2019美赛建模A题.pdf

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1、命题人：清华大学张阳阳2019MCMProblemA:AHotYoubotBackground:ThermalAnalysis,usingfiniteelementtechniques,iscarriedoutasasteady-stateortransientanalysis.Conductiveheattransferishandleddirectlybyfiniteelementtechniques;conductionoccursinasolidduetotemperaturediffe

2、rences.However,radiationheattransferanalysismayrequireadditionalparticle-trackingorray-tracingtechniquestoapproximatetheradiantenergyarrivingatagivensurface.Thematerialisassumedtobeamagnesiumalloyandtohaveathermalconductivityof52W/m∙K.Materialpropert

3、iesweretakenfrom"ThermalConductivityofMagnesiumAlloys".Sincethemodelisininchesyoucanusesymunittorewritethevalueininches.Nowyouneedremovetheunitstoobtainthevalueforthethermalproperties.Unlessoverwritten,allofthesidefacesaresettohaveanaturalconvectionc

4、oefficientof25W/m2∙Krepresentingheattransfertoanambientairtemperatureof288.15K(25℃).ConvertandcalculatetheconvectioncoefficienttoW/inch2∙Ktobeconsistentwiththemodeldimensions.Exploredifferentmaterialselectionsfortheroboticcomponent.Computethechangein

5、maxbodytemperatureasafunctionofincreasingthermalconductivity.Beforebeginingcalculatetheexpectedruntimefromthepreviousruntime.RunthemodelsusingaparforlooptospeedupthesimulationbyparallelizingtheiterationsacrossParallelComputingToolboxworkers.Ifyoudono

6、thavetheParallelToolboxchangeparfortofor.Problem:PartI:Developamathematicalmodelfortheheattransferamongthegripperpivot.IntheyouBot,thegripperpivotsitsunderneaththeelectronicsboardandisexposedtotheheatcomingoffthecircutboard.Hereyouwillcreatethepdemod

7、el,importtheSTLfileofthegripperpivot,andplotit.Createandvisualizeatetrahedralmeshofthecomponentwithamaximumvalueof0.09inches.Measurethex,yandzdimensionsofthemesh.PartII:Thebottomfaceisgivenafixedtemperatureassumingthattherestoftheroboticarmactsasahea

8、tsink.Thetopfaceandinnerholeisarbitrarilygivenaheatfluxtorepresenttheheatoffthecircuitboard.Solvethemodelandcalculatethemaxandbulkbodytemperaturesandtimehowlongthesolvetakes.ComputethemaxtemperatureinKandrewritethatto℃andF,thenplotthedistributionofte