Solar Cookstove Final Report

7/29/2019 Solar Cookstove Final Report

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1.BackgroundandContext

1.1Introduction

ThelushforestsinIndiacomprise8%oftheworldstotalbiodiversity1and

contributeroughly235.78billionrupeestothenationalGDP2

.Howeverpressurefromincreasingpopulationsbothhumanandlivestockaredestroyingthisincredibleresource.InIndia,anestimated800millionpeopleusebiomassforcooking3and55%oftheforestsnationalGDPcontributionisintheformoffirewood2.Theburningofwoodasfuelleadstomassiveincreasesindeforestationandgreenhousegasemissions.Conservationeffortstoprotecttheforestsbeganintheearly1900s4,butconservation-basedrestrictionsandbanningofwoodcollectioninprotectedareashasledtoillicitactivityinsteadofadecreaseinforestusage.ThishasbeenwelldocumentedfortheKumbalgarhWildlifeSanctuary(KWS)inRajasthan,IndiawhichisthehomeofthreatenedwildlifeincludingtheSlothBear,StarredTortoise,andSterculiaUrens.TheKWSalsoformsanimportantecological

barrierpreventingtheextensionoftheTharDesertintotheAravallihillranges.1,5,6

Thereare22villageslocatedinsidetheKWSand138incloseproximityrequiringincreasingamountsofwoodforfuelandclearedlandforfarmingandlivestock.Atypicalhouseholdintheareaconsumes6-8kgfirewoodperdayand~30%ofhouseholdssell~10kgwoodperday.1Theinhabitantsofthesevillagesarewellawareoftheeffectsofdeforestationevidentinthescarcityofwoodresources,cropraidingbyanimalsintheKWSthatarelosingtheirnaturalhabitat,andrecentclimatechangesincludingadecreaseinrainfallandanincreaseinthefrequencyofdrought.1Womennowspendupto7hoursperdaycollectingfirewoodduetoscarcewoodresources7andevenriskrapeandextortionbyventuringintoprotectedlandswhenwoodisnotavailableelsewhere.8

1.2ClimateHealersandtheSolarCookstoveSolution

1PersonalCommunicationwiththeFoundationforEcologicalSecurity(FES).2PersonallycommunicatedbyFESrepresentativefromareportfromtheInsituteofEconomicGrowth(IEG),NewDelhi,India,2002.3https://www.engineeringforchange.org/workspace/view/22/1#tabs=/workspace/files/22/14http://rajforest.nic.in/general_intro.htm

5PRobbins,KMcSweney,AChhangani,JLRice.Conservationasitis:IllicitresourceuseinawildlifereserveinIndia.HumanEcology37(5)2009.6PFRobbins,AKChhanganiJRice,ETrigosa,SMMohnot.EnforcementauthorityandvegetationchangeatKumbhalgarhWildlifeSanctuary,Rajasthan,India.EnvironmentalManagement402007.7PosterpresentedbystudentsoftheUniversityofIowatitledRuralIndiaSolarCookerImplementationbyBBehrendt,WDavies,EGuio,JMahlik,AMoffitt,BOLoughlin,EOsgood,JRichards,&MToth.8PersonalcommunicationwithSaileshRaoofClimateHealers.


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AnalternativetocookingwithfirewoodwouldgreatlydecreasethepressuresontheKWSandthegreaterforestsofIndiawhilesimultaneouslydecreasinggreenhousegasemissionsandsavingtimeforthewomenwhocurrentlyspendhourscollectingwood.Furthermoreanalternativetoburningbiomassindoorswoulddecreaseharmfulsmokeinhalationandresultingrespiratorydiseases.NGO

(Non-GovernmentOrganization)ClimateHealersbeganpartneringwithlocalenvironmentalNGOFES(FoundationforEcologicalSecurity)in2008todevelopsuchanalternative.FEShasworkedintheregionsince2002,gainingadeepknowledgeofthecomplexissuessurroundingdeforestationoftheKWS.FESalsopartnerswiththeIndianRuralEmploymentBoardtofulfilltheIndiangovernmentsNationalRuralEmploymentGuaranteeof100daysofemploymentat100rupeesperdayforonememberofeachhousehold.FESproposesandoverseesprojectsfortheIndiangovernment,butisrunningoutofworktobedone.9

Toeliminatetheuseoffirewoodforcooking,ClimateHealersproposedasolarcookstovetoreplacethe3-stonefirecurrentlyusedtoburnbiomassforcooking.ThesolarcookstovewouldtakeadvantageoftheimpressivesolarirradiationoftheregionandwouldideallybemanufacturedinthevillagestoprovideemploymentprojectsthroughFESandtheIndiangovernment.ClimateHealerschosetofocusfirstonthevillageofKarechasarepresentativeofthedryRajasthanregionandHadagoriasarepresentativeoftheOrissaregionknownformonsoons.TheworkdescribedinthisreportfocusesspecificallyonKarechwiththehopeofexpandingtoallforest-proximalregionsofIndiaoncetheconcepthasbeenproven.

Karechisavillageof240householdswherenearlyeveryhouseholdmusttakeadvantageofthegovernmentsNationalRuralEmploymentGuarantee.InitialcontactandcommunicationwiththevillageofKarechinvolvedthedistributionof2solarlightsperhousehold,whichledtoimpressivepopularityandrespectfor

ClimateHealersasthesolarlightsallowedthevillagerstoworkandstudyatnight,avoidsnakeswhenventuringintotheforestintheearlymorning,andcreateafestiveenvironmentforweddingsandfestivals.10

SixprototypesofthefirstNamastesolarcookstovedevelopedbyClimateHealerswereintroducedinthevillagesofKarechandHadagoriinJanuary2010.TheresponsewasoverwhelminglynegativeduemostlytothefactthattheNamastestoverequiresuseduringthedaywhentheinhabitantsofthevillagearebusywithworkandotherchores.Thiswasnotedtobeinstarkoppositiontothesolarlights,whichcouldchargeunattendedalldayandbeusedatnight.Otherfeedbackfrommembersofthevillageswhotestedthestoveincluded:

9PersonalcommunicationwithSaileshRaoofClimateHealers.10ClimateHealersProjectReportfromAugust2010availableontheEngineeringforChangewebsite:https://www.engineeringforchange.org/workspace/view/22/1#tabs=/workspace/files/22/1


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TheNamastestovecanonlybeusedoutdoorsandduringtheday;whereastraditionalcookingisdoneindoorsbeforesunriseandaftersunset.

TheNamastestoveisunstablegiventhehillyterrainandwindyconditionsofKarech.

TheNamastestoveistootallforthetraditionalapproachofcookingwhileseated.

TheNamastestoveisinconvenientbecauseitrequiresconstantadjustingandattendance.

TheheightandattentionrequiredmakeitdifficulttoholdachildwhileusingtheNamastestove.

