shenetal.[47]theoreticallystudiedsuchasystemtoobtainitsefficiencyandpoweroutput.TheyfoundthattheSATEGperformed

betterthantheATEGasthetemperatureratiowasbeingincreased.

Researchers[52–56]havebeendrawntotheinvestigationofthethermalstressdevelopedinathermoelectricgeneratorduetothefactthatitoperatesinatemperaturedifferenceenvironmentandthermalstressiscausedbythedifferenceinthermalexpansion

behavioursoftheTEGmaterials.Inaddition,thestudyofthermalstressisimportantbecauseitprovidesinformationonthelocationofhighstressinthemodules,thereliabilityofthemodulesandthisinformationcanpotentiallyhelpincreasethelifespanofthemodules.

Gaoet al. [57] performed a parametric analysis to study the thermal stress developed in a thermoelectric generator. Anisotropicmaterial propertieswere used, and their results revealed that both the shear stress and vonMises stress initially decreased as the

thermoelectric leglengthincreased.Al-Merbatietal.[58]studiedtheinfluenceofpingeometryontheperformanceofathermoelectricgenerator.Theyfoundthatmaximumthermalstresscanbereducedbychangingthegeometryconfigurationofthethermoelectric

generator.Similarly,Wuetal.[59]performedathermalstressanalysisforseveralthermoelectricmodulegeometryconfigurations.Inaddition,differentheatfluxconditionswereconsidered,anditwasfoundthatthethicknessoftheceramicmoduleanddistancebetween

thermoelectriclegsinfluencedonthethermalstressinthemodule.Erturunetal.[60]alsofoundthatvaryingleggeometrycanhelpreducethethermalstressdevelopedinathermoelectricgenerator.

Thermalstress inasegmentedthermoelectricgeneratorhasalsobeenstudiedby[61–63].Jiaetal.[61]developeda3Dfiniteelementmodel tostudy themechanicalperformanceofasegmentedthermoelectricgenerator.Theyfoundthatconsidering the

elastoplaticdeformationofthecopperstripsandweldingstripscansignificantlyreducethethermalstressinthedevice.Mingetal.[62,63]studiedthethermalstressinasegmentedthermoelectricgeneratorundergaussian,parabolicanduniformheatfluxconditions.

Resultsobtainedrevealedthatthepositionbetweenthehotendofthealuminaandcopperhavethehighestpossibilitytocrackinthemodule.

ThedetailedliteraturereviewaboveshowsthecurrentworksinTEG,STEG,ATEG,SATEGandthermoelectricgeneratorthermalstress.Thesignificanceofgeometryoptimization,annularshape,segmentationandthermalstressanalysiscanbeclearlyseen.

However,thereareonlyafewliteraturesavailableonthestudyofsegmentedannularthermoelectricgenerators.Infact,thereisonlyoneavailableliteratureonSATEG[47]however,thisstudywasconductedusingatheoreticalapproachandthermalstressanalysiswas

notconsidered.Also,thereisonlyoneavailableliteratureonthestudyofATEGmechanicalperformance[51].Therefore,thisresearchseekstofill inthegapsandprovidebetterknowledgeonthethermoelectricandmechanicalperformanceofasegmentedannular

thermoelectric generator. This research investigates the influence of segmented pin geometry on the performance of annular thermoelectric generators. The thermoelectric andmechanical performance of theSATEG is studied using three-dimensional numerical

simulation.Tothebestofourknowledge,thisstudyisthefirstof itskindandwouldprovidevaluableinformationonthepotentialofsegmentedannularthermoelectricgenerators.FiniteelementmethodisusedtoperformtheanalysisandCOMSOL5.3Multiphysics

softwareisemployed.Thetemperaturedependenceofthermoelectricmaterialproperties isconsideredtoensureaccuracyoftheperformancepredictionsandtheinfluenceof leg length, legangleratioandtemperaturedifferenceontheoutputpower,efficiencyand

thermalstressoftheSATEGarestudied.Finally,acomparisonbetweentheperformanceoftheSATEGandATEGispresented.

Theremainingpartof thispaper isorganizedas follows;Section2providesadetailedgeometricmodeldescriptionandTEGequivalentcircuit.Section3describes thenumericalmodelused for theanalysis including the thermoelectricand thermalstress

analyses,materialproperties,boundaryconditions,computationprocedureandmodelvalidation.Section4describestheresultsobtainedandanalysisoftheresults.Finally,Section5providestheconclusionsdrawnfromthisstudy.

