Page 31 - Design and Operation of Heat Exchangers and their Networks

18 Design and operation of heat exchangers and their networks

0.98% at RePrd/L¼2500. As is shown in Fig. 2.1, this equation offers us the
best fitting with the analytical solution.
An empirical equation of Hausen for the mean Nusselt number was
given by Stephan (1959):

0:0668RePrd=L
Nu T ¼ 3:65 + (2.10)
2=3
ð
1+0:045 RePrd=LÞ
5
The maximum deviation of this equation in 0.1<RePrd/L<10 is
4
+2.9% at RePrd/L¼1600. However, if RePrd/L is larger than 2 10 ,
Eq. (2.10) becomes lower than the analytical solution, and the relative
deviation approaches to 8.1% when RePrd/L!∞.
Another empirical equation of Hausen was presented by Stephan and
Nesselmann (1961) as

0:8
ð
0:19 RePrd=LÞ
Nu T ¼ 3:65 + (2.11)
0:467
1+0:117 RePrd=LÞ
ð
Its maximum deviation in 0.1<RePrd/L<10 6 is +9.6% at
RePrd/L¼15 but approaches to the analytical solution for RePrd/L!∞.
For detailed simulation of heat exchangers, especially evaporators and
condensers, local heat transfer coefficient might be required for the

10 3
Nu T , analytical solution (Shah and London, 1978, Table 13)
Nu T , Eq. (2.9) (Gnielinski, 1989)
Nu T , Eq. (2.10) (Stephan, 1959)
Nu T , Eq. (2.11) (Stephan and Nesselmann, 1961)
Nu x,T , analytical solution (Shah and London, 1978, Table 13)
10 2 Nu x,T , Eq. (2.12) (Gnielinski, 2010a, 2013a)
Nu T , Nu x,T

10

1
0.1 1 10 10 2 10 3 10 4 10 5 10 6
RePrd/x
Fig. 2.1 Local and mean Nusselt number Nu x,T and Nu T for thermally developing and
hydrodynamically developed laminar flow.