西安交大高等传热学热对流第四章

高等传热学AdvancedHeatTransferChap4laminarforcedconvectioninpipesandducts§4-1Introduction内部流动与外部流动的区别：外部流动，边界层在表面上自由发展，不受外部几何条件限制（边界层理论求解）内部流动，流体受通道壁面约束，在离通道进口一定距离后，壁面上边界层互相影响，通道内不再存在位流核心（边界层理论求解？）高等传热学AdvancedHeatTransfer1.入口段2.流动充分发展段0uxconstdpdx22(0,ux沿轴向动量扩散为零)简单充分发展：0vw（忽略体积力时，等截面直通道层流充分发展）复杂充分发展：0;0vw0;0vwxx（等截面通道中紊流充分发展流动；弯曲通道中的充分发展流动；受浮升力影响的充分发展流动）高等传热学AdvancedHeatTransfer3.热充分发展段0xwbwTTTT:xh(0)Tx0xrwrrconstr1wbwrrTconstTTr,wwxbwxrrxTqhTTr,1wxbwxrrxThconstrTT检验正负号的正确性该式对UHF,UWT都成立高等传热学AdvancedHeatTransfera.对UHF，qw＝constwbwTTTT:TwbwTTTTwbwdTdTdTTxdxdxdxwxbwbwqhTTTTconstbwdTdTconstdxdxwbdTdTTconstxdxdxwbwdTdTdTTxdxdxdx由高等传热学AdvancedHeatTransfer微元体热平衡dx2pwbbcruT2bpwbbdTcruTdxdxbuwr22bwwpwbdTqrdxcrudxdx222bNote：不因热边界条件或进口段而异2bwpwbdTqdxcru适用于UHF的入口段及充分发展段bdTconstdxUHFconst高等传热学AdvancedHeatTransfer流体被加热wTbTxTwTbTxT流体被冷却高等传热学AdvancedHeatTransferb.对UWT（设TwTb）0wdTdxwbwbdTdTdTdTTTxdxdxdxxdx充分发展段：由22xwbbwxxpwbpwbhTTdTqdxcrucru另外，由热平衡式2wbxwbpwbdTThdxTTcru,wbtTT设积分上式高等传热学AdvancedHeatTransfer02xintxxtpwbhdtdxtcru2expxxinpwbthxtcru2expxxinpwbhxttcruNote：对入口段（hx≠const）及充分发展段（hx=const）都适用对UWT，Tb随x按指数规律变化，x↑，(Tw–Tb)↓高等传热学AdvancedHeatTransfer流体被加热流体被冷却wTbTxTwTbTxT为什么曲线不上凹？高等传热学AdvancedHeatTransfer3.流动和热入口段与充分发展段间的关系速度分布入口段，温度分布充分发展段？？case速度分布温度分布1充分发展充分发展2充分发展入口段3入口段入口段高等传热学AdvancedHeatTransferPr1，速度分布发展快于温度分布发展Pr→∞，温度分布开始发展前速度分布已经充分发展。Pr5的流体，分析热进口时可认为流动已经充分发展。高粘油Pr1，速度分布发展慢于温度分布发展Pr=1，速度分布发展等于温度分布发展Pr→0，速度分布永远保持均匀，不再发展。液态金属高等传热学AdvancedHeatTransfer4.N-S方程在一些情况下的精确解①fullydevelopedflowbetweentwoparallelplates2210pduxdx10pyppx221dudpdxdx0:0:02duydybyuxby22122dpbuydx2max122dpbudx22222132bbbbbudydpbudxdymax32buu23122byuub高等传热学AdvancedHeatTransfer②fullydevelopedflowincirculartubes0ux0rv1ddudprrdrdrdx0:0:0wdurdrrru2214wdpurrdx2max4wrdpudx200282wwrwbrurdrrdpudxrdrmax2buu221bwruur221ruupdduuuvrxrxrdrdrx高等传热学AdvancedHeatTransfer5.Frictionfactor22wfbcu22ebdpdxDfuRe16wwfrrucr2Re24wfybucyRe64,2ewfDrRe96,2efDbabba2345Re9611.3551.9461.70120.95640.2537incomfShahRK,LondonAL.Laminarflowforcedconvectioninducts[A].Advancesinheattransfer,Supplement1[C].NewYork:AcademicPress,1978.