传热学-第五章

2020/4/161第五章对流传热的理论基础Chapter5ConvectiveheattransferfundamentalNon-dimensionalparameterNu,Re,Pr2020/4/162§5.1概述一、影响因素（1）流体的物性（导热系数、粘度、密度、比热容等）；（2）流体流动的形态（层流、紊流）；（3）流动的成因（自然对流或强制对流）；（4）物体表面的几何因素；（5）换热时流体有无相变（沸腾或凝结）。ulRe2020/4/163pcuConvectionheattransferstronglydependsonthefluidproperties:AlsodependsonthefluidvelocityItalsodependsonthegeometryandroughnessofthesolidsurface,inadditiontothetypeoffluidflow(suchasbeingstreamlinedorturbulent).Whenafluidisforcedtoflowoverasolidsurface,itisobservedthatthefluidlayerincontactwiththesolidsurface‘sticks’tothesurface.Thisisaverythinlayeroffluidandisassumedtobezerovelocityatthewall.2020/4/164dimensionalessconvectionheattransfercoefficientheattransfercoefficientCharacteristiclengthxhNuNusseltnumberInfluidflow,thisphenomenonisknownastheno-slipcondition.Animplicationoftheno-slipconditionisthatheattransferfromthesolidsurfacetothefluidlayeradjacenttothesurfaceisbypureconduction,sincethefluidlayerismotionless,itcanbeexpressedas)W/m(20yfluidcondconvyTqq)KW/(m20ywfluidyTTThthermalconductivityofthefluid2020/4/165WhatisthephysicalsignificanceoftheNusseltnumber?TheNusseltnumberrepresenttheenhancementofheattransferthroughafluidlayerasaresultofconvectionrelativetoconductionacrossthesamefluidlayer.ThelargertheNusseltnumber,themoreeffectiveistheconvection.NuhTThqqfluidfluidcondconv/2020/4/166二、分析方法),,,,,(lcufhb.近似积分法d.比拟法a.解析法c.实验法e.数值法三、研究内容1.强制对流（3）管外流体流动（2）管内流体流动（1）流体外掠平板2.自然对流a、bc3.相变对流2020/4/167Velocityboundaryandboundarylayeruy8VelocityboundaryandboundarylayerReynoldsnumberThevalueofcriticalReynoldsnumberisdifferentfordifferentgeometries.TheReynoldsnumberatwhichtheflowbecomesturbulentiscalledthecriticalReynoldsnumber.Characteristiclength2020/4/16粘性力惯性力Re2020/4/169※分类层流边界层：紊流边界层：惯性力粘性力惯性力粘性力5100.5Reuxx5100.5ReuxxVelocityboundaryandboundarylayerThecriticalReynoldsnumber粘性力惯性力RecriticalReynoldsnumber2020/4/1610Laminersublayer※边界层中的质量流量0dyuqm二、热边界层twwtttt时厚度为令99.0Thermalboundaryandboundarylayer11Thermalboundaryandboundarylayer2020/4/1612ThermalboundaryandboundarylayerPrandtlnumberFluidPrLiquidmetalsGasesWaterLightorganicfluidsOilsGlycerin0.004–0.0300.7–1.01.7–13.75–5050–100,0002000–100,000Isapropertyoftemperature2020/4/16甘油2020/4/1613三、与关系taPrta，时1Prta，时1Prta，时1Pr热量扩散率动量扩散率ThePrandtlnumberisameasureoftherelativemagnitudesofthediffusivityofmomentum(andthusthedevelopmentofthevelocityboundarylayer)andthediffusivityofheat(andthusthedevelopmentofthethermalboundarylayer).ThePrisafluidproperty,andthusitsvalueisindependentofthetypeofflowgeometry,ThePrchangeswithtemperature,butnotpressure.aPraPr2020/4/1615§5.3流体外掠平板对流换热分析解一、微分方程组的一般形式假设：（1）二维（2）不可压缩性（3）稳定（4）常物性（5）粘性耗散热忽略不计（一）质量守恒定律0yvxu（连续性方程）2020/4/1616（二）动量守恒定律2222yuxuxpFyuvxuuux2222yvxvypFyvvxvuvy动量变化体积力表面力压力梯度粘滞力2020/4/1617（三）能量守恒定律2222ytxtcytvxtutp非稳态项对流项扩散项内热源项（四）换热微分方程0yytthq0yytthdxdPxPandonly,)x(fPthen0yP2020/4/1618二、简化1.稳定流动：0tvu2.强制对流：0yxFF4.层流边界层：vu；xvxu2222xvxu；yvyu2222yvyu3.外掠平板：2020/4/16195.很小：；xuyu2222xuyu；xtyt2222xtyt6.无内热源2020/4/16200yvxu22yuyuvxuu22ytaytvxtu0yytth未知变量vu、th2020/4/1621三、定解条件0,00vuy时uuy时uux时01.速度边界层VelocityBoundaryLayer2020/4/1622三、定解条件wtty时0tty时ttx时02.热边界层TTsThermalBoundaryLayer2020/4/1623四、求解结果1.局部表面传热系数3121332.0avvxuxhx3121PrRe332.0xxxhxxNu2.平均表面传热系数31210PrRe664.021lhdxhlhllx3121PrRe664.02xNuNu3121PrRe332.0x层流边界层5100.5Re2020/4/1624※讨论hlNu1.称为努塞尔数2.特征长度：板长l3.定性温度：wmttt214.适用范围：层流边界层3121PrRe664.0Nu5100.5Re意义：大小反映平均对流换热的强弱251)速度场xuxRe2)流动边界层厚度xRex0.52020/4/1626273)摩擦系数由速度分布求出局部粘性切应力局部摩擦系数平均摩擦系数ulRe1/2f,0.664xxCRe1/2f1.328CRexxfReuC664.0221w,RexClClxff328.1d10,xuxRe4)流动边界层与热边界层之比31Prt2020/4/1628复习hlNu1.称为努塞尔数2.特征长度：板长l3.定性温度：wmttt214.适用范围：层流边界层5100.5Re意义：大小反映对流换热的强弱31216640PrRe.Nu※流体外掠平板时※边界层15/10/2012Thermofluids-II-L3Y.Y.Yan29Asimplequestion6.228602624.02301lhNu6.228602624.002.02hhdNu1.2.K)W/(m300022h2020/4/1630§5.4流体外掠平板的近似积分求解及比拟理论一、求解u332210yayayaau设边界条件00022yuuy，且时，0yuuuy，且时，,00a,231ua,02a232ua32123yyuu（一）流体外掠平板传热层流分析解2020/4/1631二、求00ywyudyuuudxd动量积分方程xxRe0.52020/4/1632三、求t332210ybybybbt令边界条件0022ytttyw，且时，0ytttyt，且时，,0wtb,231twttb,02b3321twttb32123ttwwyytttt2020/4/1633四、求t00yytadyttudxdt能量积分方程31Prt2020/4/1634（二）比拟法（紊流）动量fc热量hNuNucfTherelationbetweenfluidfrictionandheattransfer.(forturbulentboundarylayer)比较无量纲动量微分方程式和能量微分方程式221UUUUVXYReY221UVXYRePrY00()yduuuudydxyt00()ydtttudyadxy35221UUUUVXYReY221UVXYRePrY当Pr=1时，两方程的形式完全相同。对于同一对流换热现象，二者具有相同的几何条件和物理条件，如果边界条件也相同，如：Y=0:U=0、=0；Y:U1、1，则无量纲速度分布