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Heat Transfer

Heat Transfer. --- Chapter 10 Convection ---. Chapter 10 Convection. Contents Influence factors of convection heat transfer Differential convection equations Velocity boundary layer and thermal boundary layer Experimental method of convection heat transfer

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Heat Transfer

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  1. Heat Transfer --- Chapter 10 Convection ---

  2. Chapter 10 Convection Contents • Influence factors of convection heat transfer • Differential convection equations • Velocity boundary layer and thermal boundary layer • Experimental method of convection heat transfer • Forced and natural convections ( external forced convection, internal forced convection, natural convections)

  3. 若流体被加热: • 若流体被冷却: 10-1 Introduction 10-1-1 Basic Conceptions 1. Convection heat transfer(对流换热) 流体流过另一个物体表面时,对流和导热联合起作用 的热量传递现象。 2. Newton’s law of cooling(牛顿冷却公式) 平壁表面的传热机理

  4. d 管内流动 tf • h — the average convection heat transfer coefficient (固体表面的平均表面换热系数) W/m2.K • tw — the average temp of solid surface (固体表面的平均温度) • tf — the temp of fluid(流体温度) • 外部绕流(外掠平板,圆管): • tf为流体的主流温度。 • 内部流动(各种形状槽道内的流动): • tf为流体的平均温度。

  5. 4Local heat-transfer coefficient(局部表面传热系数) and average heat-transfer coefficient • For local convection heat transfer • For the whole heat transfer surface tw-tf = Const • Average heat-transfer coefficient 对流换热的核心问题

  6. For air h Natural flow Forced flow 10-1-2 Influence Factors(对流换热的影响因素) 1. Natural versus Forced Flow(强迫对流,自然对流) Depending on how the fluid motion is initiated • Forced flow -- flow generated by external means (pump, fan) • Natural flow-- flow induced by buoyancy forces – arise from • density differences generated by temp. variations.

  7. Example Oils-- the flow of high-viscosity fluid at low velocities is typically laminar. 2. Laminar versus Turbulent Flow(层流流动,湍流流动) • Laminar flow • 流速缓慢 • 沿轴线或平行于壁面作规则分层运动 • 热量传递:主要靠导热(垂直于流动方向)

  8. 湍流边界层 层流底层:导热 • 湍流核心区:对流 Example Air-- the flow of low-viscosity fluid at high velocities is typically turbulent. • Turbulent flow • 流体内部存在强烈脉动和旋涡运动 • 各部分流体之间迅速混合 • 热量传递:主要靠对流 对流 导热

  9. fluid motion induced by vapor bubbles generated at the bottom of a pan of boiling water Condensation of water vapor on the outer surface of a cold water pipe • Boiling and condensation convection heat transfer • (有相变的换热(沸腾, 凝结))

  10. 体积热容 :单位体积流体热容量的大小 常温下:水 空气 常温下:水 空气 4. Physical properties of fluid(流体的热物理性质) 对对流换热的强弱有非常大的影响。 • Density and heat capacity 换热能力强 • Conductivityλ • 影响流体内部的热量传递过程和温度分布 • λ越大,导热热阻越小,对流换热越强烈 冷却能力强

  11. Viscosityμ • 影响速度分布与流态( Laminar , turbulent flow ) • μ越大,分子间约束越强,相同流速不易发展成湍流状态 • 高粘度流体(oils)多处于层流状态,h较小 • The volume expansion coefficient α(体积膨胀系数) Reference temperature (定性温度) • 对自然对流换热有很大影响 • 影响重力场中因密度差而产生的浮升力大小

  12. d 管内流动 5. The surface geometric conditions (换热表面的几何因素) • surface geometry shape, size, relative position, • surface roughness and so on. Characteristic length 特征长度 • 对对流换热有显著影响 • 影响流态,速度分布,温度分布

  13. 浮升力项包含的因子 From above • Influence factors of convection heat transfer • For Forced flow • For Natural flow

  14. 10-1-3 Analysis Method of Convection Heat Transfer • Analysis method(分析法) 求解对流换热的微分方程,积分方程及单值性条件, 得出精确解或近似解。适用简单问题。 • Numerical method(数值法) 对对流换热过程的特征和主要参数变化趋势作出预测。 复杂问题。 • Experimental method(实验法) 相似原理和量纲分析理论。 • Analogy between momentum and heat transfer(比拟法) 利用流体动量传递和热量传递的相似机理。

  15. Assume • The fluid is incompressible • Constant properties (density, viscosity, thermal • conductivity, etc.) • The fluid to be Newtonian(牛顿流体) • No heat generation • Two-dimensional convection heat transfer 10-2 Differential Convection Equations 10-2-1 Differential Convection Equations(对流换热微分 方程组)and Condition of Single Valuedness • Conservation of mass equation(连续性方程) • Conservation of momentum equation(动量方程) • Conservation of energy equation(能量方程)

  16. Velocity distribution • Three-dimensional flow • Two-dimensional flow 1. Continuity equation(连续性方程) • From the conservation of mass principle of volume element 1D flow? 2.Momentum differential equation(动量微分方程) (Navier-Stokes equation) • From the conservation of momentum of volume element In 1823, Navier (French) In 1845, Stokes (England)

