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ID:40051815
大小:519.13 KB
页数:52页
时间:2019-07-18
《ch 4_conduction heat transfer and potential flows》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、4ConductionHeatTransferandPotentialFlowsInthischapter,thediscontinuousfiniteelementformulationforheatconductionandpotentialflowproblemsisdiscussed.Heatconductionisperhapsthesimplestheattransfermode,butplaysanimportantroleinthermalscienceandengineeringanalyses.Forintroductorypurposes,asimple
2、,steadystate1-Dheatconductionprobleminasolidslabisconsideredfirst.Throughthisexample,wewillillustratethesimilaritiesanddissimilaritiesbetweenthediscontinuousandcontinuousmethodsforthesolutionofthisclassofproblems.Thisisfollowedbyadiscussiononsteadystateheatconductionproblemsinmultidimension
3、algeometries.Thesamediscussionstyleisthenfollowedtopresentthediscontinuousfiniteelementsolutionofthetransientheatconductionproblems.Thepotentialflowproblemsandflowsinporousmediahaveasimilarmathematicalstructure,andthuscanbeanalyzedsimilarly.Oneoftheimportantissuesinadiscontinuousfiniteeleme
4、ntformulationistheappropriateselectionofnumericalfluxesacrossthediscontinuousinter-elementboundaries.Thetheoryunderlyingtheselectionofnumericalfluxesisdiscussed.Bythegeneralclassificationofpartialdifferentialequations,thesteadystateconductionequationsareelliptic,andthetransientheatconductio
5、nequationsareparabolic.Theformerhavenorealcharacteristics,whilethelatterhaveonefamilyofcharacteristiccurves.Asimpledifferencebetweenthesetwotypesofequationsisthatforasteadystateheatconductionproblem,asolutionisrequiredoveranentiredomain,whereasforthetransientheatconductionproblems,itispossi
6、bletoobtainasolutioninasmalltimeinterval.Thisdifferencealsodeterminesthenumericalschemestobeapplied,andthestabilityresultsfortheselectionofnumericalfluxes.Variousconsistentandstablenumericalfluxesaregivenforthediscontinuousformulationofbothsteadyandtransientheatconductionproblems.Fortimedep
7、endentproblems,anappropriatetimestepisimportantfornumericalsolutions.Thisremainstruewiththediscontinuousfiniteelementmethod;infactitisevenmoresobecausemostdiscontinuousformulationsusetheexplicittimeschemeformarchingintime.Higherorderaccuracyschemes,sucha
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