Page 51 - Design and Operation of Heat Exchangers and their Networks

38 Design and operation of heat exchangers and their networks

Thermal conductivity of liquid water at 1bar (Huber et al., 2012)isas
follows:

4
X
a i
λ ¼ ð W=mKÞ 0°C t 110°CÞ (2.82)
ð
b i
i¼1 ð ½ t + 273:15Þ=300Š
with a i ¼1.663, 1.7781, 1.1567, and 0.432115 and b i ¼1.15, 3.4, 6.0,
and 7.6, respectively.
Dynamic viscosity of liquid water at 1bar (Pa ´tek et al., 2009)isas
follows:
4
X a i
6
μ ¼ 10 ð sPaÞ 20°C t 110°CÞ (2.83)
ð
b i
i¼1 ð ½ t + 273:15Þ=300Š
with a i ¼280.68, 511.45, 61.131, and 0.45903 and b i ¼1.9, 7.7, 19.6,
and 40, respectively.
With these equations, we have the necessary fluid properties at the mean
temperature of hot water, t h,m ¼(100+80)/2¼90°C as follows:
c p,h ¼ 4:206kJ=kgK,λ h ¼ 0:6728 W=mK,μ ¼ 3:142 10 4 sPa,
h
Pr h ¼ c p,h μ =λ h ¼ 1:964:
h
According to the given heat duty, we can calculate the mass velocity
inside the tubes by

0
Q= c p,h t t 00
ð
½
_ m h h h 350= 4:206 100 80ފ
G h ¼ ¼ 2 ¼ 2
A c,h N tube πd =4 53 π 0:016 =4
i
2
¼ 390:5kg=m s
The tubeside Reynolds number is
Re h ¼ G h d i =μ ¼ 390:5 0:016=3:142 10 4 ¼ 19;886
h
Since it is in the turbulent flow region, so we will use the Gnielinski
correlation, Eq. (2.33), to calculate the Nusselt number and assume at
first the correction term is equal to 1:
2 2
ð
½
f =8 ¼ 1:82 lg Re h Þ 1:64½ ð Š =8 ¼ 1:82 lg 19;886Þ 1:64Š =8
¼ 0:003269
" #
2=3
ð
ð f =8Þ Re h 1000ÞPr h d i 0:11
Nu h ¼ p ffiffiffiffiffiffiffi 2=3 1+ ð Pr h =Pr w Þ
1+ 12:7 f =8 Pr 1 L
h
" #
2=3
0:003269 19, 886 1000Þ 1:964 0:016 0:11
ð
¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=3 1+ ð 1:964=Pr w Þ
1+ 12:7 0:003269 1:964 1 L
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