2GeometricmodeldescriptionThesegmentedannularthermoelectricgenerator(SATEG)geometryisshowninFig.1,anditconsistsofaluminaceramics,copper,weldinglayerandthermoelectriclegs.Thefunctionofthealuminaceramicistopreventelectricalconductivitybutenablethermal

conductivity.Thecopperisaconductivematerialwhichallowsanelectricalcircuittobeformedinthegenerator.Theweldinglayer(solder)helpstoreducethethermalstressinthedevicewhiletwodifferentthermoelectricmaterialsareusedforthedifferentsegmentsof

theSATEG.InFig.1a, representstheangleofasinglethermoelectricleg, representshalfoftheanglebetweentwolegsand representstheanglebetweenthecoldside(outer)copperandthethermoelectriclegs.Theradiusofeachofthecomponentsofthe

SATEGarerepresentedby to asshowninFig.1a.Inaddition,thelengthofthethermoelectriclegcanbeobtainedfrom: .Forsimplificationpurposes,thelengthsofthep-typeandn-typethermoelectricmaterialsareassumedequal.Also,the

lengthsofthethermoelectricelements(n-typeandp-type)inthecoldsegmentareassumedtobeequaltothoseofthehotsegment.Inordertoincreasethespeedofcalculation,onlyoneunicoupleisanalysedasshowninFig.1b.Thedifferentgeometriesanalysed

correspondingtothedifferentleglengthandlegangleoftheSATEGandATEGstudiedaredrawnwithAutoCADsoftwareandimportedintoCOMSOLindividually.Eachgeometryisthenanalysedundersimilarconditionsandtheperformanceisobserved.Thegeometric

parametersusedinthesimulationarelistedinTable1.Furthermore,thegeometryofthenon-segmentedannularthermoelectricgeneratoranalysedinthisstudyisshowninFig.2.Forallofthedrawings(SATEG,ATEG)theradiusofthecoldsideceramiciskeptconstant

andisthebeginningofeachdrawing.TheonlydifferencebetweentheSATEGandATEGstudiedisthesegmentationoftheTEGintotwodifferentthermoelectricpairsandmaterials.Allothercomponents,legangleandleglengthareexactlythesamewiththoseofthe

SATEG.ThisistoensuresimilaritybetweentheSATEGandATEGsothatpropercomparisoninperformancecanbemade.Inaddition,Bismuthtelluride(Bi2Te3)isthematerial(n-typeandp-type)usedonthecoldsegment(ncandpc)whileCoSb3Skutteruditematerial

(n-typeandp-type) isusedonthehotsegment(nhandph).Theadditionofanexternal loadresistanceRLhelps toclose theelectriccircuitso that theoutputpowercanbemeasured.When theexternal load isequal to the internal resistanceof the thermoelectric

generator,maximumpowercanbegenerated.

θ1 θ2 θ3

r1 r10 L=r7-r6=r5 - r4

Table1Geometricparametersofthesegmentedannularthermoelectricgenerator.

r1(mm) r2(mm) r3(mm) r4(mm) r5(mm) r6(mm) r7(mm) r8(mm) r9(mm) r10(mm) Length(mm) Depth(mm) Angle(degree)

Ceramic Dependsonstudy – – – – – – – 29.2 30 0.8 2 –

Copper – Dependsonstudy – – – – – 28.8 – – 0.4 1 –

Solder – – Dependsonstudy – – – 28.6 – – – 0.2 1 –

Fig.1SATEGgeometry;(a)schematicdiagramand(b)three-dimensionalview.

Bi2Te3Legs – – – – – Dependsonstudy – – – – r7-r6 1 –

CoSb3Legs – – – Dependsonstudy Dependsonstudy – – – – – r5-r4 1 –

– – – – – – – – – – – – Dependsonstudy

– – – – – – – – – – – – Dependsonstudy

– – – – – – – – – – – 1

*“Dependsonstudy”meansthevaluechangesbasedontheparametricstudybeingconsidered.Forexample,if ,then , , , , and .However,if ,4or5,theradiusvalueschange

accordingly.

2.1ThermoelectricgeneratorequivalentelectricalcircuitAsimplifiedequivalentelectricalcircuitofathermoelectricgeneratorisshowninFig.3.Thiscircuithelpstounderstandthebasicoperationofathermoelectricpowergenerator.Whenthereisnoloadconnection,theopencircuitvoltage(VOC)isgivenas,

where istheSeebeckcoefficientand isthetemperaturedifferencebetweenthehotsideandcoldsideofthethermoelectricgenerator.

θ1

θ2

θ3

L=2 r6=26.6 r5=26.4 r4=24.4 r3=24.2 r2=23.8 r1=23 L=3

Fig.2ATEGgeometry;(a)three-dimensionalviewand(b)frontview.

