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

2. 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< laminar flow
2300<Re<104 transient region
Re> turbulent flow

3. 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. 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

5. （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

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

7. 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

8. （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

9. 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

10. （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

11. Temperature difference correction
Repeat this process until tw does not change

12. 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

13. 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

14. 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

15. 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

16. 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= o because eddy motion.

17. 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)

18. 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

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

20. 6-5 Liquid-metal heat transfer
Self-learning
Canceled

21. Thank you!