2016年美国大学生数学建模大赛A题获奖论文A Hot Bath.pdf

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1、TeamControlNumberForofficeuseonlyForofficeuseonly46731T1________________F1________________T2________________F2________________T3________________ProblemChosenF3________________T4________________F4________________A2016MCM/ICMSummarySheet(Yourteam'ssummarysho

2、uldbeincludedasthefirstpageofyourelectronicsubmission.)Typeasummaryofyourresultsonthispage.Donotincludethenameofyourschool,advisor,orteammembersonthispage.SummaryOurexperienceofeverydaylifetellsusthat,bathingqualityisrelevanttothetemperatureofthewater.Henc

3、etheoptimalityofthewater-addingstrategyinbathingprocesshasbecomeanissue.Inthisarticle,weestablishtwomodels.Oneiswatertemperaturevariationanddistributionmodelandtheotheroneisfindingbeststrategymodel.Weputforwardsomeacceptablehypothesistosimplifythemodel.Wha

4、t’smore,weclearthemeaningoftheword“noticeably”.Thefirstparthasfivesections:air’sheatradiation,bathtubwall’sheatradiation,personin,hotwaterin,bubbleexisted.Wediscusssomefactorsthataffectwatertemperature,suchastheshapeandthevolumeofthebathtubandperson,especi

5、allythemotionsmadebythepersoninthebathtubbecausethetemperatureinthebathtubhasagreatconnectionwithperson.Finally,wegetthewatertemperaturevariationanddistributionmodel.Thesecondpartaimstofindingthebestwaterstrategy.Differentstrategiesareconsideredforaddingho

6、twaterandtheamountofthehotwater.Thekeyofstrategiesishowtochoosethemomentofopeningthefaucetandthelastingtime.Bydevelopinganoptimizationmodelofthestrategy,wemanagetodetermineastrategyfordifferentusersandextendthemodelwithafinitevolumemethod.Underthecondition

7、ofthesamebathingtime,westudywhat’stheidealtimetoaddthehotwatertomakeittotheinitialtemperature.Team#46731Page2of19Wetransformtheweightp.Withtherestrictconditionofthetemperatureinthebathandtheamountofthehotwater,thequestioncanbetransformedtoanonlinearoptimiz

8、ation.WegettheconclusionandoptimalresultsthroughthePDE(PartialDifferentialEquations)toolboxofMATLAB.Andtheresultshowsaclearsuperiorityforchoosingasuitablestrategyfordifferentusers.Keywords:bathtub;heat-conduc