Page 136 - Design and Operation of Heat Exchangers and their Networks

124 Design and operation of heat exchangers and their networks

Δpρd h iðÞ
f iðÞ ¼ (3.267)
2LG 2
i ðÞ
where G (1) and G (3) are based on the cross-sectional area h fs s fs and G (2) is
based on the minimum cross-sectional area h fs (s fs δ f ).
By correlating experimental heat transfer and flow friction data from
22 rectangular offset-fin plate-fin heat exchanger configurations, the follow-
ing empirical relationships have been developed by Wieting (1975):

f 1ðÞ ¼ 7:661Re 0:712 0:384 ð s fs =h fs Þ 0:092 Re 1ðÞ 1000 (3.268)
1 ðÞ l s =d h1ðÞ
0:781 0:534
0:198
f 1ðÞ ¼ 1:136Re l s =d h1ðÞ δ f =d h1ðÞ Re 1ðÞ 2000 (3.269)
1 ðÞ
0:162 0:184
0:536
j ¼ 0:483Re l s =d h1ðÞ ð s fs =h fs Þ Re 1ðÞ 1000 (3.270)
1 ðÞ
j ¼ 0:242Re 0:368 l s =d h1ðÞ 0:322 δ f =d h1ðÞ 0:089 Re 1ðÞ 2000 (3.271)
1 ðÞ
Wieting also suggested a technique in the application of these correla-
tions, which extends the correlations into the transitional Re range with
the reference Reynolds number:

Re ∗ ¼ 41 l s =d h1ðÞ 0:772 δ f =d h1ðÞ 1:04 ð s fs =h fs Þ 0:179 (3.272)
1 ðÞ, f
∗ 0:952 0:53 1:1
Re ¼ 61:9 l s =d h1ðÞ δ f =d h1ðÞ ð s fs =h fs Þ (3.273)
1 ðÞ, j
∗ ∗
Then, Eq. (3.268) is used for Re (1) <Re (1), f ,Eq. (3.270) for Re (1) <Re (1), j ,
∗ ∗
Eq. (3.269) for Re (1) Re (1), f , and Eq. (3.271) for Re (1) Re (1), j .
Joshi and Webb (1987) got the critical Reynolds number indicating the
flow transition from laminar to turbulent by visually reading the slope
changes of the j and f curves from the plots of the data and proposed a cor-
relation for the transition Reynolds number as

1:23 0:58
ð
∗ G ∗ d h2ðÞ 257 l s =s fs Þ ð δ f =l s Þ d h2ðÞ
Re ¼ ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3.274)
2 ðÞ μ δ f +1:328 l s d h2 ðÞ =Re 2 ðÞ
Their correlations for the friction factor f and Colburn j factor are as
follows:
∗
For Re (2) Re (2) ,

f 2ðÞ ¼ 8:12Re 0:74 l s =d h2ðÞ 0:41 ð s fs =h fs Þ 0:02 (3.275)
2 ðÞ