Page 52 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 39

The heat transfer coefficient inside the tube can be established by
2
α h ¼ Nu h λ h =d i ¼ 85:84 0:6728=0:016 ¼ 3610 W=m K
The outside diameter of the tube d o ¼d i +2δ w ¼0.016+2 0.001¼
0.018m.
The conductive thermal resistance of the tube wall per unit inner area is
calculated from Eq. (2.63):

d i ln d o =d i Þ 0:016 ln 0:018=0:016Þ 5 2
ð
ð
R w,i ¼ ¼ ¼ 2:356 10 m K=W
2λ w 2 40
Using Eq. (2.61), we have the expression of the overall thermal
resistance as
1 1 R w 1 1 R w 1
¼ + + ¼ + +
ð kAÞ α h N tube πd i L N tube πd i L α c N tube πd o L
i α h A i A i α c A o
which yields

ð kAÞ i 1 d i
L ¼ + R w,i +
N tube πd i α h α c d o

8087 1 5 0:016
¼ +2:356 10 + ¼ 2:711m
53 π 0:016 3610 1500 0:018
and
ð kAÞ i 8087 2
k i ¼ ¼ ¼ 1120 W=m K
N tube πd i L 53 π 0:016 2:711
According to the energy equation,
ð
ð
q ¼ α h t h t h,w Þ ¼ k i t h t c Þ
we can express the mean wall temperature at the tube inside as
ð
t h,w ¼ t h k i t h t c Þ=α h
therefore, we have

t c,m ¼ 20 + 70ð Þ=2 ¼ 45°C
ð
t h,w,m ¼ t h,m k i t h,m t c,m Þ=α h ¼ 90 1120 90 45ð Þ=3610
¼ 76:04°C
With the newly calculated tube length L and wall temperature at the
tube inside t h,w,m for the calculation of Pr w , we can recalculate the
Gnielinski correlation and repeat the earlier steps. After several iterations,
the calculation converges to L¼2.701m. For a conservative design, we
would like to enlarge the area by about 30% and set the tube length to
be L¼3.5m.
The detailed calculation can be found in the MatLab code for Example
2.4 in the appendix.