资源描述:
《国际数学建模论文二等奖》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、Team#20427第12页共2n页ThesecretofpansAbstractInthisarticle,weresearchtheinfluenceofpan-shapeonthemaximumnumberofpansintheovenandheatdistributionofpans.Firstofall,weanalyseworkingprincipleoftheovenandlearnthatthemainmethodofheatexchangeinovenisconvectivehe
2、attransfer.Tomakethissimpler,weassumethepan-shapeareregularpolygonandinternalthermalenvironmentintheovenissame.Inproblemone,inordertofindoutarelationshipbetweentheshapeandamountofpansthatareputintotheoven,wemakeresearchesonvariousshapesofpans.Theareao
3、feachpanisA,wecanusethethemaximumnumberofpanstostandforthespaceutilizationofovenwhileitsareaiscertain.Withseamlesssplicingbetweenbakingpans,wewillfulfillthemaximumutilizationoftheoven.Accordingtothemultiplerelationshipbetweenthepolygoninteriorangleand
4、thecircumferentialangle,wecometoaconclusionthatonlyequilateraltriangle,squareandregularhexagoncanfulfillseamlesssplicing.Takingtheshapeofoveninourdailylifeintoconsideration,wesetthevalueofaspectratioarrangefrom0.4to1.Witheachvalueofaspectratio,wemakea
5、narrangementofequilateraltriangle,squareandregularhexagonpan.Finally,wereachtheconclusionthatitissquarepanwhoseamountisthelargestwhenputintoacertainareaofoven.Furtherstudiesalsoshowthattheutilizationofovenislowerifthenumberofsidesofaregularpolygonincr
6、ease,wealsofindoutthatcirclepan’sutilizationofovenisthelowest.When,thenumberofpanscanbearrangedintheovenisreducedwiththedecreasedofthethepolygonedgenumberofthepan().Inproblemtwo,wemakeresearchesondifferentshapesofpanssoastofindouthowtheshapeofeachpani
7、tselfinfluenceheatdistributionwhenheated.Webuiltfiniteelementanalysismodel,andSimulatetheheatdistributionofeachpanintheovenwiththehelpofsoftwareansys10.0.Thenthefunctionalrelationshipbetweenthepan-shapeandheatdistributionisDeduced.Analysingthefunction
8、alrelationship,wefoundthatthepan'sheatdistributionuniformdegreeincreaseswiththeincreaseofthepolygonedgenumberofthepan().Whenthenumberofsidesapproachesinfinity,heatdistributionisthemostuniform.Thatistosay,theround-pan’sheatdistributionisthemost