Kuppan T. Heat Exchanger Design Handbook
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8.9
74
Chapter
2
Figure
P
for
col
75
Heat Exchanger Thermohydraulic Fundamentals
In an
El-?
overall counterflow arrangement, two tube passes are in counterflow and one
tube pass is in parallel flow, whereas in an
E,.3
overall parallel flow arrangement, two tube
passes are
in
parallel flow and one tube pass is in counterflow. Similarly,
in
an
E,
overall
counterflow arrangement, three tube passes are in counterflow and two tube passes are
in
parallel flow. The flow arrangement for
El-3
was already shown in Fig 27 and for is shown
in Fig. 30. Pignotti and Tamborenea [32] obtained an analytical solution for the
1-N
(odd
N)
case and obtained effectiveness for the 1-3 and 1-5. Explicit thermal relations are given by
Pignotti
[
181
for
E,.?
parallel flow and counterflow cases.
For
N=
3.
Thermal effectiveness formulas for
E,.?
parallel flow arrangement are given
by Eq. T16 and for
E,-3
counterflow arrangement by
Eq.
T17
in Table 7. The thermal effective-
ness chart for
E,.?
counterflow arrangement is given in Fig. 3
1.
For
N=
5.
For the overall counterflow arrangement or opposite end case, the thermal
effectiveness is given by Eq.
T18
in Table
8
and the thermal effectiveness chart is given in
Fig. 32.
For the overall parallel flow arrangement or same end case, the configuration can be
obtained from that of the opposite end case (T18) by just the inversion of the direction of flow
of the tube fluid, which leads to the expression [32]:
P,
=(I
-xT>
(70)
with
TEMA
F Shell
For the
TEMA
F
shell, as is usual with two tube passes, the arrangement results in pure
counterflow with
F
=
1.
For four tube passes, the configuration would be treated as two
El.:
exchangers in series.
As
the longitudinal baffle is exposed on one side to the hot stream and
on the other side to the cold stream, there is a conduction heat exchange that reduces the
thermal effectiveness and hence the
F
factor has to be corrected. The effect of thermal leakage
by conduction across the baffle has been analyzed by Whistler [33] and in nondimensional
form by Rozenman and Taborek [34], with proposed baffle correction methods. The baffle
correction factor based on Ref. 34 is presented in Ref.
35.
I
Figure
30
Flow arrangement
of
E
shell with one shell pass and five tube passes
(E,J.
(a) Parallel
flow;
(b) counterflow.
76
Chapter
2
Table
7
El.3
Shell (Referred
to
Tube side)
Eq.
no./
Flow
arrangement Ref. General formula
Value for R
=
1
1-ATEMA
E
shell:
T16 [18]
AC+B?
Same as
EQ.
T16
with
R=
1
PI+
-7-1
two parallel flow
and one counter-
flow passes; shell
fluid mixed, tube
fluid mixed
be-
tween passes
A
hI.2
=
(-3
*
6)/2
6=
[9R2
+
4
(R
+
l)]Os
R
12
1-3
TEMA
E
Shell:
T17 [18]
C
Same as
Eq.
T17
with
R=
1
oneparallel
flow
and
(AC
i
B')
and two counter-
flow
passes; shell
A
=
X I
(I
+
RA,)
(1
-
Rhz)/2R2h,
-
E
fluid mixed, tube
fluid mixed be-
-Xi
(1
+
Rho)
(1
-
Rhl)/2R2&
+
R/(R
-
1)
(5
+
NTU)
tween passes
B
=
~1
(1
-
R&J/R
-
x:,
(1
-
Rhl)/R
+
E
' 9
C
=
-XI
(3
+
RhJR
+
XI
(3
+
Rhl)/R
+
E
E
=
0.5
e"n'13J
k,.:
=
(-3
*
6)/2
E=
[9R2
+
4(
1
-
R)]"'
R
TEMA
G
Shell or Split-Flow Exchanger
Possible flow arrangements for the TEMA
G
shell are
GI.,, GI-*,
and
GI.4.
The solution
of
the
G,.?
counterflow case is due to Schindler and Bates
1361
and
that of the parallel flow case is
due to Pignotti
[18].