(1)

α ΔT=Th-TC

Whenanexternalloadresistance(RL)isconnected,theoutputvoltageofthethermoelectricgenerator(VL)isgivenas,

where istheinternalresistanceoftheTEGand istheTEGcurrentwhichisgivenas,

TheoutputpoweroftheTEG(PL)canthusbeobtainedas,

Therequiredpoweroutputforaparticularapplicationcanbeobtainedbycombiningseveralthermoelectricmodules.Inaddition,theoutputvoltageandpowerofthethermoelectricgeneratorcanbeincreasedbyapplyingahightemperaturedifferenceonthe

TEGandbymatchingtheexternalloadresistancetotheinternalresistanceoftheTEG.

Asidestheoutputpowerofathermoelectricgenerator,itselectricalpowerdensityisanotherimportantmetricwhichdirectlyinfluencestheTEGperformanceandcostratiowhichisveryimportantforwasteheatrecoveryapplications.Thewaystoimprovethe

thermoelectricgeneratorpowerdensity include: improvingthematerial figureofmerit, increasingthetemperaturedifferenceacrosstheTEGandoptimizingthermoelectricelementdimensionsandfillingfactors [64].Therefore,thisresearchfocusesonoptimizingthe

thermoelectricelementdimensions.

3NumericalmodelTheanalysisofthesegmentedannularthermoelectricgeneratorisdividedintotwomainsub-sectionswhichare:thermoelectricanalysisandthermalstressanalysis.Thethermoelectricanalysiswouldprovideresultsrelatingtotheoutputpowerandefficiencyof

thesystemwhilethethermalstressanalysiswouldprovideresultsrelatingtothemechanicalperformanceofthesystem.

3.1GoverningequationsofthermoelectricanalysisThegoverningequationofthethermoelectricanalysisaresolvedusingCOMSOL5.3Multiphysicssoftwarewhichisbasedonfiniteelementmethod.ThethermoelectricanalysisemployedtakesintoaccountthePeltiereffect,Fouriereffect,Jouleeffectand

Thomsoneffect.

Theheatflowequationinthethermoelectricanalysiscanbeexpressedas[20]:

where isthedensity, isspecificheatcapacity, istemperature, isheatfluxvectorand istheheatgenerationrateperunitvolume.

Theelectricchargecontinuityequationscanbeexpressedas

Fig.3EquivalentelectricalcircuitofaTEG.

(2)

Rin I

(3)

(4)

(5)

ρd Cp T

where istheelectriccurrentdensityvectorand istheelectricfluxdensityvector.

Eqs.(5)and(6)arecoupledusingthefollowingthermoelectricconstitutiveequations[65],

where istheSeebeckcoefficientmatrix, representsthethermalconductivitymatrixand istheelectricalconductivitymatrix.

where istheelectricfieldintensityvectorand istheelectricscalarpotential.

Thecoupledthermoelectricequationscanbeobtainedbycombiningtheaboveequationsas,

where representsthedielectricpermittivitymatrix.

Finally,thecoupledthermoelectricgoverningequationscanrewrittenas,

3.2GoverningequationsofthermalstressanalysisSince the thermalconductivityof thematerialsconsideredare temperaturedependent, the thermoelectricmodule isnotentirelyone-dimensional.Thus, thermodynamicandmechanicalcharacteristicsof thesystem in thez-axisdirectionarenonlinear.The

temperaturefieldisusedtocalculatethethermalstressfieldsincetemperatureinfluencesdeformationsinthesystem.

Thethermodynamicequationcanbeexpressas[59],

where and .Thetemperaturefieldisobtainedbythenumericalsimulationandisusedinthethermalstressanalysis.

Thermalstressisgeneratedduetotheunevenexpansionofthematerialsmakingupthethermoelectricgenerator.Theequationsgoverningthedisplacement–strainrelationsforthethermalstresscanbeexpressedas[62],

Thestress–strainrelationcanbeexpressedinadimensionlessformusinganonsymmetricalJacobianmatrixas,

(6)

(7)

(8)

[α] [κ]

(9)

φ

(10)

(11)

[ε]

(12)

(13)

(14)

(15)

(16)

Thethreeprincipalstressarerepresentedas , and respectively.ThevonMisesequivalentstresscanbeobtainedfromthefourthstrengththeoryofmechanicsofmaterialsalsoknownasthedistortionofenergytheory.Itdescribesthetotalcombined

stressesinallthreedimensionsas,

Thedifficultyencounteredintryingtosolvetheaboveequationsanalyticalduetothetemperaturedependenceofthematerialpropertiesnecessitatestheneedtousefiniteelementmethodtoobtainthesolutiontotheseequations.Theelectrical,thermaland

mechanicalbehavioursofthethermoelectricgeneratorcanbeobtainedfromthecoupledequationsdescribedabove.

