ch 4_conduction heat transfer and potential flows

《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