Page 132 - Design and Operation of Heat Exchangers and their Networks

120 Design and operation of heat exchangers and their networks

In order to avoid confusion, we define the fin-free spacing in fin height
and width as

h fs ¼ h f δ f (3.238)
(3.239)
s fs ¼ s f δ f
The hydraulic diameter of passages in a plate-fin heat exchanger can be
formulated by

4A c
d h ¼ (3.240)
P
where A c is the cross-sectional area of the flow and P is the wetted perimeter
of the cross-section. For nonuniform cross-sectional area along the flow pas-
sage, the hydraulic diameter can be defined with the minimum cross-
sectional area,
4A c,min
d h ¼ (3.241)
P
For complicated fin geometry, we can also define the hydraulic diameter as
4V
d h ¼ (3.242)
A
where V is the fluid volume in a flow passage and A is the wetted area of the
passage.
As an example, for rectangular plain fins, the hydraulic diameter can be
expressed as

4h fs s fs L 2h fs s fs
d h ¼ ¼ (3.243)
2 h fs + s fs ÞL h fs + s fs
ð
Another example is the rectangular offset strip fins and perfect edge cut-
ting. Taking one offset strip, we can write the hydraulic diameter by
Eq. (3.242) as

2h fs s fs
d h ¼ (3.244)
ð
h fs + s fs + h fs + s ofs δ f Þδ f =l s
where l s is the strip length and s ofs is the strip offset. For the symmetrical strip
offset, s ofs ¼s f /2. Some researchers used other expressions of the hydraulic
diameter, for example, using the hydraulic diameter for rectangular plain
fins, Eq. (3.243):

2h fs s fs
d h1ðÞ ¼ ð Wieting, 1975Þ (3.245)
h fs + s fs