ClimateHealersthereforeresolvedtodesignastoredenergysolarcookstovetoenablecookingattypicalmealtimesinKarech:aftersunsetandbeforesunrise.11

1.3Thechallengeofthestoredenergysolarcookstove

Theidealstoredenergysolarcookstovemustmeetthefollowingdesignconstraints:

Solarenergystorage:Numeroussolarcookstovesandsolarovenswithoutstorageexistasmodelsforsolarcollectionandarediscussedinsection2.Solarstorageoptionsincludestorageintheformofelectricity,sensiblestoragematerials(sand,vegetableoil,engineoil),latentheatstoragematerials(acetamide,stearicacid,acetanilide,erythritol),orchemicalstorage.Eachoftheseoptionsisexploredindetailinsection2,butmanyarestillindevelopmentforsmall-scaleapplications.12ThisaddressestheneedsoftheprimarystakeholdersthewomenofKarech.

Useoflocalmaterials:LocalmaterialsinthevillageofKarechincludesand,bamboo,brick,andofcoursethewoodthatweaimtoprotect.Outsideresourcesmustbebroughtinonroughandcurvyroads.ThereisonegeneralstoreinthevillageofKarechsuppliedviatheseroads.13ThisaddressestheneedofstakeholderClimateHealerstokeepcostslowanddecreaseimpactontheenvironment.

Manufacturinginthevillage:ManufacturinginthevillagewouldprovideprojectsfortheNationalRuralEmploymentGuaranteeandthereforefundingthroughtheIndiangovernment.Inaddition,usersofthestove

11ClimateHealersProjectReportfromAugust2010availableontheEngineeringforChangewebsite:https://www.engineeringforchange.org/workspace/view/22/1#tabs=/workspace/files/22/112RMMuthusivagami,RVelragj,RSethumadhavan.SolarcookerswithandwithoutthermalstorageAreview.RenewableandSustainableEnergyReviews (14)2010.13PersonalcommunicationwithSaileshRaoofClimateHealers.


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wouldhaveaninvestedinteresthavingconstructedthestovethemselvesandbemorelikelytobeabletofixabrokenstove.ThisaddressestheneedofstakeholdersFESandtheIndiangovernmentsuchthattheycouldusecookstovemanufacturingasaprojectfortheNationalRuralEmploymentGuarantee.ThiswouldalsoaidtheinhabitantsofKarechas

theywouldbemorefamiliarwiththecookstovesincreasingtheirabilitytofixanyproblemsthatarise.

Cookingoftraditionalmeals:MealsinKarecharepreparedbythewomenandinvolverotiadrydoughofflourandwaterthatpuffsuponfryingathighheatforseveralminutes,dahllentilsthatareaddedtoboilingwaterandthensimmeredforroughly20minutes,andteawhichalsorequiresboilingwater.Amealconsistsofroughly2rotiforeachmemberafamilyof5-6plusdahlandtea.Whenaskediftheywoulduseasolarstove,inhabitantsofKarechclaimedthatifClimateHealerscouldshowthehowtocookroti,theywouldusethesolarcookstove.Wethereforebasedourdesignconstraintsoncookingrotiasdescribedinsection4.Thisagainaddressestheneedoftheprimarystakeholders:thepeopleofKarech.

Small-scaleenergystorageforthermalapplicationssuchascookingisadifficultandunsolvedproblem.Theadditionoflocalmanufacturingandresourcesaddsanextralayerofcomplexity.


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2.PreliminaryDesign:BrainstormingandResearch

Wepurposefullyincludedallbrainstormingideasinthisreporteventhewildandcrazyideasasthesemayproveinspirationalinthefuture.Inthespiritofbrainstorming,wedidnotwanttonarrow,discourage,orjudge;howeverinthis

sectionwedooffertheprosandconsofeachpotentialsolution.

2.1Thermalenergybasedideas

2.1.1Collection

Inthissectionapproachestocollecttheradiatedsunlightandtransportittothestorageunitwillbediscussed.Allapproachesincludeacylindricalparabolicmirrorasfirstreflector,asshowninFigure2.1.ThiscollectiondesignwasusedforbrainstormingasitisthecurrentcollectiondesignproposedbyClimateHealers.

Directcollection:Thisisthesimplestoption.Reflectedlightisdirectlystoredina

suitablestoragemediuminsideanevacuatedglasstubeplacedinthefocuspointoftheparabolicmirror.(SetupsimilartoFig.2.1,buttheevacuatedtubewouldcontainthestoragemediumwithoutanexternalstoragesystem.)

Opticalcollection:Opticalcollectionrequiresatleastoneadditionalmirrortotransportthereflectedlighttothestorageunit.

Heatpipe:Thereflectedlightwillbeconcentratedonanevacuatedglasstubecontainingaheatpipe,whichtransportstheenergytoastorageunit(fig.2.1).

Fig.2.1:Heatpipecollectionsystem.

Theheatpipesystemhasthefollowingadvantages:

Itiswellknownforrooftopsolarthermalwaterheatingsystems, theevacuatedheatpipesareavailableinChina, theseparationofcollectionandstorage,and


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abiggerstoragevolumeispossible.Anddisadvantages:

theseparationofcollectionandstoragemakesthesystembigger.

2.1.2Storage

Storageofthermalenergyincludestwooptions:sensibleheatstorageandlatentheatstorage.Theseoptionsaredescribedinfurtherdetailinsection4.1.Desiredcharacteristicsofthestoragematerialare:

Highspecificheatcapacity, longtermstabilityunderthermalcycling, compatibilitywithitscontainment,and lowcost.

Sensibleheatstorage:Sensibleheatstorage(SHS)occursbyaddingenergyinformofheattoastoragemediumandincreasingitstemperaturewithoutchangingitsphase(fig.2.2).

Fig.2.2:Sensibleheatstorage.

Possiblestoragemediaareliquidslikewater,saltywater,moltensalts,andoilsandsolidslikerocks,sand,buildingfabric,andmetals.

Waterwouldbemostdesired,sinceithasthehighestheatcapacityofallstoragemedia,butithasalowtemperatureofevaporationsothatSHSaboveatemperatureof100degreeCelsiuswouldrequireputtingthesystemunderpressuretopreventvaporization.

Oilsandmoltensaltshaveabout25-40%oftheheatcapacityofwaterbuthavealowervaporpressure,sothattheycanoperateathighertemperaturesof300degreeCelsiusandabove.


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Fig.2.3:Latentheatstorage.

Advantagesoflatentheatstorageinclude

lowweightandvolumeofthestorageunit, energystorageanddeliveryatconstanttemperature,and thatthewholestoragevolumecanbereachedeasilyduetoahigh

thermalconductivity.