3.3MaterialpropertiesThematerialsusedinthisstudyhavebeencarefullychosenconsideringtheirtemperaturerangesforoptimumperformance.Theperformanceofthethermoelectricgeneratorisaffectedbythechoiceofmaterialused.Basedontheoptimaloperatingtemperature,

thermoelectricmaterialscanbedividedintothreeranges:lowtemperature < 500 K(e.g.Bi2Te3basedmaterials),middletemperature500–900 K(e.g.PbTebasedmaterials)andhightemperature > 900 K(e.g.SiGebasedmaterials)[6].Usually,Bi2Te3basedmaterialsare

usedforthelowtemperaturepartofthesegmentedthermoelectricgeneratorbecauseitisknowntobethethermoelectricmaterialwiththebestperformanceatlowtemperatureranges.Whileformiddleorhighertemperaturepartofthesegmentedleg,severalmaterials

suchasSkutterudite(CoSb3),Zintlphasematerials,half-Heuslerandleadtelluride(PbTe)couldbeused[66].Therefore,Bismuthtelluride(Bi2Te3)isusedasthelowtemperaturematerialforthecoldsegmentbecauseofitshighfiguremeritandSkutteruditematerial

(CoSb3)isselectedasthemediumtemperaturematerialforthehotsegmentbecauseofitsgoodperformanceandstrongmechanicalcharacteristics.Inaddition,thecombinationofBi2Te3andCoSb3thermoelectricmaterialshavebeenusedtostudytheperformanceof

SATEG[47],STEG[20,61]andfavourableresultswereobtained.

Themaximumallowabletemperatureforthelowtemperaturematerial(Bi2Te3)usedinthisstudyis498 Kwhilethatofthehightemperaturematerial(CoSb3)is798 K[20].Thetemperaturedependentthermoelectricpropertiesofthematerialsusedinthisstudy

areshowninFig.4whiletheremainingmaterialpropertiesusedinthenumericalsimulationarelistedinTable2.

(17)

σ1 σ2 σ3

(18)

Table2Propertiesofothermaterialsusedinnumericalsimulation[51,57,58,67–69].

Materials Thermalconductivity,

Electricalconductivity,

Specificheat

capacity,

Density, Coefficientofthermalexpansion,

Ceramic 25 1e-12 800 3970 0.68e-5

Copper 385 5.9e7 386 8930 1.7e-5

Fig.4Temperaturedependentthermoelectricproperties[47]:(a)thermalconductivity,(b)electricalresistivity,(c)Seebeckcoefficient.

Solder 55 2e7 210 7240 2.7e-5

Bi2Te3 – – 154.4 7740 0.8e-5

0.8e-5

1.32e-5

CoSb3 – – 238.7 7582 6.36e-6

Inthisstudy,ceramicandthermoelectricmaterials(Bi2Te3andCoSb3)areconsideredtobebrittlematerials.Thus,theyieldstressofBi2Te3is112 MPa[58]andtheidealstrengthofCoSb3is14.1 GPa[67].Copperandwieldinglayer(solder)areconsideredtobe

elastoplasticmaterials.Therefore,theyieldstressandtangentialmodulusofcopper70 MPaand24 GParespectively.Whilethoseofsolderare26 MPaand8.9 GParespectivelytoo[51].

3.4BoundaryconditionsThebasicassumptionsmadeinthisnumericalsimulationtosimplifythemodelwithoutsignificantdeviationsfromtherealconditionare:

(a) Allothersurfacesexceptthehotandcoldsurfacesareadiabatic.

(b) Electricalcontactresistanceandthermalcontactresistanceareignored.

(c) Heatlossesduetoconvectionandradiationonallsurfacesareneglected.

(d) Theheatsource(hotsurface)andheatsink(coldsurface)areconsideredasthermalboundaryconditionswithfixedtemperaturevalues.

(e) Afixedconstraintboundaryconditionisappliedonthehotsurfaceofthethermoelectricgeneratorwhileallotherboundariesarefree.

(f) Nodifferenceinpropertiesasafunctionofpositionexist.

Thethermoelectricgenerators(SATEGandATEG)areassumedtobecooledbyaheatsinkwhichisconnectedtothecoldsurface.Afixedtemperaturevalueof298 Kisappliedtothecoldsurfacetocoolthegeneratorandthisvalueiskeptconstantthroughout

thestudy.Thiscanberepresentedas,

3.5ComputationprocedureCOMSOL5.3MultiphysicssoftwareisusedtoperformthefiniteelementanalysisandobtainthethermoelectricandmechanicalperformancedataoftheSATEGandATEGstudied.Thestudyiscarriedoutundersteady-stateconditionandtheelectricalcircuit

interfaceinCOMSOLisusedtodescribetheloadresistance .Azeroelectricpotentialisappliedatthecopperelectrodeonthecoldsurfacen-legwhileaterminalisconnectedtothecopperelectrodeonthecoldsurfacep-leg.Allthematerialsareconsideredaslinear

(15 (Kindlychangethisequation(15)to(19).))

