Page 166 - Design and Operation of Heat Exchangers and their Networks
P. 166
154 Design and operation of heat exchangers and their networks
For cryogenic fluids such as N 2 ,H 2 , and O 2
n ¼ 0:9 0:3p 0:3 (4.20)
r
1
0:27
¼ 1:2p +2:5+ (4.21)
r
F p r p r
1 p r
The effect of the wall properties and surface roughness is taken into
account by
2=15 0:25
ð
F w ¼ R a =R a0 Þ ð λρcÞ = λρcÞ (4.22)
ð
w Cu
where R a0 ¼0.4μm, (λρc p ) w is the square of the effusivity of the surface
9 2 4 2
material, and (λρc p ) Cu ¼1.250 10 W s/m K .
For finned tubes, the earlier correlations are modified as
ðÞ
ðÞ
n R p r ¼ np r 0:1h f =s fs (4.23)
p ffiffiffiffi
ðÞ p r = ψ (4.24)
F p r ,R p r ¼ F p r
F w,R ¼ 1 (4.25)
where h f is the fin height, s fs is the fin free spacing, s fs ¼s s δ f , and ψ is area
enlargement factor that is the ratio of the surface area of the finned tube to
that of a plain tube of the same core diameter. The validity range of
Eqs. (4.23)–(4.25) is s f >1mm, 0.02 p r 0.3, or 1bar p 10bar.
Example 4.1 Nucleate boiling of R134a on a horizontal tube
Calculate the nucleate boiling heat transfer coefficient of R134a on a
horizontal plain copper tube at the saturation temperature of 15.12°C
2
and q¼12.77kW/m . The roughness of the tube surface is assumed to
be 0.4μm.
Solution
The molecular mass and critical pressure of R134a are M¼102.03kg/kmol
and p cr ¼40.593bar, respectively. At t s ¼15.12°C, the properties of
R134a are calculated by the use of RefProp as p s ¼4.903bar,
p 0 ¼0.1p cr ¼4.903bar, (dp/dT) sat,p0 ¼0.1363bar/K, σ p0 ¼0.01013Nm.
1. Cooper correlation
Since the reduced pressure p r ¼p s /p cr ¼4.903/40.593¼0.1208, we use the
Cooper correlation, Eq. (4.11), and take C¼90 to calculate the heat transfer
coefficient as
α ¼ 90q 0:67 M 0:5 p r 0:12 0:2lgR a ½ lg p r 0:55
ðÞ
0:67 0:5 0:12 0:2lg0:4 0:55
¼ 90 12,770 102:03 0:1208 ½ lg 0:1208Þ
ð
2
¼ 3453W=m K