DisadvantagesofLHSsare: DegradationofthePCMovertime, safetyissuesduetoPCMandpotentiallyhigherpressure complexdesign,and highcost.

Ataer15andHasnain14providemoreinformationaboutsensibleandlatentheat

storagesystems.

2.1.3Delivery

Heatdeliverysystemshavethefunctionoftransportingtheheatfromthestorageunittotheburneratacertaintemperatureandpower.Inordertovarytemperatureandpoweradevicetocontrolthoseshouldbeincluded.

Heatpipe/thermosyphon:

HeatpipesandthermosyphonsuseliquidtogasPCMsasheattransfermedium.Twodifferentpossiblesystemsarepicturedinfigure2.4.

Thebottompartoftheheatpipeisinsidethehotstorageunitsothattheliquidwillevaporate,flowuptotheheatsink,condense,andflowdownagain.Thedifferencebetweenaheatpipeandathermosyphonisthatheatpipescontainawickfixedtotheinsidesurfacesothatinadditiontogravity,capillaryforcesreturnthecondensatetotheevaporator.

15Ataer,O.E.:Storageofthermalenergy.inEnergyStorageSystems,EditedbyY.A.Gogus,inEncyclopediaofLifeSupportSystems(EOLSS),EolssPublishers,Oxford,UK,2006.


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Fig.2.4.Heatpipes/thermosyphons.

Heatpipes/thermosyphonshavetheadvantagesof ahighthermalconductivity, heattransferbetweenplacesofdifferenttemperatureispossible, theheatfluxiseasilytunablewithavalve,and itispossibletotransporttheenergyfromoutdoors(collection)toindoors(traditionalcookinglocation)withatubethroughthewall.

Anddisadvantagesof; youhavetofindasuitablePCMforthetemperaturerange, therearesafetyissueswhenthesystemisunderpressure, thePCMisdegradingovertime, thecostishigh, thedesignverycomplex, thesystemnotveryrobustsothatlongtimetestingisnecessary,and maintenancemightbedifficultbecauseofthecomplexityofthesystemsothatitmightbehardtofindthereasonoffailure.

MoreinformationaboutheatpipesandthermosyphonsinHeatPipesbyReayand

Kew16.

16Reay,D.A.andP.A.Kew:HeatPipes-Theory,DesignandApplications.Butterworth-Heinemann,Oxford,5thedition,2006.


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Conductiveheattransport:

Heatcanalsobetransportedbyconductionthroughmetalonly.Oneormoremetalrodsconnectthestorageunitwiththehotplate.

Advantagesofthisdesignare: thesimplicityindesign, thelowcost, thelonglifetime,and thereasonoffailureisobvioussothatmaintenanceiseasy.

Issueswithaconductiveheattransportsystemmightbe: findingawaytocontroltemperatureandpower, thecompatibilitywithothermaterials(rustmightbeanissue),and thelowerconductanceofmetalcomparedwithaheatpipesystem.

Advancedheatexchanger:

Inanadvancedheatpipesystematwofluidheatexchangerisimprovedwithsmallheatpipesconnectingthetwochannels(fig.2.5).

Fig.2.5:Advancedheatexchanger.

Advantagesare: Goodheattransfer, separationofstorageunitandburner,and transportofenergyintothehouseispossible.

Disadvantagesinclude: Theintegrationofatwofluidheatexchangerintothestorageunit, itmightoccupyabiggerspace, andthehighercosts.


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Modularcooking:

Theideaistostoreenergyinsmallseparatemodulesduringthedayandbringthemintothehousetocookonthemduringthenight.

Advantages: aneasyconcept,and youcookinsidethehousewithoutputtingaholeinthewall,

Disadvantages: theachievablepowermightnotbehighenough, lossestotheenvironmentmightbehigher,and peoplehavetobearoundtoexchangethemoduleswhilecharging.

2.1.4Completesolutions

Heatpumpsystem:

Aheatpumpisasystemwhereafluidisheatedattheheatsource(solarcollection),ispumpedtotheheatsink(burner)whereitreleasesitsheatandthengetstransportedbacktothesource(fig.2.6).Thetubingoutsidethehouseislaidintothesurfaceoftheground.

Fig.2.6:Heatpumpsystem.

Advantagesofthistechnologyare: Itsprovenforheatingandcooling, cookinginsidethehouseispossible,and


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itssimplesinceitonlyusespipesandapump.Ontheotherhandpossibleissuesmightbe

thatithasnotbeenusedforcookingyet, thatthepumpandthetubingisexpensive,

thattheenergystoredinthepipesisnotenough,and thelossesmightbetoohigh.

Pizzaoven:

ThepizzaovenideaistouseThiscouldbeaccomplishedbyThiscouldbeintegratedwiththemodularcookingideadescribedearlierorusedtocookrotithroughouttheday.

Advantages: Thistechnologyhasbeenusedextensively Anddoesnotrequireattendanceduringtheday.

Disadvantages:

Solarovensarenotcompatiblewith

Cookingslowlyovertheday:

Therearealreadyalotofideasforcookingslowlyoverthedayoutthere.ForexampletheHotPot17,aspecialpanelcooker,whichhasadarkpotsuspendedinsideaclearpotorboxcookers.Alternatively,apizzaovendesignwouldrequireaninsulatedcubeofsandwithaslitinsidetobaketheroti.Anotheroptionincludesan

insulatedbulkofsandinthegroundwithawindowontopwherethesolarradiationcomesinsideandheatsthesand.

Advantagesofslowlycookingoverthedayincludes: Itischeap, simple,and alreadyproven

Disadvantagesare: Somebodyhastoobservethefoodtoavoidburning traditionalcookingofroti,whichrequireshighheatforseveralminutesonly.

Eitherway,slowcookingrequiresachangeintraditionalhabits.

17http://www.she-inc.org/cooking.php


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Hybridstoragesystem:

Inahybridsystemtwoormoresolarcookingsystemsarecombined.InthiscaseweimagineawaterstoragetankcombinedwithinsulatedcavityandaHotPot.The

HotPotwillcookDahlslowlyovertheday,theinsulatedcavitywillbaketheRotiandthewatertankpreheatswaterforcookingteaandDahlandcanalsobeusedforotherpurposessuchasbathing.

Fig.2.7:Hybridsystem.

Advantagesofahybridsystemare: Hotwaterasextraservice(luxuryitem)andpreheatingforcooking, waterstoragesystemeasyandwellknown, HotPotcommerciallyavailableoreasyandcheaptobuild, sandstorageeasy(holeinground,insulator,absorberandglassplate),

lessstorageforeachsystem,and highreliability.

Disadvantagesmightbe thatitismorecomplicatedtousethreedifferentsystems,and thatachangeinhabitsisnecessarytocookRotiintheinsulatedcavity


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2.2Electricalenergybasedideas

Analternativetothermalsolarenergystorage,transport,andcookingistogenerateelectricity,storetheelectricityinbatteriesanduseanelectricalstoveforcooking.

