Page 187 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 175

The Reynolds number at the tube bottom is

" # 1=4
Γ gρ ρ ρ Þλ T s T w Þ d
_
3
3 3
ð
ð
Re d ¼ ¼ 0:759 l l v l (4.160)
5
μ μ Δh 3
l l v
The mean heat transfer coefficient can be easily obtained as
_ 7=4 3=4 3 1=4
ð
ð
ΓΔh v 2 Γ 2=3Þ gρ ρ ρ Þλ Δh v
l
l
v
l
α ¼ ¼
ð
ð
πdT s T w Þ 3π 5=8 Γ 7=6Þ μ T s T w Þd
ð
l
(4.161)
3 1=4
ð
l
l
v
gρ ρ ρ Þλ Δh v
l
¼ 0:728
μ T s T w Þd
ð
l
We can also express Eq. (4.161) with the mean Nusselt number

αl 4 2 1=3 Γ 2=3Þ 1 ρ =ρ l 1=3 1 ρ =ρ l 1=3
ð
v
v
Nu ¼ ¼ ¼ 0:959
π
λ l 3 4=3 1=2 Γ 7=6Þ Re d Re d
ð
(4.162)
4.2.2.2 Condensation in a horizontal tube bundle
The mean Nusselt number for a tube bundle can be theoretically obtained as
Nu tb 1=4
¼ n tb (4.163)
Nu
where n tb is the number of tube rows. However, compared with the exper-
imental data, this result seems to be conservative, and it is suggested to use
Nu tb 1=6
¼ n tb (4.164)
Nu
for the evaluation of the heat transfer coefficient in a tube bundle (Kern,
1950, 1958).
For a downward vapor flow over a horizontal tube or through a hori-
zontal tube bundle, Fujii et al. (1972a,b) proposed a correlation as
1=4
0:276 1=2
Nu ¼ Cχ 1+ Re ∞ (4.165)
4
χ FrH
where C¼1 for staggered tube bundles and C¼0.8 for in-line tube bundles,
1=2
ρ μ
1 1/3
ð
χ ¼0.9[1+(RH) ] , R ¼ l l , H ¼ c p,l T s T w Þ ,Re ∞ ¼ u ∞ d , and
ρ μ Pr l Δh v ν l
v v
u 2 ∞
Fr ¼ , and u ∞ is the oncoming velocity of vapor.
gd