传热学第10讲非稳态导热2.ppt

《传热学第10讲非稳态导热2.ppt》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、4.5TransientHeatConductioninMultidimensionalSystemsMethod:——ProductSolutionLongSolidBarSuppose:theResultofthesolutionistheproductsoftwoPlane’ssolutionsSuppose:Conclusion:TheEquationsarethesameAlsotheboundaryconditionsarethesameChapter5NumericalMethodsinHeatTransfer

2、ThelimitationsofanalyticalMethodsTheGeometricalShapeandboundaryConditionsMustbeSimple!5.1FiniteDifferenceDifferenceofDifferentialEquationandFiniteDifferentialEquationSubstitute:Methods:1)equationchanging2)pointscontinuesCommutativeerror:Therefore,thesmallerthex,the

3、smallertheerror,andthusthemoreaccuratetheapproximation.Meaning:TangentLinereplacingNowconsidersteadyone-dimensionalheattransferinaplanewallofthicknessLwithheatgeneration.WiththeconstancyofForeachofpoints.(M+1points0,1,2,...,m－1,m,m＋1,...,M)TheerrorwillbeNote:thesec

4、ondderivativesthefirstderivativeoftemperaturedT/dxatthemidpointsm-1/2andm+1/2ofthesectionssurroundingthenodemcanbeexpressedasNotingthatthesecondderivativeissimplythederivativeofthefirstderivative,thesecondderivativeoftemperatureatnodemcanbeexpressedaswhichisthefini

5、tedifferencerepresentationofthesecondderivativeatageneralinternalnodem.Foreachpointsyouhavedesignedherearecalledasnodesornodalpoints.Thelinesweusedtodividethewholesolvingspacewillbecalledasmeshlineslatter.StepsToSolving:1)MakingMeshesinasolvingterritory2)MakingDiff

6、erentialEquationtoFiniteEquations3)MakingConditionEquationstotheformofFinite4)SolvingalltheLinearEquationswithComputer5)ArrangingtheDatainaProperWayProblemswe’llhaving:1)Themeshesaresame2)TheconductivityshouldbeconstantInthemostcircumstances,thenodesdispatchesandth

7、anthemeshlinesdispatcheswillbedesigneddifferentlywitheachother.Thusweusethefollowingmethod.Innernodes:Onedimensionproblem：Makingintegrationforeachofthem.Intimefromttot+Δt,thetemperatureofnodePwillchangeformTttoTt+Δt.ThechangingEnthalpyofthecontrolvolumerepresentedb

8、yNodePAssumption:thatthetemperatureontheborderistheaverageoftheneighbor’s.Whileintegratingforthetimethenweneedsomeassumptions.Assumption1：whentim