2016年美赛论文

Team#32150page1ofContentsⅠIntroduction……………………………………………………………………….11.1ProblemBackground………………………………………………...11.2OurWork………………………………………………………….....2ⅡGeneralAssumptions.............................................................................................3ⅢSymbolDescription……………………………………………………………...3ⅣBathtubWaterTemperatureModel…………………………………………..44.1PrincipleandWayofThinking………………………………………44.2Thecalculationofhotwatertemperatureandwaterflowrate………54.3Theresultsofthemodel……………………………………………ⅤThetemperaturegradientmodel……………………………………………….95.1PrincipleandWayofThinking……...……………………………...105.2Derivationoftheformulaoftemperaturedistribution……………..115.3Theresultsofthemodel…………………………………………….ⅥImprovedModel………………………………………………………………..6.1PrincipleandIdeas6.2ModelImplementationandResultsⅦTheInfluenceofOtherFactors…………………………………………….....117.1People’smovement7.2ModelImplementationandResults7.3InterventionofbubblebathⅧSensitivityAnalysis……………………………………………………………228.1Impactofthetemperatureofheatsource8.2ImpactoftheradiusofthestabletemperaturefieldⅨConclusion……………………….…………………………………………….259.1Strengths…………………………………………………………..269.2Weaknesses………………………………………………………..279.3FutureWork……………………………………………………….28LettertotheUsers………………………………………..........................................30References…………………………………………………………………………...31Team#32150page1ofⅠIntroduction1.1.ProblemBackgroundTakingahotbathisconsideredtobeoneofthesecretsoflivinglonger.Itcanmakeusrelaxed,improvebloodcirculationandenhancetheimmunityabilitywhichcontributestoourhealthalot.Definitely,ifthetemperatureofwateristoohigh,itwillnotonlyhurtourskin,butalsoexpandthebloodvesselsonthesurfaceoftheskin,increasethebodysurface’bloodflowanddecreasethebloodsuppliedtoheartandbrain,whichcanleadtohypoxiaandfainting.Meanwhile,weshouldn’ttakeabathforalongtime,especiallychildrenshouldtakemorecareofit.Thetimetheytakeabathshouldn’tmorethanhalfanhour.Takealongbathwillmakeusfeeltiredandleadtoheadache.Sotheexpertsuggeststhatthebesttemperatureforbathis℃37,anditisthebesttotakeabathfor20minutes.Withtheimprovingofpeople’slivingquality,mostofusprefertobuythedevicewithaconstant-temperaturesystem.Now,therearebathtubwithconstant-temperatureheatingsystemandconstant-temperaturetapinthemarketThereinto,athermostatisinstalledinsidethebathtubwithconstantheatingsystem.Thethermostathaselectricheatingelementormaterialsattachedinthewallsofthefibertougheningceramicpipe.Afterelectrifying,theheatradiationsfromtheheatingelementsormaterialsheatthebathwatercirculatingthepipelinethoroughlythroughthetougheningceramicpipe.Then,coverainsulatinglayeroutsidethepipetopreventfromtheheatlosing.Theprincipleoftheconstant-temperaturetapissettingaheatsensitivetemperaturecomponentsatthemixedwateroutletofconstanttemperaturemixingvalve,whichcontrolsthemovementofspool,closeoropenthecoldandhotwater’sinlet.Whenthetemperaturecontrollerissetintoaspecifictemperature,themixingvalvewillkeepthewatertemperatureconstantbyadjustingtheproportionofthehotandcoldwaterwhenthemixingwatergoesintooutlet.Bothofthemkeepthewatertemperatureconstantwhichbringsconveniencetopeople’slife.1.2.OurWorkWeareundertheconditionoftheinitialtemperatureofthewatertemperaturekeeps,buildamodelofthetemperatureofthebathtubwater.Andthenwedeterminedthebeststrategytoadopt.Meanwhilewealsoneedtoconsiderotherimportantfactorsontheimpactofthemodel.Tofulfillthese,wedecomposetheproblemintoseveralsteps:Inkeepingtheinitialtemperatureofthestrategy,weproblemamodelofauniformwatertemperatureconstant,useitasaframeworkforfurtheranalysis.Accordingtotheconservationofenergy,toensurethebathtubincreasedheatinsteadoflost.Byusingtheformulafurthercalculation,wedesignaconstanttrickleofhotwater.Team#32150page1ofBuildthetemperaturegradientmodeltoreflectthetemperatureatdifferentpointofthedistancefromthebathtubheatsource.Accordingtothetemperaturegradientmodel,wedeterminetheinitialtemperatureandthengetbathcrockedgedistanceawayfromheatsource,finaljudgeoutthesizeandshapeofbathcrock.Becauseofthemotionsmadebythepersoninthebathtubandtheuseofbubblebathagentwillhaveaneffectonheatdissipation,wemadesomeadjustmentbeforethewatertemperaturemodel.Implementsensitivitytestandanalyzemodelstrengthsandweaknesses.Afterfinishinganalyzingalltherelevantfactors,wereachedourfinalconclusionandoptimalstrategy.Inthelaststage,weprovideanon-technicalletterfortheworldmedicalassociationtodescribesyourstrategyforusersofthebathtubandexplainwhyitissodifficulttogetanevenlymaintainedtemperaturethroughoutthebathwater.ⅡAssumptionsComparedtotheoverflowofwater,theamountofwaterreducedbyevaporationisquitelittle,sowecanignorethelossofwaterintheform.Giventhattheheatconductivitycoefficientofairisfarlessthanthetubwall,thatistosay,waterlosslessheatinthebathtub,sowedonotneedtoconsidertheeffectoftubwallonheatdissipation.Inmodelone,weconsiderthewaterinbathtubisinsimilarheat,andsupposethehotwatermixupevenlybythetimeitispouredintothebathtub,whichmakesthewaterallinthesameheat.Inmodeltwo,wewillmakethetemperatureofthewaterastheheatsourcetemperature,andassumethed