The thermal effectiveness
P
of this shell with two tube passes is higher
than that of the conventional E!-* exchanger for a given
NTU,
and
R.
It is also possible
io
have
only a single pass on the tube side, which is stream symmetric
[37].
'Tne the-mal effectiveness
formula for
GI.!
is
given by
Eq.
T19
in Table
9
and the thermal effectiveness chart is given
in
Fig.
33.
For the
G,
arrangement, the thermal relations for the parallel
flow
and counterflow
77
Heat Exchanger Thermohydraulic Fundamentals
1
.e
8.0
8.S
Figure
31
TEMA
E,
shell.
One parallel flow and two counterflow passes; shell fluid mixed, tube fluid mixed between passes.
F
as
a function
of
P
for constant
R
(solid lines) and constant
NTU
(dashed lines).
-
-
78
Chapter
2
Table
8
Formula for
El.S
Shell and Tube Exchanger with Three Tube Two Tube Passes
in
Parallel Flow Arrar
ment; Shell Fluid Mixed, Passes (Referred to Tube
Side)
[32]
where
PI
=(1
-XK)
for
N=J
T18
-
-
Hp
=
Hi,
=
-
-
H??
=
H:,
=
2N-
I
+NTU+
1
-N
x7
+
N-
-
1
x,
for
R
=
I
N: (N+l)N‘ N+I
(1
+
RA,,)(
1
+
Rh,)
(1
+
Rh1)(
1
+
Rh,)
x,
-
__
XI
-
for
R#
1
R’
(N
-
i)h$
R‘ (N- l)h:6
R-
1
(
1
+
RA,)(
1
-
RAJ
-
(1
-
Rhl)(
I
+
RAJ
x,
-
-
2
xi
+
__
R’ (N
+
l)h16
R‘
(N+ l)h,6 N+I R-1
for
R;
2N-l+NTU+ 1-N 2
x,
-
-
X,
for
R
=
1
N2
(N+~)N’
N+1
(l-RhI)(l +R&)
(I
+Rhi)(l -RA,)
X?
+
N-3
-
x,
-
__
XI
-
for
R;
R’ (N-
1)h,6
R‘ (N
-
l)h:6
N-1 R-1
2N+
1
-NTU+
1
+N N-3
x:
+
__
x4
for
R=
1
N2
(N-
I)
N: N-
I
(1
-
RA,)(
1
+
Rh?)
(1
+
RA,)(
1
-
RhJ
X2------
XI
-
2xd
for
R
#
1
R’
(N
-
l)h16
R’ (N
-
l)h$
N-1 R-1
79
Heat Exchanger The
rmo
h
y
draul
ic
Fundamentals
Figure
32
TEMA
El.S
shell.
Two
parallel
flow
and three counterflow passes; shell fluid mixed, tube fluid mixed between passes.
F
as
a
function
of
P
for
constant
R
(solid lines) and constant
NTU
(dashed
lines).
80
Chapter
2
Table
9
G
Shell (Referred to Tube Side)
Eq.
no.1 Value for
R
=
1
Flow arrangement
Ref. General formula and special cases
1
T19
[371
p
=
-
[A
+
B
-
AB (1
B=-
NTU
forR=1
R 2
+
NTU
+
1IR)
+
AB'IR]
12
1-1
G
shell: tube fluid split into two
streams; shell fluid mixed. stream sym-
metric
T20
[lS]
PI
=
(B
-
a')
For
R
=
0.5
R
(A
-
a'/R
+
2)
1+2RNTU-P
P,
=
(1
-
a)'
R(4
+
4R NTU
+
R'
NTU2)
A=------
(R
-
0.5)
p
=
e(-ZR
KTUI
B=
4R-P(2R-l)
1-2 TEMA
G
shell: overall parallel flow
(2R+ 1)
arrangement; shell fluid mixed, tube
fluid mixed between passes
-NTU(MtII
P=e
2
T21
[36] (B
-
a')
For
R
=
0.5
PI
=
R (A
+
2
+
B/R)
1
+
2R
NTU
-
a'
PI
=
-(
1
-
a)'
R [4
+
4R NTU
-
(1
-
a)']
A=-------
(R
+
0.5)
a
=
e(-R
NTUI
4R-P(2R+
1)
B=
1-2
TEMA
G shell: overall counterflow
(2R- 1)
arrangement; shell fluid mixed, tube
-NTU
(2RtI)
fluid mixed between passes
a=e
4
-NTU(ZR-
I
)
P=e
2
arrangements are given by
Eqs.
