Finding the harmonious Brownie Pan

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1、FindingtheharmoniousBrowniePan　　Summary：Asforthefirstsub-problem，weproposeamodelofprogressiveheatdistribution，modelI.Withthehelpofourknowledgeinhowovenworksandheattransfertheory，wederivetheheatconductionpartialdifferentialequation.Weobtainanumericalsolutionoftheequationi

2、nMATLABbyapplyingNeumannboundarycondition.Inaddition，weillustratethesolutionbyplottingthefiguresoftheheatdistributionacrosstheouteredgeforthepanswithrectangleshapeandcircleshaperespectively.Weproposeanovelmethodtodealwiththeshapebetweentherectangularshapeandthecircularsh

3、ape.Inthismethod，wegraduallychangetheshapeofpanfromrectangletocircleandexploretheinherentlawshowtheheatdistributionacrosstheouteredgechangesbyapplyingfittingmethod.Specifically，westartthechangingprocessbygraduallychangingthearclengthofthe4cornersoftherectangleshapewhilek

4、eepingthearcradianasW/L.Aftertheshapebecomesanoval，wethenchangetheradianofthetwosidesuntilitfinallyturnsintoacircle.Ourconclusionbasedontheproposedmodelisthattheheatdistributionacrosstheouteredgeofarectangularpanisthemostunevenoneamongallpossibleshapes，andthecircularpani

5、sconsideredtobemuchbetterthan6therectangularpan.　　KeyWords：heattransfertheoryprogressiveheatdistributionmodeldynamicparametersevaluationmodeloverallprogrammimgmodel　　1Introduction　　Inordertoindicatetheoriginofpan’sproblems，thefollowingbackgroundisworthmentioning.Panisasi

6、gnificantpartoftheoven，andtheelectricovenisanelectricapplianceusingtheradiantheatfromtheelectricheatingelements.Itcantoastchickenandduck，bakebreadandcakes，etc.Accordingtothedifferentneedsofbakingfood，thetemperatureofelectricovencangenerallybe60～240degree[1].Andelectriche

7、atingelementsaredistributedallaroundtheovenwall.Fromthereference，weknowthatheatconduction，onewayofheattransfer，isthemethodofheatingthefood.Thatistosay，thehighheatemittedfromtheovenwalltransferstotherelativelycoldfoodandthepanthroughtheair.Also，weknowthatthedifferentsizea

8、ndshapeofpancaninfluencethedistributionofheatacrosstheouteredge.So，inthispassage，weusemodelscombinedwit