Empirical and Practical Relations for Forced-Convection Heat Transfer Chapter 6 Empirical and Practical Relations for Forced-Convection Heat Transfer

6-2 Empirical relations for pipe and tube flow 6-1 Introduction 6-2 Empirical relations for pipe and tube flow Mean flow velocity 2. Laminar and turbulent flow Re<2300 laminar flow 2300<Re<104 transient region Re>104 turbulent flow

3. Bulk temperature Energy-averaged fluid temperature or mixing cup For constant physical properties The calculation of Tb needs the distribution of u. The practical method is to measure Tb after mixing.

4. Dittus-Boelter expression for fully developed turbulent flow in smooth tubes For heating of the fluid For cooling of the fluid Characteristic length, inside diameter Reference temperature, Applicability Fully developed Moderate temperature difference

（1）审题内容，确定类型。（2）定性温度，查取物性。 （3）计算准则，选用公式。（4）代入计算，考虑修正。 Example : Water is heated from 25.3℃ to 34.6 ℃ in a tube with a diameter of d=20mm and a length of 5m, the velocity is u=2m/s. Calculate the convection heat transfer coefficient. （1）审题内容，确定类型。（2）定性温度，查取物性。 （3）计算准则，选用公式。（4）代入计算，考虑修正。 Solution （1）Forced convection in tube （2）Reference temperature Physical properties: k=0.618W/(m.K), v=0.80510-6m2/s, Pr=5.42, ρ=995.7kg/m3, cp=4.17 kJ/kg （3）Calculate dimensionless group and choose equation For heating of the fluid n=0.4

(4) Calculation and correction Check whether the parameters are in the range of application

5. Qualitative analysis and correction (1)length Laminar flow x ,   , h Turbulent flow x ,   , h as turbulent growth h goes up and then down Entrance length of laminar L/d=0.05RePr For turbulent flow, the influence of entrance is negligible when L/d>60 If L/d<60 the effect of entrance must be considered. The method is

（2）Temperature b>a Φ 1≠Φ 2 Φ 2 liquids gases Φ 1 The value of n is different because physical properties liquids gases Take liquid as an example No heat transfer, velocity profile of fully developed flow is shown in curve1. If curve2 curve3

For gases, T has effects on  , , k, cP , the correction is Flow rate is constant. T  ,  ,   , du/dr  , dT/dr  Temperature has effect on heat transfer through laminar sublayer, heating q 1> q 2, or h1>h2. There is a difference between heating and cooling. If T is small, the difference is not large, it is exact enough to taken into account by n , that is Prn=(v/a)n。 If T is large, the following method is used. For liquids, T only has influence on  , the correction is For heating of the fluid For cooling of the fluid For gases, T has effects on  , , k, cP , the correction is

（3）bend R curvature radius The secondary flow enhances the heat transfer. gases liquids Example : Water is heated from 25.3℃ to 34.6 ℃ in a tube with a diameter of d=20mm and a length of 0.5m, the velocity is u=2m/s. Calculate the convection heat transfer coefficient. Solution: Except for L=0.5m, other conditions are the same with the last example. We have got h=7987 W/(m2K). L/d=0.5/0.02=25<60

Temperature difference correction Repeat this process until tw does not change

characteristic dimension: hydraulic (equivalent) diameter DH. 6. Convection in ducts characteristic dimension: hydraulic (equivalent) diameter DH. A—the cross-sectional area of the flow P — the wetted perimeter This method suitable for many cases There are some notable exceptions where the method does not work Annular tube Rectangular tube Tube bank

Information of fully developed laminar in ducts by Shah and Londun 7. Heat transfer in laminar tube flow Information of fully developed laminar in ducts by Shah and Londun

The characteristic of heat transfer in laminar duct flow Nuq=const>NuTw=const Nu is independent of Re Generally the h of ducts with different cross sections, the same DH are different Generally In practice, the flow in entrance is often laminar The length of entrance is Gz=RePrd/L=0.05 Graetz number The results is in fig. 6-5 7. Entrance effects in Turbulent flow We have considered it by L

6-3 Flow across cylinders and spheres Separation point at A -- frontal area of the body is the product of diameter and length Drag force

1. Correlation for heat transfer At Re of the order of 10, no flow separation At Re=70800～101300, laminar,φ↑,δ↑, h↓. At φ=82o, boundary layer separation causes turbulent eddy motion in the separated flow, φ↑， h ↑。 At Re>1.5×105 the flow is turbulent. Two minimum points of h are observed. The 1st occurs at the point of transition from laminar to turbulent, the 2nd occurs when the turbulent boundary layer separates atφ=130-140o because eddy motion.

Reference temperature (Tw+T∞)/2 Characteristic length d The constant C and n are given in Table 6-2 Other correlations equation (6-19) ～(6-24) 2. Choice of equations for cross flow over cylinders 3. Noncircular cylinders The constant are given in Table 6-3 4. Spheres Correlations equation (6-25) ～(6-30)

6-4 Flow across tube banks 10 or more rows of tubes in the direction of flow Reference temperature Characteristic length d Re is based on the umax For staggered If not The constant C and n are given in Table 6-4

For fewer rows the ratio of h for N rows deep to that for 10 rows is given in table 6-5

6-5 Liquid-metal heat transfer Self-learning Canceled

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