Page 165 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 153

2
2
with α in W/m K, q in W/m , and p in bar. The validity range of Eq. (4.10)
4 2 6 2
is 0.5bar<p<20bar, and 10 W/m <q<10 W/m .
A widely used correlation was proposed by Cooper (1984):
α ¼ Cq 0:67 M 0:5 p r 0:12 0:2lgR a ½ lg p r 0:55 (4.11)
ðފ
2
2
with α in W/m K, q in W/m , molecular mass M in kg/kmol, and rough-
ness R a in μm. For stainless steel C¼55, and for horizontal copper tube
C¼93.5. We can take C¼90 for evaluation. The reduced pressure is
defined as

p r ¼ p=p cr (4.12)
For an accurate evaluation, it is suggested to use the Gorenflo correlation
(Gorenflo, 2013):

F (4.13)
α ¼ α 0 F q F p r w
n
where F q ¼(q/q 0 ) , α 0 is the heat transfer coefficient for a specific fluid at a
2
reference state, α 0 ¼α(q 0 , p r0 ), the reference heat flux q 0 ¼20,000W/m ,
and the reference reduced pressure p r0 ¼0.1. The values of α 0 for many fluids
can be found in Table 1 of Gorenflo (2013). In the absence of data, α 0 can be
evaluated by
2
0:6
α 0 ¼ α 0,calc ¼ 3:58P f0 kW=m K (4.14)
1
(μmK) .
¼ p r0
in which P f0 ¼[(dp/dT ) sat /σ] p r
,
The effects of heat flux and pressure are expressed by F q , and F p r
respectively:
n
F q ¼ q=q 0 Þ (4.15)
ð
For organic fluids and NH 3
n ¼ 0:95 0:3p 0:3 (4.16)
r
¼ 0:7p 0:2 +4p r + 1:4p r (4.17)
F p r r
1 p r
For water

n ¼ 0:9 0:3p 0:15 (4.18)
r
0:68p 2 r
0:27
2
¼ 1:73p +6:1p + (4.19)
r r 2
F p r
1 p
r