Page 32 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 19

determination of local heat flux and wall temperature distributions. An
asymptote can be used for local Nusselt number (Gnielinski, 2010a, 2013a)
h i 3
3
3
Nu 3 ¼ 3:66 +0:7 +1:077 RePrd=xÞ 1=3 0:7 (2.12)
ð
x,T
6
The maximum deviation of Eq. (2.12) in 0.1<RePrd/x<10 is +6.2%
at RePrd/x¼25.
For constant heat flux boundary condition (H), the local Nusselt number
can be expressed as (Gnielinski, 2010a, 2013a)
h i 3
3
Nu 3 ¼ 4:354 +1+ 1:302 RePrd=xÞ 1=3 1 (2.13)
ð
x,H
6
The maximum deviation of Eq. (2.13) in 5<RePrd/L<10 is 4.0% at
RePrd/L¼200.
Shah and London (1978) recommended a combination of their work and
the approximate equation of Grigull and Tratz (1965) as follows:
8
1=3
ð
ð
1:302 RePrd=xÞ 1, x= dRePrÞ 0:00005
>
>
< 1=3
1:302 RePrd=xÞ 0:5, 0:00005 < x= dRePrÞ < 0:0015
ð
ð
Nu x,H ¼ 0:506
ð
ð
> 4:364 + 8:68 0:001RePrd=xÞ x= dRePrÞ 0:0015
>
:
ð
e 41= RePrd=xÞ ,
(2.14)
4
which has the maximum deviation of 1.0% around RePrd/x¼10 .
With a similar asymptote of Gnielinski, the mean Nusselt number can be
calculated from (Gnielinski, 2010a, 2013a):
h i 3
3 3 3 1=3
Nu ¼ 4:354 +0:6 +1:953 RePrd=Lð Þ 0:6 (2.15)
H
6
of which the maximum deviation in 0.1<RePrd/L<10 is 0.89% at
RePrd/L¼50.
A comparison among these correlations is shown in Fig. 2.2. It is inter-
esting to notice that the experimental correlation of the mean Nusselt num-
ber of Sieder and Tate (1936)
1=3 0:14
Nu ¼ 1:86 RePrd=LÞ ð μ=μ Þ ð Re < 2200, 0:0044 < μ=μ < 9:75,
ð
w
w
and RePrd h =L > 10Þ (2.16)
is close to the analytical solution for uniform heat flux boundary condition.
Their experiments were carried out in a concentric-tube heat exchanger.
The inner tube had a total length of 27.7m including a calming section