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ID:13066130
大小:1.01 MB
页数:24页
时间:2018-07-20
《2013年美赛a题h奖论文--100749418》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、SummaryWebuildtwobasicmodelsforthetwoproblemsrespectively:oneistoshowthedistributionofheatacrosstheouteredgeofthepanfordifferentshapes,rectangular,circularandthetransitionshape;anotheristoselectthebestshapeforthepanundertheconditionoftheoptimizationofcombinationsofmaximalnumberofpansinth
2、eovenandthemaximalevenheatdistributionoftheheatforthepan.Wefirstusefinite-differencemethodtoanalyzetheheatconductandradiationproblemandderivetheheatdistributionoftherectangularandthecircular.Intermsofourisothermalcurveoftherectangularpan,weanalyzetheheatdistributionofroundedrectanglethor
3、oughly,usingfinite-elementmethod.Wethenusenonlinearintegerprogrammingmethodtosolvethemaximalnumberofpansintheoven.Intheevenheatdistribution,wedefineafunctiontoshowthedegreeoftheevenheatdistribution.WeusepolynomialfittingwithmultiplevariablestosolvetheobjectivefunctionForthelastproblem,co
4、mbiningtheresultsabove,weanalyzehowresultsvarywiththedifferentvaluesofwidthtolengthratioW/Landtheweightfactorp.Atlast,wevalidatethatourmethodiscorrectandrobustbycomparingandanalyzingitssensitivityandstrengths/weaknesses.Basedontheworkabove,weultimatelyputforwardthattheroundedrectangulars
5、hapeisperfectconsideringoptimalnumberofthepansandevenheatdistribution.AndanadvertisementispresentedfortheBrownieGourmetMagazine.Contents1Introduction31.1Browniepan31.2Background31.3ProblemDescription32.Modelforheatdistribution32.1Problemanalysis32.2Assumptions42.3Definitions42.4Themodel4
6、3Resultsofheatdistribution73.1Basicresults73.2Analysis93.3Analysisofthetransitionshape—roundedrectangular94Modeltoselectthebestshape114.1Assumptions114.2Definitions114.3Themodel125ComparisionandDegreeoffitting196Sensitivity207Strengths/weaknesses218Conclusions219AdvertisementfornewBrowni
7、eMagazine2310References241Introduction1.1BrowniepanTheBrowniePanisusedtomakeBrownieswhichareakindofpopularcakesinAmerica.Itusuallyhasmanylatticesinitandismadeofmetalorothermaterialstoconductheatwell.Itistrivially9×9inchor9×13inchinsize.OneexampleoftheconcreteshapeofBrowni
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