Page 56 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 43

between the inlet and outlet temperatures. Strong variations can be taken
into account by a refinement of the method (Roetzel, 1988).

Example 2.6 Sizing the counterflow heat exchanger in Example
2.4 considering variable tubeside heat transfer coefficient
The problem is the same as Example 2.4, however, with the consideration
of variable tubeside heat transfer coefficient depending on the fluid
temperature.
Solution
In Example 2.4, we have got d o ¼0.018m, (kA) i ¼8087W/K,
2
G h ¼390.5kg/m s, and R w,i ¼2.356 10 5 K/W. The shell-side heat
2
transfer coefficient is given as 1500W/m K. We will use Eq. (2.89) to
calculate the mean overall heat transfer coefficient k i .
According to Eqs. (2.86)–(2.88), we have

0 00 00 0
ð
θ ¼ t t = t t ¼ 100 70ð Þ= 80 20Þ ¼ 0:5
h
h
c
c
p ffiffiffi p ffiffiffi
m 1 ¼ 1=2+ 3=6 ¼ 0:7887,m 2 ¼ 1=2 3=6 ¼ 0:2113
θ 1 0:5 0:7887 1 θ 1 0:5 0:2113 1
m 2
m 1
ψ ¼ ¼ ¼ 0:8422,ψ ¼ ¼
1
2
θ 1 0:5 1 θ 1 0:5 1
¼ 0:2725
The two reference temperatures of hot water are obtained with
Eq. (2.84):

00
t h,1 ¼ t + ψ t t 00 ¼ 80 + 0:8422 100 80Þ ¼ 96:84°C
0
ð
h 1 h h

00
0
t h,2 ¼ t + ψ t t 00 ¼ 80 + 0:2725 100 80Þ ¼ 85:45°C
ð
h 2 h h
The two reference temperatures of cold water are obtained with
Eq. (2.85):

0 00 0
t c,1 ¼ t + ψ t t ¼ 20 + 0:8422 70 20ð Þ ¼ 62:11°C
c 1 c c

0 00 0
t c,2 ¼ t + ψ t t ¼ 20 + 0:2725 70 20ð Þ ¼ 33:63°C
c 2 c c
We assume initially the wall temperatures are equal to the reference
temperatures of the hot water, t h,w,1 ¼t h,1 and t h,w,2 ¼t h,2 , and take the
tube length calculated in Example 2.4 as the initial tube length, L¼2.701m.
With the same calculation steps described in Example 2.4, we can get
the thermal properties and heat transfer coefficients as well as the overall
heat transfer coefficients at these two reference temperatures as follows:
c p,h,1 ¼ 4:213 kJ=kgK,λ h,1 ¼ 0:6760 W=mK,μ h,1 ¼ 2:912 10 4 sPa,
Pr h,1 ¼ 1:815
Continued