2.2.1Generation

Solarphotovoltaics(PV):

UsingsolarPVpanelswouldbeadirectmethodtogenerateelectricityfromsolarradiation.

Theadvantagesofthisgenerationmethodare thatthelossesaresmallthroughdirectgenerationofsolartoelectricalenergy

theenergycanbedirectlystoredintoachemicalstorageunit, itisaproventechnology,and itisquiet.

Disadvantagesare: PVmodulesarequiteexpensive lossesuponconversionbacktothermalfordeliveryarepotentiallyhigh,and

anenginehastoconnectthePVmoduleswiththemechanicalorgravitationalstoragemechanism.

Thermoelectricdevice:

AthermoelectricdeviceusesthetemperaturedifferencebetweenconcentratedsolarradiationandtheenvironmenttogenerateelectricitybyaphenomenoncalledtheSeebeckeffect.

Advantagesare thedirecttransformationtoelectricalenergywithoutthermalenergy, thedirectconnectiontoachemicalstorageunit,and thatitisquiet.

Disadvantagesinclude highcost, thelowvoltage,and thatitcannotbedirectlyconnectedtoamechanicalorgravitationalstoragemechanism.


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Fig.2.9:PVandhydrogencombinedsystem.

2.3Mechanicalenergybasedideas

2.3.1Generation

Stirlingengine:

AStirlingengineusesairorothergasasworkingfluid,whichundergoescycliccompressionandexpansionbypushingthegasalternatingfromtheheatsourcetotheheatsink.Thetranslatorymovementofthepistongetstransformedintoarotatingmovementofthecrankshaftwhichcanbeconnectedtotheshaftofageneratorordirectlytoapump,flywheel,etc.,whichwillstoretheenergy.

AdvantagesoftheStirlingengineare thatitcanbedirectlyconnectedtothemechanicalorgravitationalstoragemechanism,

itisaproventechnology,and itiscommercialavailable.

IssueswithaStirlingenginemightbe thatitisexpensive, noisy,and itcontainsmovingpartssothatmaintenanceismorefrequentlynecessary


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3.Collaboration:IntroductiontotheHawkeyeCookerand

designtrade-offs

3.1HawkeyeCooker:descriptionanddesigntrade-offs

ClimateHealersfounderSaileshRaotoldusinourfirstmeetingthataclassofabout30undergraduatestudentsattheUniversityofIowa18isworkingondesigningthestored solarcookstoveaswell and that theyare concentratingoncollectionandstorage.UntilourfirstSkypemeetingwithIowa,whichtookplaceinthebeginningofMarch,wehadnotplannedtocollaborateonaprototype.Iowapresentedustheirapproach,showninFigure3.1Acylindricalparabolicmirrorconcentratesthesolarradiationona second V-shapedmirror in the focalpointwhich reflects the lightdownthroughinsulatedglasstoanabsorberplateinthestorageunit.Thestorageunit consists of sand and aluminum cans arranged in an array to maximizeconductionthroughouttheunit.Thesandunitiskepttogetherbycementboards,which are surrounded by rice husks that insulate the storage unit from the

environment.Thecookingsurfaceisthermallyconnectedwiththestorageunitbyaheatdeliverysystem.TheHawkeyesolarcookerincludestwoseparatestorageunitsforeveningandmorningcooking.Eachunitismountedoncastersandrailssothatitcanberolledintothehouseforcooking19.

Fig.3.1:HawkeyeCooker20.

18http://www.uiowa.edu/19Iowaclasspresentationslidesandpersonalcommunication20Iowaclasspresentationslides


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The Iowa teamaimed touse localmaterials resulting ina designusing sandandaluminiumcansforenergystorage.Thisisasensibleheatstoragesystem,whichisbig insize(storagesizealone:6 feetx 3 feetand~500lbs)andcannot storeanddeliverheatataconstanttemperature.Thecircumstancemakesthedesignofaheatdeliverysystemmorecomplexandthelosseshigher.19

OurfirstmeetingwithIowaoccurredafteralreadybrainstormingdesignideasandresearchingstorageoptionsandmaterialoptions.Severalofourideasoverlappedwiththeirssuchastheuseoflocalmaterials,sand,andaluminumasheatstorageandtheneedtobreakdownthedesignintosolarcollection,heatstorage,andheatdelivery.TheIowateamhadplansanddesignsinprogressforallelementsofthestored energy solarcookstoveexcept the heatdelivery.Wetherefore tookonthetaskofdesigningaheatdeliverysystemthatcouldintegratewiththeIowateamsdevelopingstoragedesignforsuccessfulcookingofroti.

3.2Designconstraintsforheatdelivery

Iowasdesignapproachandfirstsimulationsetsomedesignconstraintsforus.Thefactthattheyuseasensibleheatstoragesystemwithvariablestoragetemperaturerequiresatemperaturecontrolunitinourheatdeliverysystem.Anotherconstraintisthetemperatureavailableinthestoragetankduringcooking.Iowastemperaturesimulation predicts storage temperatures of 90 to 200 degrees Celsius for themorning cooking and 250 to400 degree Celsius temperature ranges for eveningcookingtimes.19

3.3RedefinitionofBerkeleyteamgoals

Our overall team goals remain as originally defined: to preserve the forests ofRajasthan and improve the standard of living and quality of life in Karech. Toaccomplishthisweoriginallydefinedbothoptimalandminimalgoalsasfollows:

Optimal:Designastoredenergysolarcookstovethatcansuccessfullycookrotiintheeveningandthenextmorning.

o Minimal:Designastoredenergysolarcookstovethatcansuccessfullycookrotiintheevening.

Optimal:Usealllocalmaterials.o Minimal:Uselocalmaterialsasmuchaspossible.

Optimal:Designsuchthatmaterialcostsarelessthan$50.o Minimal:Design such that material costs are less than $100. (Both

recommendationsfromClimateHealers.)

Oncewedecided to collaboratewith Iowa,our goals changed to reflect this newfocus:


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4.CalculationsandExperimentsLeadingtoDesign

Constraints

Inthefirsthalfofthesemester,ourgroupworkedtobuildpartnerships,evaluatepotentialdesigns,andconductexperimentsaimedatdevelopingdesignconstraints.WehavemetseveraltimeswithSaileshRaooftheClimateHealersparentproject,maintainingcontactthroughemailandmeetingsinperson.WehavemetweekywiththeIowaundergraduateclassworkingonthisprojectinparallel.WehaveattendedtheirdesignpresentationsviaSkype,offeringfeedback,learningabouttheiraspectsoftheproject,andworkingtowardeventualintegration.Inaddition,wehavemetwithlocalcontactstosuccessfullysecurefabricationfacilities,andwehaveinitiatedcontactwithheattransferexpertstohelpaddresstechnicalquestions.

