Page 213 - Design and Operation of Heat Exchangers and their Networks

202 Design and operation of heat exchangers and their networks

For the staggered tube bundles with s l <d o ,
1=3
2
ð
Nu id ¼ 0:404 0:92HgPr 4s t s l =π d = s l s d Þ (5.42)
o
where the diagonal pitch s d is given by
2 1=2

2
s d ¼ s + s t =2ð Þ (5.43)
l
The Hagen number is defined as
ζ
Hg ¼ Re 2 tb (5.44)
2
For inline tube bundles,
(
Hg , Re tb 1000
lam
h i
Hg ¼ 1 Re tb + 1000Þ=2000 (5.45)
ð
Hg +Hg 1 e ,Re tb > 1000
lam tur,i
For staggered tube bundles,
(
Hg lam , Re tb 800
h i
Hg ¼ 1 Re tb + 200Þ=1000 (5.46)
ð
Hg +Hg 1 e ,Re tb > 800
lam tur,s
where
Re tb ¼ ρu max d o =μ (5.47)
For the inline tube bundles and the staggered tube bundles with s l s l,min ,

s t
u max ¼ u 0 (5.48)
s t d o
where

2 1=2
s l,min ¼ 0:52s t d o + d (5.49)
o
For the staggered tube bundles with s l <s l,min ,
s t =2
u max ¼ u 0 (5.50)
s d d o
The Hagen number for laminar flow can be expressed as

2
0:5
ð s l =d o Þ 0:6 +0:75
Hg (5.51)
lam ¼ 140Re tb ∗ 1:6
ð
ð s t =d o Þ ½ 4 s l =d o Þ s t =d o Þ=π 1Š
ð
∗
in which s t ¼s t for inline tube bundles and for staggered tube bundles with
s l s l, min . For staggered tube bundles with s l <s l, min , the diagonal pitch s d is
∗ ∗
taken as s t , where the maximum flow velocity occurs, s t ¼s d .