2018年美赛a题h奖论文

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1、SummaryWebuildtwobasicmodelsforthetwoproblemsrespectively:oneistoshowthedistributionofheatacrosstheouteredgeofthepanfordifferentshapes,rectangular,circularandthetransitionshape;anotheristoselectthebestshapeforthepanundertheconditionoftheoptimizationofcombinationsofmaximalnumberofpansintheovenandthem

2、aximalevenheatdistributionoftheheatforthepan.Wefirstusefinite-differencemethodtoanalyzetheheatconductandradiationproblemandderivetheheatdistributionoftherectangularandthecircular.Intermsofourisothermalcurveoftherectangularpan,weanalyzetheheatdistributionofroundedrectanglethoroughly,usingfinite-eleme

3、ntmethod.Wethenusenonlinearintegerprogrammingmethodtosolvethemaximalnumberofpansintheoven.Intheevenheatdistribution,wedefineafunctiontoshowthedegreeoftheevenheatdistribution.WeusepolynomialfittingwithmultiplevariablestosolvetheobjectivefunctionForthelastproblem,combiningtheresultsabove,weanalyzehowr

4、esultsvarywiththedifferentvaluesofwidthtolengthratioW/Landtheweightfactorp.Atlast,wevalidatethatourmethodiscorrectandrobustbycomparingandanalyzingitssensitivityandstrengths/weaknesses.Basedontheworkabove,weultimatelyputforwardthattheroundedrectangularshapeisperfectconsideringoptimalnumberofthepansan

5、devenheatdistribution.AndanadvertisementispresentedfortheBrownieGourmetMagazine.Contents1Introduction31.1Browniepan31.2Background31.3ProblemDescription32.Modelforheatdistribution32.1Problemanalysis32.2Assumptions42.3Definitions42.4Themodel43Resultsofheatdistribution73.1Basicresults73.2Analysis93.3An

6、alysisofthetransitionshape—roundedrectangular94Modeltoselectthebestshape114.1Assumptions114.2Definitions114.3Themodel125ComparisionandDegreeoffitting196Sensitivity207Strengths/weaknesses218Conclusions219AdvertisementfornewBrownieMagazine2310References241Introduction1.1BrowniepanTheBrowniePanisusedto

7、makeBrownieswhichareakindofpopularcakesinAmerica.Itusuallyhasmanylatticesinitandismadeofmetalorothermaterialstoconductheatwell.Itistrivially9×9inchor9×13inchinsize.OneexampleoftheconcreteshapeofBrowni