4.1StorageMediaConsiderationsPriortomeetingwithIowaandlearningabouttheirdesign,weevaluatedseveralpotentialoptionsforsolarcollectionandthermalstorage,aswellasheatdelivery.Aprincipleconsiderationforthermalstoragewaswhetherenergywouldbestoredinheatcapacity(temperaturechange)orlatentheat(phasechange).Storingenergyinaphasechangeofferstheadvantagethatthetemperatureremainsconstant;allenergyisthereforeequallycapableofdoingwork.Incontrast,storingenergyintemperaturechangerequiresahighinitialtemperature.Asstoredenergyisusedorlost,thetemperatureofthestoragemediafalls.Sincethepoweravailableisdependentonthetemperaturedifference,decreasingtemperaturesmeanadecreasingmaximumavailablepower.Whilethephasechangesystemoffersadvantages,itrequiresamaterialwithaphasetransitionwithinaspecifictemperaturerange,inadditiontorequirementsbasedonenergycapacity,safety,affordability,andpreferenceforlocalmaterials.

Forthethermalstoragematerialsearch,weconsideredmetals,waxes,moltensalts,glasses,andsand(seeAppendixA).Ofelementalmetals,onlyBi,Cd,In,Li,Pb,Po,Sn,andThhadmeltingpointsinafeasiblerange(150400C).Unfortunately,Cd,Pb,andThhavetoxicityconcerns;Poisradioactive;Inisprohibitivelyexpensive;andLiburnsincontactwithwater.BiandSnaresubstantiallycheaper,butnotsufficientlysogiventherequiredquantities.Thoughlowmeltingtemperaturealloysarealsoavailable,mostrelyonthesamemetalsandsufferfromrelated

problems.

Fortypicalwaxes,themeltingpointsaretoolow,thoughhighheatcapacitysuggeststheymightbeusableintemperaturechangeconfigurations.Unfortunately,theliquidwaxeswillflashattemperaturesabove200-250C.Specialtywaxescanreachhighertemperatures,butaresubstantiallymoreexpensive.Saltsgenerallymeltmuchhigherthanourdesiredtemperatures,andslurrieswilllosetheirwaterabove100C.Finally,glassestransitionatarangeoftemperaturesbutduetotheir


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uniquephasechange,lacklatentheatoffusion.Othermaterialsthatweresuggestedbutnotexploredincludenitrates,hydroxides,andrubber.

Withoutagoodphasechangematerial,fewfeasiblematerialsoutperformsandforstoringenergyintemperaturechange.Giventheadvantagesincostandlocalavailability,thislookedthemostpromising.Foragivenenergystorage

requirement,thevolumeofsandcanbefound:

!!"#$ =!!"#$%!"&

!!"#$!!!

Inourcase(Erequired=4kWhrs,T=150K,targetsprovidedbyClimateHealers),thisgaveVsand0.06m3,farmorethancouldfitatthefocusoftheparabolicmirrorasinitiallyenvisionedbyClimateHealers.

WhenwemetwiththeIowateam,wediscoveredthattheyhadcometothesameconclusions,withregardtobothusingsandandseparatingthestoragefromthecollector.Withinitialinformationontheirdesignandagreaterunderstandingof

ourexpectedrole,webeganexperimentsaimedatdevelopingdesignspecificationsfortheheattransfermechanism.

4.2Experiment1:Canhotsandalonecookroti?

PreparingrotihadprovedthemostdemandingoftheKarechcooktasks,requiringthehighesttemperaturesandthemostpower.Ourfirstexperimentinvolveddeterminingifthethermalconductivitythroughablockofsandcouldprovideenoughpowertocookarotiplacedonthetop.Forthis,wecalculatedtheamountofsandrequiredbasedoninitialestimatesforenergyandtemperature,heatedthesandinakitchenoven,andmonitoredtherisewiththermometry.Attemperature,thesandwasremovedandpouredintoashallowglasstray.Aluminumfoilwasplacedontop,followedbyrotidough.Theresultwasvirtuallynochangeinthedoughsimpleconductionwasinsufficient.

Inadditiontothelimitedconductivityofdrysand,severalotherfactorsmayhavecontributedtothefailure.First,onethermometermaxedoutbeforereachingourtargettemperature,wecannotbesuretheinteriorsandreachedfulltemperature.Second,heatmayhavebeenlostwhenthesandwastransferredfromthepottothetray.Finally,theshallowtraymayhavecreatedaworst-casescenariowithregardtothermalconduction.Whiletheseeffectsmayhaveimpactedperformance,itseemsunlikelytheycouldaccountforthefullfailure.Thatis,evenifthesefactors

weremitigated,weexpectthepowerdeliveredwouldstillproveinsufficient.

4.3Experiment2:Powerandtemperaturerequiredforroti

Thesecondexperimentaimedtoquantifythetemperatureandpowerrequirementsformakingaroti.Forthistest,wecookedthirteenrotisunderdifferentconditionsonagasstove,varyinginputpowerandinitialpantemperature.Pantemperature


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requiredheatwhenthestoragemediawasatlowtemperaturesandavoidwastewhenthemediawashot.

4.4ThermalConductionCalculations

Wefirstconsideredheatdeliverythroughthermalconduction.Conductiveheatflowisdescribedby

!!= !"

!"

!"

wherePispower,kisthermalconductivity[power/length/degree],Aiscross-sectionalarea,xisflowdirection,andTistemperature.Wefoundthatmeetingourspecificationswitha30CtemperaturedropandphysicaldimensionsgivenbytheIowateamrequiredverylargecross-sections:6.7inchdiameterinCuor8.4inchdiameterinAl.Asidefromthetechnicaldifficultiesofdesigningamechanismtograduallybringthatmuchsurfaceareaintothermalcontact,therequiredmetal

prices(est.$125forAl,$900forCu)putthissolutionoutsideofClimateHealersper-stovebudget.Aworksheetforthisanalysiscanbefoundinourteambinder:ConductorbasedDeliveryAnalysisv3.xlsx;ConductorEstimates.


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5.HeatSiphonDesignandFabrication

Wenextconsideredenergydeliverythroughaheatsiphon.Inaheatsiphon,liquidatalowerhotreservoirisevaporatesandrisesashotgas.Thisgascondensesatthecoldertopandflowsdownviagravity.Whilethereisextensiveliteratureonheat

pipeandheatsiphondesign,verylittlefocusesondesigninginourtemperatureandpowerregimes.Wethereforeapproachedmanyofthedesignconsiderationsfromfirstprinciples.Thephase-changefluidswereevaluatedbasedonvaporpressureandcriticalpoint.Energytransfercapabilitieswereevaluatedforconductionthroughthepipewall(1),atthephasechange(2),throughfluidflow(3),andthroughradialconductionattheburner(4).Additionalconsiderationsincludedthermalexpansionatbimetaljointsandoptimizingthefilllevel.

