Page 185 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 173

The local Reynolds number in Eq. (4.143) is defined as
_
Γ gρ ρ ρ Þδ 3
ð
v
l
l
Re x ¼ ¼ (4.145)
μ l 3μ 2 l
_
where Γ is the condensate mass flow rate per unit width
gρ ρ ρ Þδ 3
ð
_ l l v
Γ ¼ (4.146)
3μ l
and δ is the local film thickness.
For the case that the condensation begins at the top of the plate, that is, at
_
x¼0, the condensate mass flow rate per unit width Γ 0 ¼ 0, we have
" # 1=4
3
3 3
4 3=4 gλ ρ ρ ρ Þ T s T w Þ x
ð
ð
_ l l l v
Γ ¼ 3 (4.147)
3 μ Δh V
l
3 1=4
ð
gρ ρ ρ Þλ Δh v
l
l
v
l
α x ¼ (4.148)
4μ T s T w Þx
ð
l
_
_
If there is an initial condensate flow rate at x¼0, Γ x¼0 ¼ Γ 0 , we can add
an additional plate length x 0
_
3 4=3 Δh v Γ 4=3 μ l 1=3
0
x 0 ¼ (4.149)
ð
4 λ l T s T w Þ gρ ρ ρ Þ
ð
l
l
v
Then, we can use Eqs. (4.147), (4.148) by adding this fictitious plate
segment.
The mean heat transfer coefficient can be obtained by
ð
1 L + x 0 4 L + x 0 Þα x¼L + x 0 x 0 α x¼x 0
ð
α L ¼ α x dx ¼ (4.150)
L 3 L
x 0
The local and mean Nusselt numbers for the turbulent condensate film
can be found in Numrich and M€uller (2013) as follows:
α x,tur l 0:0283Re 7=24 Pr 1=3
x
l
Nu x,tur ¼ ¼ 1=6 (4.151)
λ l 1+9:66Re 3=8 Pr
x l
7=24 1=3
α L,tur l 0:02Re L Pr l
Nu L,tur ¼ ¼ 3=8 1=6 (4.152)
1+20:52Re L Pr l
λ l