Kuppan T. Heat Exchanger Design Handbook
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104
Chapter
2
Heat Exchanger Thennohydraulic Fundamentals
I05
18
T
09
08
07
06
05
04
0.3
02
01
00
.6
NTU
Figure
50
(a) Three pass cross-counterflow arrangement with complete mixing between passes.
In
each pass
both
the fluids unmixed; R-P-NTU chart.
(b)
F-R-P-NTU chart; F as a function
of P
for
constant
R
(solid
lines) and constant
NTU
(dashed lines).
I06
Chapter
2
0.4
0.5
0.8
0.7
0.8
P,,
Thermal
effectiveness
(b)
Figure
50
Continued.
1.0
Heat Exchanger The rmo h
y
dra
u
1
ic Fundamentals
107
Table
13
Thermal Effectiveness Relations for Two-Pass Assemblies of
Heat Exchangers Arrangement with One Fluid Unmixed Throughout
[29]
Eq.
no./
Formula for overall
Flow arrangement
Ref. cross-counterflow exchangers
T34
[28]
Fluid
1
unmixed throughout;
fluid
2
mixed throughout
T35
[28]
+,
It
K-
-
1
-
e(-Rh'TUI>~
Fluid
1
mixed throughout; fluid
Eq.
for
P2
=
Eq. T34
2
unmixed throughout
T36
[28
2
Fluid
1
unmixed throughout,
identical order; fluid
2
mixed
throughout
T37
[28]
K
=
1
-
e(-RNTL'12~
I
Eq.
for
P2
=
Eq.
36
4?'$fh
Fluid
1
mixed throughout; fluid
2
unmixed throughout, identi-
cal order
Note:
for
an
individual
case,
at
R
=
1,
PI
=
Pz.
108
Chapter
2
I
.0
0.9
e.5
0.2
0.4
0.6
a.
e
8.7
0.8
8.9
I
.a
pl,
Thermal effectiveness
Figure
51
Two
pass cross-counterflow arrangement. Fluid
1
unmixed throughout, inverted order coupling; fluid
2
mixed throughout.
F
as
a
function
of
P
for constant
R
(solid lines) and
constant
NTU
(dashed lines).
109
Heat Exchanger Thermohydraulic Fundamentals
0.8
I
I0
Chapter
2
0-0
0.5
Figure
53
Two
pass cross-counterflow arrangement. Fluid
1
unmixed throughout, identical order
coupling; fluid
2
mixed throughout.
F
as a function
of
P
for constant
R
(solid lines) and constant
NTU
(dashed lines).
111
Heat Exchanger Thermohydraulic Fundamentals
Figure
coupling
112
Chapter
2
Table
14
Thermal Effectiveness Relations for Two-Pass Assemblies of
Heat Exchangers Arrangement with
Both
Fluids Unmixed in the Passes
[1,45,46]
Eq.
no./ Formula for overall
Flow arrangement Ref. cross-counterflow exchangers
T38 [45]
Q.
for
E~
=
T39
2-
-2
Fluid
1
unmixed throughout; fluid 2
un-
mixed
in
each pass and mixed be-
tween passes
7
T39 [45]
&1=1-----
v
;/2
VIE
+
P1/2
Eq.
for
E~
=
T38
2
Fluid
1
unmixed in each pass and
mixed between passes; fluid
2
un-
mixed throughout
T40 [46]
1
El
=-
2
C*
-Lr
2-
Fluid
1
unmixed throughout, identical
order; fluid 2 mixed between passes
and unmixed in each pass
n
T41 [46]
E[=l-
V
in
7
1
+
2VI/?
-
2vy/
2
Eq.
for
E~
=
T40
-t
2-
Fluid
1
mixed between passes and
un-
mixed
in
each pass; fluid
2
unmixed
throughout, identical order
Note:
for individual case at
C*
=
1,
=
E~.
Heat Exchanger The
rmo
hydrau
1
ic
Fundamentals
I13
3.
Two-pass cross-counterflow arrangement. Fluid 1 unmixed throughout, identical-order
coupling; fluid
2
mixed between passes and unmixed
in
each pass (111-d of Fig.
44).
4. Two-pass cross-counterflow arrangement. Fluid 1 mixed between passes and unmixed in
each pass; fluid
2
unmixed throughout, identical-order coupling (IV-c of Fig. 44).
Thermal relation formulas (T38-T41) for these cases are given in Table 14. The thermal effec-
tiveness chart for case
2
is
given in Fig.
55
and for case
3
in
Fig.
56.
Two
Passes
with Both Fluids Unmixed Throughout, Cross-Counterjlow Arrangement.
1. Fluid
1
unmixed throughout; fluid
2
unmixed throughout. Both fluids coupling in inverted
order (11-b
of
Fig.
44).
The
thermal effectiveness chart is given
in
Fig. 57. This is
also
equivalent to the
TEMA
X-shell, two passes on the tube side with counterflow arrange-
men
t
.
For cross-parallel flow, the thermal effectiveness is given
by
[45]:
1-
E
=
Pl/2
+
-
C*
p112
where the terms of the equation were defined earlier. This is also equivalent to the TEMA
X-shell, two passes on
the
tubeside with parallel flow arrangement.
Table
14
Continued (Footnotes)
Terms
of
the
equations:
Set
C*
=
l/C*,
hTU
=
C*NTU
and
C*hTU
=
hTU
in
Eq.
(A),
then,
Eq.
(B)
is
obtained by
The expressions
for
Uln
and
a,,
are
given
by,
1
-
c*
P
n.2