5.1PhaseChangeFluidConsiderations

Becausethefluidisheatedwhilecaptiveinthesealedtube,pressureposesaserioussafetyconcern.VaporpressurecanbedeterminedbyintegratingtheClausius-Clapeyron(CC)relation:

!"

!"=

!!

!!

wherepispressure,Tistemperature,Leisthelatentheatofevaporation[energy/mass]attheoperatingtemperature,andVisthechangeinvolumebetweenthestates.Forexample,at350C,waterhasavaporpressureof~16MPa(158atm).Ethyleneglycol,amajorconstituentinantifreeze,provedtohavethelowestpressuresofreadilyavailableandaffordablefluidsexamined.Bycomparison,ithasavaporpressureofonly1.6MPa(16atm)at350C.Thoughwehopetooperatethesiphonbetween170and230C,thestoragesystemisdesignedtopeakat350C.Further,ifthestoveisnotused,excessheatcanbuildupinthemedia.TheIowamodelingteamprovided550Casaconservativeworst-casetemperatureforthemedia.

PressuresestimationsviaCCarevalidonlywhilebothphasesexistandwhilethetemperatureandpressureremainbelowthefluidscriticalpoint.Abovethispoint,theboundarybetweenphasesislostandthefluidbeginstobehavemorelikeagas.

Figure5.1Diagramshowingenergyflowinaheatsiphon.


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AppendixC?.WorksheetsusingthoseequationsforlinearandhyperbolicprofilescanbefoundinHeatSiphonCalculationsv4.xlsx;PlateConduction.

5.3OtherConsiderations.

GiventhatanAlburnerwouldbematedtoastainlesssteeltubeandfittings,weconsidereddifferentialthermalexpansion.Usinglinearapproximationsandaconservativeuppertemperatureof350C,wefoundradialchanges~50mandsocketdepthchanges~125m.Basedonthesevalues,wechoseataperedpipethread(NPT)andteflontapefortheconnection.Aworksheetforthesecalculationscanbefoundinourteambinder:HeatSiphonCalculationsv4.xlsx;ThermalExpansion.

Finally,wemustconsidertheoptimalfillvolume.Iftoolittleethyleneglycolisincluded,alltheliquidwillvaporizeasthesiphonisheated.Onceallliquidisgone,theevaporation-condensationheattransferwillbecomeineffective.Iftoomuch

fluidisadded,thevolumefractionofliquidwillincrease(liquiddensitiesfallastemperaturesrise)untilittakesupmostofthevolume.Again,thiswillleadtoinefficientheattransfer.Additionally,behaviorabovethecriticalpointapproachesthatofgasses,sopressureatveryhightemperaturesisdependentonthetotalamountofethyleneglycolincluded.Thisparameterhasnotyetbeenaddressedandshouldbeevaluatedbeforetesting,especiallyathightemperatures.

5.4Fabrication

Giventhehighpressuresinvolved(estimated16.8MPaat550Cforethyleneglycol),weacquiredmostpartsfromvendorswithpublisheddataonworkingpressures.Thepipe,end-capsandNPTadapterwerepurchasedfromSwagelok.Ofthoseparts,thepipewasmostvulnerabletofailurethroughinternalpressure,withaworkingpressureratingof21.5MPa.Theburner,however,requiredcustomfabrication,andwascompletedintheUCBerkeleyEtcheverryshop.ShopexpertsMickandGordonbothgavecrucialadviceonhowtomachineforsuchhighpressureapplications.ImagesofthecustompieceandofthecompletedheatsiphonareavailableinAppendixD.


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6.AnAlternativeFluidDesign6.1IntroductionAs noted in our revised team goals, we think that it will be useful to present some

further design concepts which reflect the scope of the stored solar cook stoveproblem.

The figure below encapsulates the input/output relationship for our stored thermal

energy problem. The Sun and roti dough (timedelayed) are inputs to the system.

arm roti is the output, with required heat transfer characteristics specified by our

arlier experiments.

W

e

Figure 6.1. Input/Output Relationship of Stored Thermal Stove

The design discussed in this section is conceptual, and as such we do not providedetailed physical models or specifications. Rather, it is intended as a possible

direction for further development.

6.2AMoreFluidApproachHere we consider a design in which three fluids perform the roles of thermal

collection, storage, and delivery. They are denoted as FC, FS, and FD, respectively

nd have temperatures of vaporization of TC, TS, and TD.a

Before presenting the proposed concept, we discuss heatexchangers, importantsubcomponents of this design. Heat exchangers are modular components designed

to transfer heat from one liquid to another. Kakac and Liu21 note that the fluids can

be allowed to mixed or physically separated, as will be the case with those that we

21 Sadik Kaka and Hongtan Liu (2002). Heat Exchangers: Selection, Rating and Thermal

Design (2nd ed.). CRC Press.


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consider here. Heat exchangers can transfer thermal energy between fluids of the

same phase or used to evaporate or condense fluids, also. As far as building

prototypes is concerned, an advantage of using heat exchangers is that they are

commonly used in industrial applications such as car radiators and can therefore be

purchased offtheshelf.

The below figure is a diagram of a shellandtube heat exchanger, in which a tubeside fluid is to be heated or cooled. The shellside fluid passes over the tubes,

absorbing or transferring respectively its energy to the tube side fluid.22

Figure 6.2. Shell and Tube Heat Exchanger, image taken from wikimedia 23In short, a heat exchanger is a device with through which two fluids pass (with two

nputs and two outputs). One fluid is cooled, transferring its heat to the other fluid.i

6.3ADesignConceptThe figure below presents a systemlevel overview of the allfluid concept.

22 [W] http://en.wikipedia.org/wiki/Heat_exchanger23 [W] http://en.wikipedia.org/wiki/Heat_exchanger


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Figure 6.3. AllFluid Design.

The process can be decomposed as follows:

A tube containing FC runs along the line defining the focus of theparabolic collector.

Reflected solar energy vaporizes the FC. FC gas enters the FC/FS heat exchanger, where it condenses, returning as

a liquid to the parabolic collector. When the sun sets, a valve can be shut

off to prevent energy loss.

The heat exchanger absorbs the condensation energy of FC, heating FS.Until cooking begins, FS is stored at a temperature higher than TD (and

lower than TS).

To cook, the user turns on a valve regulating FD. FD liquid enters theFS/FD heat exchanger, where it is heated and exits as a vapor.

Conceptually similar to our current design, the FD vapor condensesagainst the stove, releasing heat and cooking the roti before returning to

the second heat exchanger.