RL

elasticmaterialsandtheirrespectivepropertiesarelistedinTable2.

Thethermoelectriccouplingequationscanbeusedtoobtain theheat input( ) to thehotsurfaceof the thermoelectricgenerators (SATEGandATEG).Theelectricalperformanceof the thermoelectricgenerator isdetermined from itsoutputpowerand

efficiency,whicharedefinedas[51],

where istheoutputpowerand isthecircuitelectriccurrent.

Thetotallegangleofthethermoelectricgeneratorcanbeexpressedas,

3.6ModelvalidationMeshconvergencetestisperformedforthenumericalmodelusingfiniteelementmethod.AstructuredmeshisgeneratedforthecomputationdomainusingCOMSOL’sbuilt-inmeshcomponentandasimulationmeshmethodemployedin[51]isemployedinthis

study.AlongthepathL1showninFigs.1band2a,severalcasesofdistributionofmeshelementsareapplied.Afixednumberofelementsisappliedalongthatpathandthenumberofelements(N)arevariedtotestthemeshconvergence.ItcanbeseenfromtheFig.5

thatthemeshconvergencesandtheresultsarealmostidenticaltherefore,N = 20isselectedinallsimulations(SATEGandATEG)toensureaccuracyandconvergence.

Inorder tovalidate themodelandnumerical simulationmethodsused in thisstudy, thesimulationwhichwasconductedby [52] isconsidered.Thesimulationsconditionsare reset inaccordance to theonesusedby theauthorsand thesamesimulation

Qin

(16) (Kindlychangethisequation(16)to(20))

(17) (Kindlychangethisequation(17)to(21))

Pout I

(18) (Kindlychangethisequation(18)to(22))

Fig.5MeshconvergencetestfortheSATEG’s(a)vonMisesstress(thermalanalysis)(b)voltage(thermoelectricanalysis).

parametersareused.Thethermalstresspredictionsfromthepresentstudyandpreviousstudy[52]areshowninFig.6.Itcanbeseenclearlythatbothresultsareveryidenticalthereforeresultsobtainedfromthispresentstudyarejustifiable.

4ResultsanddiscussionTheresultsobtainedfromthisstudyarepresentedinthesectionsbelowandanalysisoftheseresults isalsodone.TheinfluenceofseveralparametersonthethermoelectricandmechanicalperformanceofboththeSATEGandATEGareanalysedinthis

section.

4.1EffectofheatsourcetemperatureDuetothefactthattheinputheatflux( isdependentontheloadresistance,thereisavariationbetweentheoptimumloadresistanceformaximumoutputpowerandefficiencyfordifferentsegmentationcase[61].Therefore,tobetterobservetheeffectof

segmentationontheconversionefficiencywhichisthemostimportantperformanceindicatorconsideredinthisstudy,thecalculationsarecarriedoutataconstantloadresistancecondition.Sincetheheatsinktemperatureiskeptconstantthroughoutthisstudy,theeffect

oftheheatsourcetemperatureontheelectricalperformanceoftheSATEGandATEGcanbeseeninFig.7.IncreaseintemperaturedifferenceleadstoanincreaseintheefficiencyandoutputpoweroftheSATEGandATEG.Thisisanormalandexpectedphenomenon.

However,theadvantageoftheSATEGovertheBismuthtellurideATEGintermsofefficiencycanbeclearlysincewhenthetemperaturedifferencestartsincreasingfrom100 KasshowninFig.7a.ItisalsoobviousthattheSkutteruditeATEG’sefficiencyislowerthanthe

othertwoandtheSATEGisthebestperformingdeviceinalltemperatureranges.TheconversionefficiencyoftheSATEGis21.7%and82.9%greaterthanthatoftheBismuthtellurideATEGandSkutteruditeATEGrespectivelyatatemperaturedifferenceof200 Kas

showninFig.7a.Furthermore,Fig.7bprovesthepointthattheoptimumloadresistanceforefficiencyandoutputpoweraredifferent.ItcanbeseenthatalthoughtheSATEGhasthehighestefficiencyatthatloadresistance,itsoutputpowerisactuallylowerthanthatof

theBismuthtellurideATEG.However,theadvantageoftheSATEGisitsbetterperformanceoverahighertemperaturerangecomparedtothelimitedtemperaturerangeofBismuthtelluride.Therefore,theSATEGcanbeusedbeyondthemaximumtemperaturerangefor

Bismuthtelluride(498 K)thus,ithasahigherpotentialcomparedtotheothertwosingle-materialATEGforrecoveringwasteatalargetemperaturedifference.

Fig.6Validationofpresentnumericalsimulationwithpreviousstudy[52].

