Page 137 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 125

j ¼ 0:53Re 0:5 0:15 ð s fs =h f Þ 0:14 (3.276)
2 ðÞ l s =d h2ðÞ
∗
For Re (2) Re (2) +1000,
0:65 0:17
0:36
f 2ðÞ ¼ 1:12Re l s =d h2ðÞ δ f =d h2ðÞ (3.277)
2 ðÞ
0:24 0:02
0:4
j ¼ 0:21Re l s =d h2ðÞ δ f =d h2ðÞ (3.278)
2 ðÞ
∗ ∗
For the Reynolds number between Re (2) and Re (2) +1000, the linear
interpolation can be applied for f and j:
f 2ðÞ ¼ 1 γð Þf 2 ðÞ,Re 2ðÞ ¼Re ∗ + γf 2 ðÞ,Re 2ðÞ ¼Re ∗ + 1000 (3.279)
2 ðÞ 2 ðÞ
j ¼ 1 γÞj Re 2ðÞ ¼Re ∗ + γj Re 2ðÞ ¼Re ∗ + 1000 (3.280)
ð
2 ðÞ 2 ðÞ
Re 2ðÞ Re ∗
2 ðÞ
γ ¼ (3.281)
1000
Manglik and Bergles (1995) used a multivariable regression method to
analyze the data for airflows (Pr¼0.7) of 18 fin geometries from the liter-
ature and obtained the following corrections for the friction factor f and
4
Colburn j factor, covering the parameter ranges of 120 Re (3) 10 ,
0.134 α f 0.997, 0.012 β f 0.048, and 0.041 γ f 0.121, where
(3.282)
α f ¼ s fs =h fs
(3.283)
β ¼ δ f =l s
f
γ ¼ δ f =s fs (3.284)
f
∗
For Re (3) Re (3) ,
β
α
γ
f 3ðÞ ¼ 9:6243Re 0:7422 0:1856 0:3053 0:2659 (3.285)
3 ðÞ f f f
γ
α
β
j ¼ 0:6522Re 0:5403 0:1541 0:1499 0:0678 (3.286)
3 ðÞ f f f
∗
For Re (3) Re (3) +1000,
α
γ
β
f 3ðÞ ¼ 1:8699Re 0:2993 0:0936 0:6820 0:2423 (3.287)
3 ðÞ f f f
β
α
γ
j ¼ 0:2435Re 0:4063 0:1037 0:1955 0:1733 (3.288)
3 ðÞ f f f
∗ ∗
Re (3) ¼Re (2) d h(3) /d h(2) . They also provided the following equations cover-
ing the whole range of Reynolds number:
β
α
f 3ðÞ ¼ 9:6243Re 0:7422 0:1856 0:3053
3 ðÞ f f
0:1 (3.289)
α
γ
γ 0:2659 1+7:669 10 8 Re 4:429 0:92 3:767 0:236
β
f 3 ðÞ f f f