美赛论文模板(超实用)

ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber50930ProblemChosenAForofficeuseonlyF1________________F2________________F3________________F4________________2015MathematicalContestinModeling(MCM/ICM)SummarySheetSummaryOurgoalisamodelthatcanuseforcontrolthewatertemperaturethroughapersontakeabath.Afterapersonfillsabathtubwithsomehotwaterandthenhetakeabath,thewaterwillgetscooler,itcausethepersonbodydiscomfort.Weconstructmodelstoanalyzethetemperaturedistributioninthebathtubspacewithtimechanging.OurbasicheattransferdifferentialequationmodelfocusesontheNewtoncoolinglawandFourierheatconductionlaw.Weassumethatthepersonfeelscomfortableinatemperatureinterval,considerwithsavingwater,wedecidethetemperatureofwaterfirstinjectadopttheupperbound.Thewatergetsmorecoolerwithtimegoesby,weassumeatimeperiodandstipulationitisthetemperaturerange,usethismodelcangetthethefirstinjectwatervolumethroughthetemperaturedeclinefrommaximumvaluetominimumvalue.Thenwebuildamodelwithapartialdifferentialequation,thismodelexplainthewatercoolingafterthefillbathtub.Itshowsthetemperaturedistributionandwatercooldownfeature.WeTeam#9530Page2of10canobtainthewatertemperaturechangewithspaceandtimebyMATLAB.Whenthetemperaturedeclinetothelowerlimit,thepersonaddsaconstanttrickleofhotwater.Atfirstthebathtubhasacertainvolumeofminimumtemperatureofthewater，inordertomakethetemperatureaftermixedwithhotwatermoreclosertotheoriginaltemperatureandaddinghotwaterless,webuildaheataccumulationmodel.Intheprocessofaddinghotwater,wecancalculatethetemperaturechangefunctionbythismodeluntilthebathtubisfull.Afterthewaterfillup,watervolumeisaconstantvalue,someofthewaterwilloverflowandtakeawaysomeheat.Now,temperaturerisedidn'tquicklyasfillitupbefore,itshouldmaketheinjectheatandtheairconvectionheatdifferencesmallest.Forthemovementofpeople,canbeseenasasimplemixingmovement,Itplaysaverygoodroleinpromotingtheevenlyofheatmixture.soweputthehumanbody'sdegreeofmotionasafunction,andthenestablishthefunctionandtheheattransfermodelofthecontact,anddrawtherelationshipbetweenthem.Fortheimpactofthesizeofthebathtub,duetotheinsulationofthewallofthebathtub,theheatradiationofthewholebodyisonlyrelatedtotheareaofthewatersurface,Sotheshapeandsizeofthebathisjusttheareaofthewatersurface.Therebyaffectingtheamountofheatradiation,therebyaffectingtheamountofwateraddedandthetemperaturedifference,Soafteralongandwidebathtodeterminethelengthofthebath.Thesurfaceareaisalsodetermined,andtheheatTeam#9530Page3of10transferratecanbesolvedbytheheatconductionequation,whichcanbeusedtocalculatetheamountofhotwater.Finally,consideringtheeffectoffoamingagent,afteraddingthefoam,thefoamfloatsontheliquidsurface,whichisequivalenttoalayerofheattransfermedium,Thislayerofmediumishinderedbytheconvectiveheattransferbetweenwaterandair,therebyaffectingtheamountofhotwateradded.,Team#9530Page4of10ContentTitile..............................................................................................错误!未定义书签。Summary.......................................................................................错误!未定义书签。1Introduction..........................................................................................................11.1RestatementoftheProblem......................................................................11.2Background...............................................................................................11.1.1CommonSolvingTechnique..............................错误!未定义书签。1.1.2PreviousWorks..................................................错误!未定义书签。1.3Example....................................................................错误!未定义书签。2AnalysisoftheProblem.......................................................................................22.1OutlineoftheApproach............................................错误!未定义书签。2.2BasicAssumptions....................................................................................32.3DefinitionsandKeyTerms.......................................错误!未定义书签。3CalculatingandSimplifyingtheModel.............................................................44TheModelResults................................................................................................45ValidatingtheModel............................................................................................56StrengthsandWeaknesses...................................................................................56.1Strengths...................................................................................................56.2Weaknesses...............................................................................................57FoodforThought.................................................................................................58Conclusion............................................................................................................5References.......................................................................................................