Page 186 - Design and Operation of Heat Exchangers and their Networks

174 Design and operation of heat exchangers and their networks

The Nusselt number for laminar and turbulent regions was superimposed
by Numrich and M€uller (2013) as follows:
α x l q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Nu x ¼ ¼ f μ ð f well Nu x,lam Þ +Nu 2 (4.153)
x,tur
λ f
α L l q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Nu L ¼ ¼ f μ ð f well Nu L,lam Þ +Nu 2 (4.154)
L,tur
λ f
in which the waviness correction f well is expressed as

Nu x,lam,well 1, Re x < 1
f well ¼ ¼ 0:04 (4.155)
Nu x,lam Re x ,Re x 1
and the correction factor for temperature-dependent viscosity is given by
1=4
f μ ¼ μ =μ (4.156)
l,s l,w
4
The validity range of Eqs. (4.153), (4.154) is Re x ,Re L <10 ,
0.5<Pr l <500, 0.2<μ l,s /μ l,w <5.

4.2.2 Condensation in tube bundles
4.2.2.1 Condensation on a horizontal tube
The laminar film condensation on a horizontal tube can be obtained by fol-
lowing the Nusselt film theory. The analytical solution reveals that the film
thickness at the top position of the tube at θ¼0is
1=4
3μ λ l T s T w Þd
ð
l
δ θ¼0 ¼ (4.157)
2gρ ρ ρð l v ÞΔh v
l
which corresponds to the local heat transfer coefficient of
3 1=4
ð
λ l 2gρ ρ ρ Þλ Δh v
l
l
v
l
α θ¼0 ¼ ¼ (4.158)
ð
δ θ¼0 3μ T s T w Þd
l
The condensate mass flow rate per unit tube length at the bottom of the tube
at θ¼π can be obtained as
" # 1=4
3=4

π

3
3 3
2 3=4 3=8 Γ 2=3Þ gρ ρ ρ Þλ T s T w Þ d
ð
ð
ð
_ l l v l
Γ θ¼π ¼ 2
3 Γ 7=6Þ μ Δh 3 v
ð
l
" # 1=4
3
3 3
gρ ρ ρ Þλ T s T w Þ d
ð
ð
v
l
l
l
¼ 0:759
μ Δh 3
l v
(4.159)