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Selection of the working fluids will inform the hardware design. Fluids should meet

the following criteria:

TC should be fairly high and must be larger than TD so that the finalphase change can take place.

TS should be higher than TC, as vapor in the storage container may createunsafe pressure. TD should be a little higher than the temperature required to cook the

roti so that the temperature transfer to the stove

ronmental impact. Fluids should be nontoxic.Safety and evi Affordability.

For example, candidates for FC, FS, and FD respectively are glycerine (290 C),

mineral oil (330 C) and propelyne glycol (187 C), with boiling points

arenthesized.p

24

6.4PotentialBenefitsandRisksComparedtotheCurrentDesignGenerally speaking, the design process for this project was complicated by the many

interactions and tradeoffs between various system components. A considerable

benefit of an allfluid design is that heat exchangers simplify specifications of the

interfaces between collection, storage, and delivery processes. This should improve

the modularity, making it easier to design and test a particular subsystem without

completely redesigning the others, as well as easing the integration of outdoor solar

collection and indoor cooking.

A specific concern with the current design is the interface between the paraboliccollector and the sand storage unit. As the sun sets, the ambient temperature cools

and if left open, the temperature of the sand will decrease. Therefore, just as the

sand reaches its peak temperature, the aperture should close. This presents

numerous challenges. In particular, it is difficult to size the aperture and time its

closing. If not properly controlled, an open aperture will leak energy from the

thermal storage unit. Closing the aperture manually requires additional human

interaction while shuttering it automatically adds much greater design complexity.

Such concerns might be lessened with the allfluid design. The use of wellinsulated

offtheshelf pipes (e.g. evacuated tubes) should reduce potential energy losses

compared with the current design. Furthermore, when the sun sets, it is simpler to

turn a valve to stop fluid flow than actuate the aperture shutter mechanism.As well as the solar collection problem, sand as a thermal storage medium presents

challenges in delivering heat for cooking. The primary advantage of sand is that it

can reach high temperatures, has a fairly high specific heat, and is dirt cheap.

However, it is a formidable challenge to design a robust conductive pathway

th hermosyphon. An advantage of using fluid to storeroughout the sand into the t24www.engineeringtoolbox.com
http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/


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thermal energy is that convection can be employed to our advantage, whereas doing

so with sand is more of a challenge.

Another problem with the current design is the large mass of sand required to store

the required cooking energy. Here too, fluids should perform better: the specific

heat of sand is approximately .8 kJ/kg K, while that of mineral oil, a storage fluid

candidate is 1.67 kJ/kg K. (For reference that of water is 4.19.)25

While there are some potential benefits, a number of risks are associated with the

three fluid design:

Repeated heating and cooling of the fluids may break them down,particularly organic oils.

Safety measures should be taken to ensure that pressures are kept at safelevels for each fluid container. This may add additional significant

complexity and be expensive.

Heat exchangers are expensive components, being complex to bothdesign and manufacture. While they can be bought offtheshelf, thereare many design parameters that determine its performance, such as

yout of the tubes.material, diameter, thickness, length, and la

Fluid storage containers may be expensive. As with the previous design, insulation of the fluid at high temperatures

for several hours is a challenge.

25www.engineeringtoolbox.com
http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/http://www.engineeringtoolbox.com/


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provideavenueforfeedbackandtrouble-shootingwhilepotentiallyraisingmoneyforfurtherdevelopmentandsubsidizingofstovedistributioninimpoverishedvillages.4

7.2DesirabilityOveralldesirabilityofastoredenergysolarcookstoveremainshighasthevillageofKarechiswellawareoftheneedtodecreasewoodusage,asdiscussedinsection1.Timesavednotcollectingwoodmaybespentcraftingproductsforsale(forexamplecurrentlyvillagersfashionplatesoutofleaves)orstudying.5Furthermore,FESworkscloselywiththevillagetoemphasizetheneedforchangetosavetheforest.Finally,ifthestovesaremanufacturedinthevillage,thevillagerswillhaveanadditionalinvestmentofpride.

Thecurrentprototypehasseveralundesirablefactorsthatshouldbefixedbeforeintroductiontothevillage:

Convenience.Thecurrentprototypeistoolargeandwillbeunstableonthehillyterrainofthevillage.Furthermore,itistooheavytobemovedtoandfromthehouseforcookingassuggestedandadjustmentofcollectoronadailybasisisnotoptimal.Amodulardesignhasbeensuggestedtohelpaddresstheseissues.

Safety.Thecurrentdesignrequiresbuildingtoextremetemperatureandpressurerequirements,whichwillalwayspresentasafetyissueaslongasthepotentialforthestoragereaching550Cremains.PrototypesmustcertainlybetestedextensivelybeforebeingbroughttoIndiaandwerecommendamechanismforheatdissipation.Alternativelyanon-fluid

designorbetterheattransferefficiencyallowingforloweroveralltemperatureswouldaddressthisissue.

TheseissueswillcertainlybeaddressedinfutureiterationsandwenotethatthecurrentprototypedoesmeetthemainconcernoftheoriginalNamasteprototypeinthatitallowscookingwhensunlightisnotavailable.

7.3TechnicalFeasibility

Theoreticalcalculationssuggestthatthecurrentdesigniscapableofcookingrotiandexperimentshaveconfirmedthateveningcookingispossible.Energystorageto

allowcookingofrotiinthemorningremainsaverydifficultproblemandmayeitherbeachievedinfutureiterationsor,alternatively,amoreefficientstovemaybeusedinthemorningasanalternativetoa3-stonefire.Asecondtechnicalhurdleremainsintheabilitytomanufacturethestoveinthevillageoutoflocalmaterials.Full

4ImplementationstrategyideasweredevelopedinbrainstormingwithSusanAddy,ECARProjectLead,2011.5PersonalcommunicationwithSaileshRaoofClimateHealers.


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8.ConcludingRemarks

Ultimately,adefiningfeatureofourworkwasthechallengeofdesigningasinglecomponentinisolationfromtherestofthesystem.Insomerespects,thiswasbeneficialbecauseitfocusedourenergy(nopunintended)--makingusthink

deeplyabouttheheattransferprinciplesandmanydesigntradeoffswithinasinglemodule.

Yet,wealsocametoappreciatethatanysuccessfuldesignrequiresaholisticplan.Thecomplexinterfacesbetweenthethermalcollection,storage,anddeliverycomponentsofthesolarcookerdemonstratetheneedforamoremodularstrategy.Althoughanynumberofconceptsappearfeasible,weexpectthatthethree-fluidapproachwillbebothmodularandaffordable.Wehavenotyetundertakenacomprehensiveanalysisofit,andassuchweareunabletosaywithcertaintythatsuchanapproachisevenviable.However,wedothinkthatitwarrantsfurtherconsiderationbyfutureengineeringteamswhoconsiderthisworthyyetchallengingproblemofdesigningastoredsolarenergycookstove.