  17. x-direction 粘性力 压力梯度 体积力 惯性力 • y-direction Note Consider gravity field only Where • Forced flow: gravity is negligible • Natural flow: buoyancy forces is important

  18. 对流项 导热项 非稳态项 or • For a stationary fluid 3. Energy differential equation(能量微分方程) • From the conservation of energy of volume element Conduction differential equation

  19. Differential convection equations • Unknown quantity • Applicability • Natural and forced flow • Laminar and turbulent flow

  20. The local heat flux at the wall From Newton’s law of cooling • Local convection heat-transfer coefficient • Average convection heat-transfer coefficient Conductivity of fluid (流体的导热系数) 4. Convection heat transfer differential equation (换热微分方程) Temperature field

  21. (3) Condition in time(时间条件) • steady-state:no initial condition(无初始条件) • unsteady state: initial condition 5. Condition of single valuedness of convection heat- transfer(对流换热的单值性条件) (1) Geometric condition (几何条件) the geometry shape and the dimension size of heat-transfer surface. (2) Condition in physical property (物理条件) physical property of fluid(ρсλ), heat sources or no heat generation.

  22. The first kind boundary condition(第一类边界条件) • ----- temperature boundary condition 对比导热的 边界条件 Constant temp B.C • The second kind boundary condition(第二类边界条件) • ------heat flux boundary condition Constant heat rate B.C (4) Boundary condition(边界条件) velocity distribution and temperature distribution imposed at the convection heat transfer boundary 说明对流换热边界上的状态(边界上速度分布,温度分布 及与周围环境之间的相互作用)

  23. 10-2-2 Theory of Boundary Layer(边界层理论) 1. Velocity boundary layer(流动边界层) • 1904年,德国科学家普朗特(Ludwig Prandtl 1875~1953) • 提出著名的边界层概念。 • Velocity boundary layer • The region of flow that develops from the leading edge of • the plate in which the effects of viscosity are observed. • Consider:the parallel flow of a viscosity fluid over • a flat plate(流体平行外掠平板的对流换热) 边界层厚度δ: u=0.99u∞ 边界层特点 δ<< l no-slip condition u y=0= 0

  24. Flow field(流场分区) • Velocity boundary layer region(边界层区) • 速度梯度大,粘性力不能忽略 ; • 粘性力与惯性力处同一数量级; • 动量交换的主要区域,用动量微分方程描述。 • Free stream region(主流区) • 速度梯度趋于零,粘性力忽略不计; • 流体可近似为理想流体; • 用理想流体的欧拉方程描述。

  25. Transition point ( 转戾点) • Structure of turbulent boundary layer • (湍流边界层的三层结构模型) 外掠平板 • Laminar sublayer(层流底层) • Buffer layer(缓冲层) • Turbulent region(湍流核心区) 管内流动 • Development of boundary layer • Laminar boundary layer • (层流边界层) • Transition region(过渡区) • Turbulent boundary layer • (湍流边界层)

  26. The thickness of the thermal • boundary layerδt 2. Thermal boundary layer(热边界层) • 1921年,波尔豪森(Pohlhausen)提出。 • Thermal boundary layer • The region where temp gradients • are present in the flow. • Temperature field(温度场分区) • 热边界层区 • 存在温度梯度,发生热量传递的主要区; • 温度场由能量微分方程描述。 • 主流区 • 温度梯度不计,近似等温流动。

  27. 表面传热系数 3. The relationship between velocity boundary layer and thermal boundary layer • Fluid velocity will have a strong influence on the • temperature profile(流体温度分布受速度分布影响) • The change of local heat transfer coefficient 对流 导热 导热 热阻增大 导热热阻增大 扰动

  28. Definition • When , • When , • When , • Prandtl number(普朗特准数) • Meaning the ratio of molecular diffusivity of momentum to the molecular diffusivity of heat. (流体的动量扩散能力与热量扩散能力之比) • For laminar boundary layer 若热边界层和流动边界层 从平板前缘点同时发展 • Liquid metals 0.05 • Gas 0.6-0.8 • Heavy oils 102-103 • The value of Pr: for most fluid: 0.6—4000

  29. 4. Characteristics of boundary layer • The thickness of boundary layerδ<< l (x); δt<<l (x) • The flow field is divided into two regions • boundary layer region • free stream region • Two types of boundary layer • laminar boundary layer • turbulent boundary layer • Three-layer structure model of turbulent boundary layer • laminar sublayer • buffer layer • turbulent region • Characteristics of heat transfer • laminar layer—conduction • laminar sublayer -- conduction • turbulent region -- convection

  30. Differential convection equations 10-2-3 Differential Convection Equations of Boundary Layer(边界层内对流换热微分方程组) • Consider:constant properties, no heat generation, • incompressible Newtonian fluid, 2D flow.

