Page 35 - Design and Operation of Heat Exchangers and their Networks
P. 35
22 Design and operation of heat exchangers and their networks
The local and mean Nusselt numbers in circular tubes with uniform heat
flux at the tube wall (H) can be expressed with similar asymptotes
(Gnielinski, 2010a, 2013a);
h i 3 h i 3
3
Nu 3 ¼ 4:354 +1:302 RePrd=xÞ 1=3 1 +0:462 Red=xÞ 1=2 Pr 1=3
ð
ð
x,H
(2.21)
h i 3
3 3 3 1=3
Nu ¼ 4:354 +0:6 +1:953 RePrd=Lð Þ 0:6
H h i 3
1=2 1=3
ð
+0:924 Red=LÞ Pr ð Pr > 0:7Þ (2.22)
Another available correlation was proposed by Churchill and Ozoe
(1973a):
n o 3=10
10=9
Nu x,H ¼ 5:364 1 + π=220ð½ ÞRePrd=x
33=10
2 0 1
5=3
ð π=115:2ÞRePrd=x
6 B C 7
1+ @4 A 5
h i 1=2 n o 3=5
2=3 10=9
ð
ð
1+ Pr=0:0207Þ 1+ π=220ÞRePrd=x
½
1 (2.23)
The curves of these equations for Pr¼0.7 and Pr¼10 are shown in
Fig. 2.4. The maximum deviation between Eqs. (2.20) and (2.23) is 6.5%
for Pr¼0.7 and 3.8% for Pr¼10.
10 3
Nu H , Eq. (2.22) (Gnielinski, 2010a, 2013a)
Nu x,H , Eq. (2.21) (Gnielinski, 2010a, 2013a)
Nu x,H , Eq. (2.23) (Churchill and Ozoe, 1973)
Pr = 0.7
10 2
Nu H , Nu x,H Nu H Pr = 10
10
Nu x,H
1
0.1 1 10 10 2 10 3 10 4 10 5 10 6
RePrd/x
Fig. 2.4 Local and mean Nusselt number Nu x,H and Nu H for thermally and
hydrodynamically developing laminar flow.