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Appendices

AppendixA.Potentialmaterialsforthermalstorage

Material Tm

(C)

Lf

(kJ/kg)

cp

(kJ/kgK)

Safety Cost

($/kg)

Puremetalsa

Bismuth 271.40 Xc(54.1) 0.122 Xc(~22)

Cadmium 321.07 213 0.232 X(toxic)

Indium 156.60 28.6 0.233 X(~4,500)

Lead 327.46 23.0 0.129 X(toxic)

Litium 180.5 432 3.582 X(combustible)

Polonium 254 - - X(radioactive) Thallium 304 20.3 0.129 X(toxic)

Tin 231.93 Xc(59.2) 0.228 Xc(~11)

Fusablealloysb

5:3Bi:Sn 202 Xc Xc

1:1Bi:Sn 286 Xc Xc

Waxes

Typical 60-70 2.14-2.9 Xd

(combustible) Paraffin 47-64 2.9 Xd(combustible)

Beeswax 62-64 3.4 Xd(combustible)

Specialty upto180 X

Salt X(~800) 0.88-0.92

Glasses X(~0) 0.5-0.9

Rubbers

Typical 2.0 IndiaRubber 1.13-4.1

Sand 0.8

TableA1:Potentialphasechangeandtemperaturechangematerials.Xsindicateincompatibilitywithourdesign.a:Forpuremetals,onlythosewithphasechangesbetween


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150-400Cshown;physicalpropertiesarefromCRC.b:Alloysincludeonlythosewithoutcadmiumorleadfortoxicityissues,orindiumforcost.Dataisfrom

http://www.gizmology.net/fusiblemetals.htm.c:Bismuth,tin,andtheiralloysarecheaperthanmost,butstillcost-prohibitivewhencombinedwiththeirspecificheatcapacities.d:Liquidwaxeswouldbepromisingastemperature-changematerials,exceptthattheyflashat200-250C.Dataforwaxes,rubber,glassfromhttp://www.engineeringtoolbox.com/specific-heat-solids-d_154.html.


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AppendixB.ConductiveRadialHeatFlow

Thisseekstoderivetheequationsforradialheatflowoverafinitecirculardomain

withno-flowboundariesattheouteredgeandanaxialsourceorsink.The

mathematicsareexpectedtobeanalogoustogroundwaterflowthroughporous

mediaaroundawellorinjectionsite.

Ringshapedcontrolvolume,whereJoutisanylossuniformoverthediskwith

dimensions[Energy/Area/Time]:

Conservationofenergy:

(1) ! ! + ! = ! ! + ! ! ! ! ! + ! ! !!"#!"#$!

Rearranging,(Uenergydensity[Energy/Volume]):

(2) !! ! + ! !" ! + ! ! + ! ! ! ! ! = !!"#2!"!!

Dividingbyunit:

(3)!

!!"!!

! !!! !! !

!+

! !!! !!! !

!!"!!=

!!!"#

!

Passtolimitsasr0,t0:

(4)!"

!"+

!

!!"!

!"

!"=

!!!"#

!

Jout

P r+rP(r)

r

h

r


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Thermalenergy(density,heatcapacity,temperature,andvolume):

(5) ! = !!!! = !!!!Powerthroughconduction(thermalconductivity,area)

(6) ! = !" = !"!"

!"= !2!"

!"

!"

Combining(4),(5),and(6):

(7)!

!"!!!! +

!

!!"!

!

!"!2!"

!"

!"=

!!!"#

!

Forconstantdensity,heatcapacity,height,anddelta,andforuniformthermal

conductivity:

(8) !!! !"!"

!

!

!

!"! !"

!"= !

!!"#

!

Wewillnowconsider2possibilities:(A)NooutsidelossesanduniformfallofT,(B)

totallossesthroughJout=totalinputpower.

(A9) !!!!"

!"

!

!

!

!"!!"

!"= 0

Sototalpowerinattheinnerradiuswillcorrespondtoauniformtemperaturerise:

(A10)!!"!#$

= !!!"#

!!!!

!"

!"

Combining(A9)and(A10):

(A11)!!"!#$

!!!"#!!!

=

!

!

!

!"!!"

!"

(A12)!!"!#$

!!!"#!!!

!"! = ! !!"

!"

Integrating(recallthatno-flowattheperimeter):

(A13) !!"!#$!!!"#

!!!!!"

!

!!"#

= ! !!!!

!"

!

!"

!"

!

(A14)!!"!#$

!!!!"#!!!

!! !!"#

!= !

!"

!"

(A15)!!"!#$

!!!!

!

!!"#!

!

!

=

!"

!"


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(A16)!!"!#$

!!!!

!

!!"#!

!

!

!"!!

!!

= !"!!

!!

(A17)!!"!#$

!!!!

!!!!!!

!

!!!"#! !"

!!

!!

= !! !!

(B9) !!"#!=

!

!

!

!"!!"

!"

Here,totalpowerwillbetheJoutovertheentiretoparea:

(B10)!!"!#$ = !!"#!!!"#!Combining(B9)and(B10):

(B11)!!"!#$

!!!"#!!!

=

!

!

!

!"!!"

!"whichisidenticalto(A11)andsolutionfollowsfrom

there

ThisresultA/Bcanbeappliedtothesandmixturedeliveringheattothesiphonasit

removesitfromthecenter.Italsoappliestoheatdistributiontotheedgesofthe

burnerasitisdeliveredtothecenterbythesiphon.

Inthecaseofaconductorwhereheightvarieswithr,theanalysisholdsuntil

equation(7).Fromthere,itprogressesasfollows:

(C8) !!!

!"

!"

!

!!

!

!"

!!"

!"

=

!!!"#

!

Fromhere,wetakethecasewhereJout=totalinputpower.

(C9)!!"#

!=

!

!!

!

!"!

!"

!"

With(B10),wehave:

(C11)!!"!#$

!!!"#!!=

!

!

!

!"!

!"

!"

(C12)!!"!#$

!!!"#!! !"!

= ! !

!"

!"

(C13)!!"!#$

!!!"#!!

!!"!

!!"#

= ! !!!"!

!"

!!!"

!"

!

(C14)!!"!#$

!!!!"#!!

!! !!"#

!= !

!"

!"


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(C15)!!"!#$

!!!

!

!!"#!!

!

!!=

!"

!"

(C16)!!"!#$

!!!

!

!!"#!!

!

!!!"

!!

!!

= !"!!

!!

Atthispoint,thespecificfunctionh(r)mustbeknown.Asanexample,wetakeh=a/rforuniform,constanta:

(C17)!!"!#$

!!!"

!!!!!!

!

!!!"#! !! !! = !! !!


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AppendixD:Designdrawingsandprototypeimages


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Solar Cookstove Final Report

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