  31. Further consider:steady state, 2D forced flow • (gravity field is negligible) • Differential convection equations are therefore

  32. First define • Then have • And • Continuity equation • How to simplified differential convection equations • in the boundary layer ---- Base upon dimensional or order-of-magnitude analysis(数量级分析)

  33. x-direction • Energy differential equation(能量微分方程) • Momentum differential equation(动量微分方程) • y-direction negligible

  34. Convection heat transfer differential equation(换热方程) • Differential convection equations in the boundary layer • (边界层内对流换热微分方程组) 未知数: u,v,p,t • Bernoulli equation out of the boundary layer • (边界层外伯努利方程) 可求温度分布 求出表面 传热系数

  35. 在流体温度边界层中,何处温度梯度 • 的绝对值最大?为什么? 2. 对流换热边界层微分方程组是否适用于 粘度很大的油和Pr数很小的液态金属。

  36. 10-3 Solution of Laminar Boundary Layer on a Flat Plate of Constant Temp (流体外掠等温平壁层流对流换热分析解简介) • Differential convection equations in the boundary layer 适用 不适用 • Applicability: flow of boundary layer

  37. 布拉修斯(H.Blasius)解 • 波尔豪森(E.Pohlhausen)解 • 偏微分方程-常微分方程 u v t δδt cf hx h qx q • Consider: • constant properties, • no heat generation, • incompressible Newtonian fluid, • steady two-dimensional parallel • flow over a flat plate. • Differential convection equations in the boundary layer

  38. where • Local friction coefficient • Average friction coefficient 10-3-1 Solution of Velocity Field 1. Thickness of velocity boundary layer 2.Friction coefficient(摩擦系数)

  39. Laminar flow 10-3-2 Solution of Temperature Field 1. Thickness of thermal boundary layer 2.Nondimensionalized equation(特征数关联式) (1) For an isothermal surface thus

  40. Nusselt number(努塞尔特准数) • Average Nusselt number • Average heat-transfer coefficient Tw=const • Applicability: laminar heat transfer • surface temp is constant • Pr≥0.6

  41. qw=const • Average Nusselt number • Average temp difference along the plate (2) For a constant heat flux surface • Local Nusselt number • Applicability: laminar heat transfer • surface heat flux is constant • Pr≥0.6

  42. 例 10-1 20℃的空气在常压下以10m/s的速度流过平板, 板表面温度tw=60℃,求距平板前缘200mm处的 速度边界层厚度和温度边界层厚度δ,δt. 以及 表面换热系数h, hx和单位宽度的换热量。

  43. 简单求解过程: 解:定性温度 以此为定性温度查40℃空气的物性参数: 求雷诺数: 属层流 。 故可求解: 局部Nu数: 解得: 单位宽度的换热量:

  44. Example10-2 Air at 27℃ and 1atm flows over a flat plate at a speed of 2m/s. Calculate the boundary-layer thickness at distances of 20 and 40cm from the leading edge of the plate. Assume that the plate is heated over its entire length to a temperature of 60 ℃. Calculate the heat transferred in (a) the first 20cm of the plate and (b) the first 40cm of the plate.

  45. 10-4 对流换热的实验研究方法 • 对流换热问题的主要任务之一就是确定各种情况下的表面传热系数及其影响因素。求解的基本方法主要有分析解法,数值解法,实验解法及比拟理论。 • 到目前为止,相似原理指导下的实验研究方法仍是解决复杂对流换热问题的可靠方法。运用相似原理可以将影响对流换热过程的各种物理量组合成无量纲的特征数,如Nu, Re, Pr等,这样不仅使问题的自变量数目减少,大大简化实验研究工作,而且对扩大实验结果的应用范围大有益处。

  46. b’ b’’ a’ a’’ c’ c’’ τ τ 10-4-1相似概念 1. 几何相似(空间相似) 几何体的各对应边成比例。 式中:Cl为几何相似倍数。 • 几何相似体现了空间相似,是两现象相似的必要条件之一。 2. 时间相似 过程进行的对应时间间隔成比例。

  47. 速度场: • 温度场: • 物理常量场: 3. 物理量相似 物理量场一般指速度场,温度场,导热系数场,   密度场等。 物理量相似是指两现象在空间相似的前提下, 各对应物理参量在空间对应点和时间对应间隔上 互成比例。

  48. 10-4-2相似原理 • 从事模型实验研究,需要解决三个问题: • 实验研究应当测量哪些参量? • 如何对测量结果进行数据的整理和加工? • 如何作到模型现象和原型相似? • 相似三定理可回答(相似原理的核心内容): • 物理现象相似的性质; • 相似准数间的关系; • 判断相似的充要条件。

  49. 1. 相似第一定理 彼此相似的现象,它们的同名准数必定相等。 • 相似现象的性质: • 相似现象必属同类现象,可用文字和形式 完全相同的完整方程组描述; • 相似现象必定发生在几何相似的空间; • 用来表征现象的对应物理量场相似; • 各相似倍数间具有约束关系。

  50. 以对流换热为例,说明相似的性质及准 数的导出:对流换热现象A和B相似。 举例 • 根据换热微分方程: • 现象A: • 现象B: • 对应的物理量场应相似:

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