Page 57 - Design and Operation of Heat Exchangers and their Networks

44 Design and operation of heat exchangers and their networks

c p,h,2 ¼ 4:201 kJ=kgK,λ h,2 ¼ 0:6703 W=mK,μ ¼ 3:313 10 4 sPa,
h,2
Pr h,2 ¼ 2:076
At the first reference temperature,
Re h,1 ¼ G h d i =μ ¼ 390:5 0:016=2:912 10 4 ¼ 21456
h,1
2 2
f h,1 =8 ¼ 1:82lg Re h,1 Þ 1:64½ ð Š =8 ¼ 1:82lg 21456Þ 1:64Š =8
½
ð
¼ 0:003207
" #
2=3
ð
ð f h,1 =8Þ Re h,1 1000ÞPr h,1 d i 0:11
Nu h,1 ¼ 1+ ð Pr h,1 =Pr w,1 Þ
p ffiffiffiffiffiffiffiffiffiffiffi 2=3
1+12:7 f h,1 =8 Pr 1 L
h,1
" #
2=3
0:003207 21456 1000Þ 1:815 0:016 0:11
ð
¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=3 1+ ð 1:815=1:815Þ
1+ 12:7 0:003207 1:815 1 2:701
¼ 91:01
2
α h,1 ¼ Nu h,1 λ h,1 =d i ¼ 91:01 0:6760=0:016 ¼ 3845 W=m K
1
1 d i
k i,1 ¼ + R w,i,1 +
α h,1 α c d o
1
1 5 0:016 2
¼ +2:356 10 + ¼ 1141 W=m K
3845 1500 0:018
ð
t h,w,1 ¼ t h,1 k i,1 t h,1 t c,1 Þ=α h,1 ¼ 96:84 1141 96:84 62:11ð Þ=3845
¼ 86:54°C
Similarly, at the second reference temperature, we can obtain
2
Re h,2 ¼18,859, f h,2 ¼0.003314, Nu h,2 ¼87, α h,2 ¼3645W/m K,
2
k i,2 ¼1123W/m K, and t h,w,2 ¼69.48°C.
The mean overall heat transfer coefficient is calculated by Eq. (2.89):
2 2 2
k i,m ¼ ¼ ¼ 1132 W=m K
1=k i,1 +1=k i,2 1=1141 + 1=1123
Since (kA) i ¼k i,m πd i L, the tube length can be determined as
ð kAÞ i 8087
L ¼ ¼ ¼ 2:681 m
k i,m N tube πd i 1132 53 π 0:016
With the newly calculated tube length L and wall temperatures at the tube
inside t h,w,1 and t h,w,2 for the calculation of Pr h,w,1 and Pr h,w,2 ,we can
recalculate the Gnielinski correlation and repeat the earlier steps. After
several iterations, the calculation converges to L¼2.697m. The result
shows that in this case, the common calculation method is sufficiently accurate.
The detailed calculation can be found in the MatLab code for Example
2.6 in the appendix.