ThemechanicalperformanceoftheSATEGandATEGunderdifferentheatsourcetemperaturecanbeseenfromFig.8.ThefigureclearlyshowsthesignificanceofsegmentationasthemaximumvonMisesstressinthelegsoftheSATEGislowerthanthatin

theATEG.ItcanalsobeseenthattheheatsourcetemperatureandmaximumvonMisesstressinthelegsofboththeSATEGandATEGhavealinearrelationship.ThemaximumstresslevelinthelegsoftheBismuthtellurideATEGisbelowtheyieldstressofthe

materialevenatitsmaximumallowabletemperaturerange.However,theBismuthtelluridematerialintheSATEGwillfailthemechanicalstrengthtestoncethetemperaturedifferenceappliedontheSATEGisgreaterthan400 K.Atatemperaturedifferenceof200 K,the

maximumvonMisesstressinthelegsoftheBismuthtelluridematerialintheSATEGislowerby35.4%comparedtothatoftheBismuthtellurideATEG.Whileat500 Ktemperaturedifference,themaximumvonMisesstressinthelegsoftheSkutteruditematerialinthe

SATEGislowerby5.7%comparedtothatoftheSkutteruditeATEG.Therefore,SATEGhasabettermechanicalperformancecomparedtotheATEGasshowninFig.8.

Fig.7VariationofSATEGandATEG(a)efficiencyand(b)outputpowerwithtemperaturedifferencewhen , , and .L=2 θ1=6 θ2=2

4.2EffectofthermoelectricleglengthTheeffectofthermoelectricleglengthontheelectricalperformanceofBismuthtellurideATEG,SkutteruditeATEGandSATEGcanbeseeninFigs.9–11respectively.Itcanbeseenthattheefficiencyandoutputpowerforeachofthedevicesfollowthesame

trend.Thelengthofthethermoelectricleghasasignificantinfluenceontheperformanceanditisfoundthatshortthermoelectricleglengthprovidesbetterelectricalperformancethanlongerthermoelectricleglength.FromFig.9a,itcanbeseenthattheefficiencyofthe

deviceusingtheshortestleglength( )consideredinthisstudyis35.7%greaterthanthatofthedeviceusingthelongestleglength( )consideredinthisstudy.Similarly,theoutputpowerwhen is73.1%greaterthantheoutputpowerwhen asshownin

Fig.9b.Thisshowshowsignificanttheinfluenceoftheleglengthisontheelectricalperformance.InthecaseoftheSkutteruditeATEG,theinfluenceoftheleglengthoverthedeviceefficiencyisnotthatobvious(Fig.10a)unlikewhenitsoutputpowerisconsideredas

showninFig.10b.TheoutputpoweroftheSkutteruditeATEGwhen is59.4%greaterthanitsoutputpowerwhen asseeninFig.10b.ThesametrendisobservedinFig.11aandbfortheefficiencyandoutputpoweroftheSATEG.Inaddition,anefficiencyand

outputpowerenhancementof45.3%and79.1%respectivelyisobservedwhentheSATEGthermoelectricleglengthisreducedfrom to .

Fig.8VariationofmaximumvonMisesstressinlegsofSATEGandATEGwithtemperaturedifferencewhen , and .L=2 θ1=6 θ2=2

L=2 L=5 L=2 L=5

L=2 L=5

L=5 L=2

Fig.9VariationofBismuthtellurideATEGleglengthwith(a)Efficiencyand(b)Outputpowerwhen , ,and .θ1=3 θ2=3

Fig.10VariationofSkutteruditeATEGleglengthwith(a)Efficiencyand(b)Outputpowerwhen , ,and .θ1=3 θ2=3

TheeffectofthethermoelectricleglengthonthemechanicalperformanceofthethermoelectricdevicesisshowninFigs.12and13.IncreaseinthermoelectricleglengthhasapositiveeffectonthevonMisesstressdevelopedintheleg.AsshowninFig.12,the

lowestvonMisesstressisobservedwhentheleglengthishigh( )forboththeSATEGandATEG.ThemaximumvonMisesstressintheBismuthtelluridematerialisreducedby20.4%and7.9%fortheATEGandSATEGrespectivelywhenthethermoelectricleg

lengthis increasedfrom to .Thisshows that increasing the thermoelectric leg lengthcan improve themechanical reliabilitybut reduce theelectricalperformanceof the thermoelectricdevicesand this finding is inagreementwith [51].Theadvantageof

segmentationcanalsobeseenfromFig.12asthemaximumvonMisesstressintheBismuthtelluridematerialoftheSATEGislowerthanthatoftheATEGforallleglength.Inaddition,Fig.13alsoshowstheeffectofleglengthonthemechanicalperformanceofthe

SATEGandATEG.However,thetrendobservedisslightlydifferentduetothedifferenceinthematerialanditsmechanicalproperties.ItcanbeseenfromFig.13thatthethermoelectricleglengthof providesthelowestvonMisesstressinthelegsoftheSkutterudite

materialoftheSATEG.

