Page 71 - Design and Operation of Heat Exchangers and their Networks

58 Design and operation of heat exchangers and their networks

For γ ¼0 (parallel plates), Eq. (2.135) approaches to

f Re ¼ 24 (2.136)
A polynomial correlation was provided by Shah and London (1978,
Eq. (341))as

2
3
4
f Re ¼ 24 1 1:3553γ +1:9467γ 1:7012γ +0:9564γ 0:2537γ 5
(2.137)
with the maximum error of 0.05%.
2.2.1.3 Frictional pressure drop in laminar flow in isosceles
triangular ducts
For fully developed laminar flow in isosceles triangular ducts, the Fanning
friction factor was obtained in a closed form by Migay (See Shah and Lon-
don, 1978, Eq. (365)) as

2
ð
12 B +2Þ 1 tan θÞ
ð
f Re ¼ (2.138)
2
ð
ð B 2Þ tanθ + secθÞ
where θ is half of the apex angle of the isosceles triangle and B is given by
Eq. (2.139):
1=2
5 1
B ¼ 4+ 1 (2.139)
2 tan θ
2
For a equilateral triangle, Eq. (2.138) yields
1 (2.140)
f Re ¼ 13 ⁄3
2.2.1.4 Frictional pressure drop in laminar flow in concentric
annular ducts
For fully developed laminar flow in a concentric annular duct, the velocity
distribution can be expressed as (Lundberg et al., 1963)

lnr
2
2
21 r + r 1
u i lnr i
¼ (2.141)
u m 2 2 lnr
1+ r r 1
i i
lnr i
where r ¼ r=r o and r i ¼ r i =r o . According to the definition of the Fanning
friction factor,

1
τ i ¼ μ du ¼ f i ρu 2 (2.142)
dr 2 m
r¼r i