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Nomenclature
r
radius,mm
angleofasinglethermoelectricleg,degree
halfoftheanglebetweentwolegs,degree
Highperformanceandthermalstressanalysisofasegmentedannularthermoelectricgenerator
SamsonShittua
GuiqiangLia,⁎
XudongZhaoa,⁎
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.