Fig.11VariationofSATEGleglengthwith(a)Efficiencyand(b)Outputpowerwhen , ,and .θ1=3 θ2=3

L=5

L=2 L=5

L=4

4.3EffectofthermoelectriclegangleTheeffectofthethermoelectriclegangleontheefficiencyandoutputpoweroftheSATEGisshowninFig.14aandbrespectively.Itcanbeseenfrombothfiguresthattheefficiencyandoutputpowerdecreaseswhen increases.Thisimpliesthatasmallangle

betweentheSATEGthermoelectriclegs(n-typeandp-type)canenhancetheefficiencyandoutputpowerofthedevice.Also,itcanbeseenthatshortthermoelectriclegsprovidethebestperformanceintermsofefficiencyandoutputpower.Fig.14aandbshowthatthe

optimumgeometryoftheSATEGformaximumelectricalperformanceiswhen , and .ItcanbeseenfromFig.14aandbthatatoptimumlength( ),anefficiencyandoutputpowerenhancementof17.8%and55.5%canbeachievedrespectivelyjust

byreducingtheanglebetweenthethermoelectriclegsfrom to .

Fig.12EffectofBismuthtelluridethermoelectricleglengthinSATEGandATEGwhen and .θ1=6 θ2=2

Fig.13EffectofSkutteruditethermoelectricleglengthinSATEGandATEGwhen and .θ1=6 θ2=2

θ2

L=2 θ2=2 θ=8 L=2

θ2=5 θ2=2

Theeffectof the leg lengthon themaximumvonMisesstress in theBismuth telluridematerialof theSATEGcanbeseen inFig.15a.Forall the thermoelectric leg lengthsconsidered, themaximumvonMisesstressdecreasesas theanglebetween the

thermoelectriclegsincreasesfrom to .ThisshowsthattheelectricalandmechanicalperformanceoftheSATEGhaveaninverserelationshipwhenleglengthand/orlegangleisbeingvaried.Therefore,anoptimumgeometrymustbeobtainedwhichwill

satisfyboththeelectricalrequirementandmechanicalreliabilityoftheSATEG.Inaddition,Fig.15ashowsthatatoptimummechanicalreliabilitylength( ),athermalstressdecreaseof5.67%canbeachievedjustbyincreasingtheanglebetweenthethermoelectric

legsfrom to .Fig.15bshowstheeffectoflegangleonthemaximumvonMisesstresspresentintheSkutteruditematerialoftheSATEG.Thetrendobservedinthiscase(Fig.15b)isoppositetothatinFig.15a.Thisimpliesthatwhileanincreaseintheangle

betweenthethermoelectriclegsfrom to leadstoadecreaseinthemaximumvonMisesstresspresentintheBismuthtelluridematerial(coldsegment)oftheSATEG,anoppositeeffectiscreatedintheSkutteruditematerial(hotsegment).Therefore,theleg

angleandleglengthofthesegmentedannularthermoelectricgeneratormustbecarefullychosentosatisfylowstressrequirementsinbothsegmentsofthedevice.

Fig.14VariationofleganglewithSATEG(a)efficiencyand(b)outputpowerwhen , and .θ=8 Th=623K RL=0.001

θ2=2 θ2=5

L=5

θ2=2 θ2=5

θ2=2 θ2=5

4.4SATEGvonMisesstressnephogramThevonMisesstressnephograminthecoldandhotsegmentofthesegmentedannularthermoelectricgeneratorcanbeseeninFigs.16and17respectively.ItcanbeseenclearlythatthemaximumvonMisesstressoccursatthehotsurfaceofthethermoelectric

legswhichisindirectcontactwiththesolder.ItcanalsobeseenthatthemaximumvonMisesstressoccurattheedgeofthethermoelectriclegsthus,thatregioncaneasilybreakoff.Thermalstressintensityisaveryimportantfactorthatinfluencesthelifecycleofa

thermoelectricgenerator.Sincethemechanicalmaterialproperties(e.g.Young’smodulus,Coefficientofthermalexpansion)ofeachofthecomponentsintheTEGaredifferent,thermalstresswillbegeneratedwheneveralargetemperaturegradientisapplied.Asseen

fromFigs.16and17,thepositionsthataremostlikelytocrackarethecontactareasbetweenthehotsurfaceofthethermoelectriclegsandthesolderstrips,andtheedgesofthelegs.ItshouldbenotedthatthestressvaluesshowninFigs.16and17areobtainedwhile

consideringtheelastoplasticcharacteristicsofthecopperandsoldermaterials.Ifthisisnotconsidered,themaximumvonMisesstressinthelegswillbehigher.

