Page 180 - Mechanical Engineers' Handbook (Volume 4)

2 Convection Heat Transfer 169

Nu 0.023 Re 0.8 Pr n
D
D
for 0.7 Pr 160, Re 10,000, and L/D 60, where
D
n 0.4 for heating, T T b
s
0.3 for cooling, T T b
s
For temperature differences greater than specified above, use 5
Nu 0.027 Re Pr 0.14

0.8
1 / 3
D
D
s
for 0.7 Pr 16,700, Re 10,000, and L/D 60. In this expression, the properties are
D
all evaluated at the mean bulk fluid temperature with the exception of , which is again
s
evaluated at the tube surface temperature.
For concentric tube annuli, the hydraulic diameter D D D (outer diameter
i
h
o
inner diameter) must be used for Nu and Re , and the coefficient h at either surface of the
D
D
annulus must be evaluated from the Dittus-Boelter equation. Here, it should be noted that
the foregoing equations apply for smooth surfaces and that the heat-transfer rate will be
larger for rough surfaces, and are not applicable to liquid metals.
Fully Developed Turbulent Flow of Liquid Metals in Circular Tubes
Because the Prandtl number for liquid metals, is on the order of 0.01, the Nusselt number
is primarily dependent on a dimensionless parameter number referred to as the Peclet number,
which in general is defined as Pe RePr:
Nu 5.0 0.025Pe 0.8
D
D
which is valid for situations where T a constant and Pe 100 and L/D 60.
s
D
5
2
3
For q constant and 3.6 10 Re 9.05 10 ,10 Pe 10 , and L/D
4
D
D
60, the Nusselt number can be expressed as
Nu 4.8 0.0185Pe 0.827
D
D
2.2 Forced Convection—External Flow
In forced convection heat transfer, the heat-transfer coefficient, h, is based on the temperature
difference between the wall surface temperature and the fluid temperature in the free stream
outside the thermal boundary layer. The total heat-transfer rate from the wall to the fluid is
given by q hA (T T ). The Reynolds numbers are based on the free stream velocity.

s
The fluid properties are evaluated either at the free stream temperature T or at the film

temperature T (T T )/2.
ƒ

s
Laminar Flow on a Flat Plate
When the flow velocity along a constant temperature semi-infinite plate is uniform, the
boundary layer originates from the leading edge and is laminar and the flow remains laminar
until the local Reynolds number Re U x/v reaches the critical Reynolds number, Re .

x
c
When the surface is smooth, the Reynolds number is generally assumed to be Re 5
c
5
10 , but the value will depend on several parameters, including the surface roughness.
For a given distance x from the leading edge, the local Nusselt number and the average
5
Nusselt number between x 0 and x L are given below (Re and Re 5 10 ):
x
L