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1、Godhelpsthosewhohelpthemselves！Chapter4Numericalmethod ofheatconduction数值解法本章主要内容什么是数值解法？本章主要内容区域离散化节点的离散方程迭代法求解数值解法PrimaryContentsnumericalanalysisofheatconductiondiscretizationequationoftheinnergridpoints离散方程内节点discretizationequationoftheboundarygridp
2、oints边界节点solutionmethod–iterationmethod迭代法4-1NumericalAnalysisofHeatConductionVocabularynumericalmethod数值解法discretization离散Solvingzone求解区域algebraic代数的gridpoints&node节点Vocabularyconvergence收敛iteration迭代controlvolume控制容积steplength步长Solutiontoheattransferp
3、roblemsanalyticalsolution-differentialequation&solvingconditionsnumericalsolution-discretizationequation&iterationmethodtemperaturepatternSolutiontoheattransferproblemsanalyticalsolution-differentialequation&solvingconditionsnumericalsolution-discretiza
4、tionequation&iterationmethodexperimentalsolution气体微通道流动阻力测定实验系统示意图直径D=75微米的石英玻璃管实验测定结果当量直径D=52微米的石英玻璃管实验测定结果直径D=119微米的不锈钢管实验测定结果Basicstepsofnumericalmethodestablishgoverningequationandsolvingconditionssettheinitialvaluetoiterationestablishthealgebraiceq
5、uationofnodediscretizationofthesolvingzone代数的solvingthealgebraicequationsconvergencenomodifyinitialvalueanalysisofthesolutionyes收敛离散AexampleWHxy0h1,tfh3,tfh2,tft0Assumptionsteady-statewithoutheatsourceλρcareconstantWHxy0h1,tfh3,tfh2,tft0(1)establishgove
6、rningequationsandsolvingconditionsWHxy0h1,tfh3,tfh2,tft0(2)discretizationofthesolvingzonexynmHW(m,n)node(节点)steplength(步长)controlvolume(控制容积)离散求解区域4-2DiscretizationEquationofTheInnerGridPoints(内节点离散方程)Vocabularythermalbalancemethod热平衡法Discretizationequa
7、tionofinnernodeTaylorseriesexpansionmethod泰勒级数展开法Thermalbalancemethod热平衡法Thermalbalancemethod(热平衡法)m,nm+1,nm-1,nm,n+1m,n-1newsΔx=Δy4-3DiscretizationEquationofTheBoundaryGridPointsandsolutionmethods(边界节点离散方程及求解)Vocabularyflatboundary平直边界exteriorcornernod
8、e外部角点interiorcornernode内部角点thermalinsulationboundary绝热边界iterationmethod迭代法Discretizationequationofboundarynode(1)atflatboundary平直边界m,nm,n-1m-1,nm,n+1qw还是热平衡法！Δx=Δy(2)theexteriorcornernode外部角点m,nm,n-1m-1,nqwqw(3)theinteriorcornern