高等传热学AdvancedHeatTransfer6.SlipboundaryconditionxbyKnb22122:wuuwalluuccnnTangetal,ComparisonofgasslipmodelswiththesolutionsofthelinearizedBoltzmannequationanddirectsimulationofMonteCarlomethod,IntJModPhysC,2007,18(2):203-216高等传热学AdvancedHeatTransfer221dudpdxdx0::uyuyuybuy222Kn2bdpyyudxbb2Kn2sbdpudx21Kn26bbdpudx2224Re16Knwfbcu2DParallelplates高等传热学AdvancedHeatTransfercirculartubes1ddudprrdrdrdx22214Kn4wwrdprudxr2Knwsrdpudx218Kn8wbrdpudx0:0:wurrurrur2216Re18Knwfbcu高等传热学AdvancedHeatTransfer0.00.51.01.52.00.00.20.40.60.81.02r·D-1u·uav-1Kn=0Kn=0.05,v=1.0Kn=0.05,v=0.8Kn=0.1,v=1.0Kn=0.1,v=0.8无量纲速度分布0.52rD高等传热学AdvancedHeatTransfer高等传热学AdvancedHeatTransfer7.其他进口区滑移分析解：SparrowEM,LundgrenTS,LinSH,Slipflowintheentranceregionofaparallelplatechannel,Proc15thHeatTransferandFluidMechanicsInstitute,StanfordUniversityPress,Stanford,1962:223-238充分发展区矩形及圆环通道滑移分析解：EbertWA,SparrowEM,Slipflowinrectangularandannularducts,ASMEJBasicEngineering,1965,87:1018-1024.充分发展矩形通道高阶滑移分析解：AubertC,ColinS，High-orderboundaryconditionsforgaseousflowsinrectangularmicroducts,MicroscaleThermophysicalEngineering,2001,5:41-54.高等传热学AdvancedHeatTransfer8.EOFsolution++++++++++++++++++++++++++++-------------------+-+-+-++-+-+-+--pxStreamingpotentialStreamingcurrent高等传热学AdvancedHeatTransfer9.ThermalboundaryconditionIIIIBCBCwTconst()wqconst轴向()wTconst周向0T()wqconst周向()wqconst轴向高导热系数材料管壁低导热系数材料管壁高等传热学AdvancedHeatTransfer§4-2Laminarforcedconvectioninpipeswithfullydevelopedboundaryconditions1.物理问题数学描写1ddudprrdrdrdx221prTTTTcuvrxrrrrx221pTTTurxcrrrx轴向对流径向导热轴向导热高等传热学AdvancedHeatTransfer221pTTTurxcrrrx轴向对流径向导热轴向导热PrpcaPr1,所以，除Pr1外（液态金属），都可忽略轴向导热很大，导热能力很强xt，r方向温度变化与方向相当Pr1,tr方向温度变化远大于x方向高等传热学AdvancedHeatTransfer1.物理问题数学描写1ddudprrdrdrdx1uTTraxrrr轴向对流=径向导热0:0:0:221bwruur高等传热学AdvancedHeatTransfer2.UHF2211bbwudTrddTrardxrdrdr对UHF,轴向导热精确为零0:0:wwTrrqdTrrconstdrbdTTconstxdx220Tx322bbwudTdTrdrrdrdradxr积分两次2412224bbwudTdTrrrcdradxr高等传热学AdvancedHeatTransfer10:00Trcr,uT代入241222ln416bbwudTrrTcrcadxr2223:16bb020021222242202131121216416wrbbbb