Fig.15VariationofleganglewithmaximumvonMisesstressin(a)Bismuthtellurideand(b)SkutteruditematerialsoftheSATEGwhen and .θ=8

Fig.16NephogramofthevonMisesstressinBismuthtelluridematerialoftheSATEGwhen , , ,(a) ,(b) ,(c) and(d) .L=2 Th=623K θ2=3 θ1=3 θ1=5 θ1=7 θ1=9

5ConclusionIn this study, the thermoelectric andmechanical performance of a segmented annular thermoelectric generator has been investigated using finite element analysis. The influence of segmented pin geometry on the performance of annular thermoelectric

generatorshasbeenstudiedindetailandacomparisonbetweenthesegmentedannularthermoelectricgeneratorandnon-segmentedannularthermoelectricgeneratorshasbeenmade.COMSOL5.3Multiphysicssoftwarewasusedtoperformthenumericalsimulations

andtemperaturedependentthermoelectricmaterialpropertieswereconsidered.Bismuthtelluride(Bi2Te3)materialwithamaximumoperatingtemperatureof498 KandCoSb3basedSkutteruditematerialwithamaximumoperatingtemperatureof798 Kwereusedasthecoldandhotsegmentmaterialsrespectively. Inaddition, theelastoplasticbehaviourofcopperandthewelding layer(solder)wereaccount for in thesimulationstoensureaccuratepredictionsof thethermalstressdeveloped in thethermoelectricgenerators.All the

geometriesof theSATEGandATEGanalysedcorresponding to thedifferent leg lengthand legangleconsideredweredrawnwithAutoCAD2018softwareand theywere individually imported intoCOMSOLfor thenumericalsimulations.Theeffectsofheatsource

temperature,thermoelectricleglengthandleganglewereinvestigatedandtheresultingnephogramfromthethermalstresssimulationoftheSATEGwasprovidedforvisualrepresentationofthemaximumvonMisesstresslocations.Someoftheimportantconclusions

fromthisresearchare:

1. TheadvantageoftheSATEGovertheBismuthtellurideATEGintermsofefficiencybecomesclearwhenthetemperaturedifferenceisgreaterthan100 K.

2. TheefficiencyoftheSATEGis21.7%and82.9%greaterthantheefficiencyoftheBismuthtellurideATEGandSkutteruditeATEGrespectivelyat200 Ktemperaturedifference.

3. ThemaximumvonMisesstressinthelegsoftheBismuthtelluridematerialintheSATEGis35.4%lowerthanthatoftheBismuthtellurideATEGat200 Ktemperaturedifference.

4. Efficiencyandoutputpowerenhancementof45.3%and79.1%respectivelywereobservedwhentheSATEGleglengthwasreducedfrom to .Therefore,shorterthermoelectriclegsprovidebetterelectricalperformance.

5. Increaseinthermoelectricleglengthleadstodecreaseinthermalstressandanincreaseinelectricalperformance.Therefore,increasingthermoelectricleglengthcanimprovethemechanicalreliabilitybutreducetheelectricalperformanceofthethermoelectricgenerator.

Fig.17NephogramofthevonMisesstressinSkutteruditematerialoftheSATEGwhen , , ,(a) ,(b) ,(c) and(d) .L=2 Th=623K θ2=3 θ1=3 θ1=5 θ1=7 θ1=9

L=5 L=2

6. TheoptimumgeometryformaximumelectricalperformanceoftheSATEGstudiediswhen , and .Thisgeometryprovidesthebestelectricalperformanceforthesystem.

7. TheMaximumvonMisesstressintheSATEGdecreasesastheanglebetweenthethermoelectriclegsincreasesfrom to forallleglengthsconsidered.

8. Thepositionsmostlikelytocrackarethecontactareasbetweenthehotsurfaceofthethermoelectriclegsandthesolderstrips,andtheedgesofthelegs.

ConflictofinterestNone.

AcknowledgementThisstudywassponsoredbytheProjectofEUMarieCurieInternationalincomingFellowshipsProgram(745614).TheauthorswouldalsoliketoexpressourappreciationforthefinancialsupportsfromEPSRC(EP/R004684/1)and InnovateUK

(TSB70507-481546)fortheNewtonFund–China-UKResearchandInnovationBridgesCompetition2015Project‘AHighEfficiency,LowCostandBuildingIntegrate-ableSolarPhotovoltaic/Thermal(PV/T)systemforSpaceHeating,HotWaterand

PowerSupply’andDongGuanInnovationResearchTeamProgram(No.2014607101008).

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Highlights

• Asegmentedannularthermoelectricgenerator(SATEG)isstudiednumerically.

• ThethermoelectricandmechanicalperformanceofSATEGisinvestigated.

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• ComparisonbetweenSATEGandannularthermoelectricgenerator(ATEG)ispresented.

• TheeffectofthermoelectricgeometryonSATEGandATEGperformanceisstudied.