T20
and
T21,
respectively in Table 9, and the thermal effec-
tiveness chart
for
the counterflow arrangement is given in Fig. 34.
G,-4
arrangement was
ana-
lyzed by Singh et al.
[38]
and the thermal effectiveness chart is given at the end of this chapter.
TEMA
H
Shell
The arrangement of the
TEMA
H
shell exchanger resembles a configuration in which two
TEMA
G
shell exchangers are connected side by side. The solution for the
TEMA
H
shell
with
1-2
flow arrangement was analytically derived by Kohei Ishihara and Palen [39]. It
is
also possible
to
have only a single pass
on
the tube side
[40].
The thermal effectiveness relation
referred to the shell side for
H,.,
is
given by
Eq.
T22
in Table 10, and the thermal effectiveness
81
Heat Exchanger Thermohydraulic Fundamentals
1
.w
0.85
U
d
0.70
pI,
Thermal
effectiveness
Figure
33
G,
I
shell.
Tube
fluid split into two streams
with
shell
of
mixed fluid. Stream symmetric.
F
as
a
function
of
P
for
constant
R
(solid
lines)
and constant
NTU
(dashed lines).
0.5
82
Chapter
2
1.0
0.8
pl,
Thermal effectiveness
r
Fimiv~
t
'0
am
-*a
0,9
0.2
0.3
0
44
0.6
0.6
0,7
0 4 8
0.0
1
r0
e,
Thermal effectiveness
Figure
34
TEMA
G,
shell.
Overall
counterflow arrangement; shell fluid mixed, tube fluid mixed between passes.
F
as
a
function
of
P
for
constant
R
(solid
lines) and constant
NTU
(dashed lines).
F
min curve
is
also
shown.
83
Heat Exchanger Thermohydraulic Fundamentals
Table
10
H
Shell (Referred
to
Tube Side)
Eq.
no./
Value for
R
=
1
Flow arrangement
Ref. General formula and special cases
Same as
Eq.
T22
with
T22 [371
P,
=
R
{E[
1
+
(1
-
B/2R)
For
=
o.5
+*-+
(1
-
Al2R
+
ABIR)]
B=
R NTU
3‘
‘2
-AB
(1
-
BI2R))
(2
+
R NTU)
1-1
H
shell: tube fluid split into two
1
streams; shell fluid mixed
A=------(l
1
+
1/2R
-exp
[-R NTU(
1
+
1/2R)/2]
E
=
(A
+
B
-
AB/2R)/2
T23
[39]
P,
=
[l
---I
B
+
4GR
For
R
=
0.25
(I
-
D)4
B
+
4GR
B=(1
+N)(l
+E)’
G
=
(1
-
0)‘ (0’
+
E‘)
D
=
-NTU/8
+D2(1
+E)’
1-2 TEMA
H
shell: overall parallel
flow arrangement; shell fluid mixed,
tube fluid mixed between passes
1
-
e-a
D=-----
1
-4R
e+-
E=----
1
4R+
1
-1
H=-------
-2P
4R+
1
NTU
8
a=-(4R-
1)
p=y(4R+
1)
chart referred to the shell side is given in Fig. 35. For the
H,-2
arrangement, the thermal
relations for the parallel flow and counterflow arrangements are given by
Eqs.
T23 and
T24
respectively, in Table
10,
and the thermal effectiveness chart for the counterflow arrangement
is given in Fig. 36.
TEMA
J
Shell or Divided-Flow Shell
The use
of
divided-flow exchangers with one shell pass and one or more tube passes is very
common. If the shell-side heat-transfer resistance is not a limiting factor, and entrance and exit