Page 54 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 41

t h,w,m ¼ t h,m k i t h,m t c,m Þ=α h ¼ 90 1120 90 45Þ=3709
ð
ð
¼ 76:30°C
This temperature is used for the calculation of Pr w appearing in the
Gnielinski correlation.
The logarithmic mean temperature difference for the parallel-flow
arrangement is

0
00
0
t t t t 00 c ð 100 20Þ 80 70Þ
ð
h
c
h
Δt LM,p ¼ ¼ ¼ 33:66 K
00
0
ln t t = t t 00 ln 100 20Þ= 80 70ފ
0
ð
ð
½
h c h c
Now, we shall use Eq. (2.68) to check the heat duty:
Q 0 ðÞ ¼ k i N tube πd i LΔt LM,p ¼ 1129 10 3 53 π 0:016 3:5 33:66
¼ 354:4kW
Because the calculated heat duty does not agree with its demanded
value, we shall change the flow rate of the hot water by correcting the
outlet temperature of the hot water:
Q n ðÞ 354:4
0
t 00 n +1ð Þ ¼ t t t 00 nðÞ ¼ 100 ð 100 80Þ ¼ 79:75°C
0
h h h h
Q 350
With the newly calculated hot water outlet temperature and wall
temperature at the tube inside t h,w,m for the calculation of Pr w , we can
repeat the earlier calculation. After several iterations, we finally obtain
the outlet temperature and mass flow rate of the hot water:
t ¼ 79:87°C
00
h
Q 350
_ m h ¼ ¼ ¼ 4:134 kg=s
0
c p,h t t 00 h 4:206 100 79:87Þ
ð
h
It is interesting to compare the parallel-flow arrangement with the
counterflow arrangement. If we connect the water streams to the heat
exchanger as a counterflow heat exchanger, that is,

00
t t 00 c t t c 0 ð 100 70Þ 80 20Þ
0
ð
h
h
Δt LM, cf ¼ ¼ ¼ 43:28K
ln t t = t t 0 ln 100 70Þ= 80 20ފ
0
00
00
ð
½
ð
h c h c
00
After several iterations, the calculation results in t h ¼68.83°C and
_ m h ¼ 2:673 kg/s, which are much lower than those in the parallel-flow
heat exchanger.
The detailed calculation can be found in the MatLab code for Example
2.5 in the appendix.