Kuppan T. Heat Exchanger Design Handbook
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64
Chapter
2
1
.e
0.8
0.6
0.5
Figure
function
65
Heat Exchanger The rmo h
y
draul
ic
Fundamen ta
Is
:n
h
Q
R,
Thermal effectiveness
Figure
20
Four tube
rows,
four passes. Both
fluids
unmixed throughout;
fluid
1
inverted coupling between passes.
F
as a function
of
P
for
constant
R
(solid lines) and constant
NTU
(dashed lines).
66
Chapter
2
/ a
.8
0
.e
8
.I
e.0
0.8
y,
Thermal
effectiveness
Figure
21
Five tube rows, five passes.
Both
fluids unmixed throughout; fluid
1
inverted coupling between passes.
F
as
a function
of
P
for constant
R
(solid lines) and constant
NTU
(dashed lines).
67
Heat Exchanger Thennohydraulic Fundamentals
0
.e
0.7
y,
Thermal
effectiveness
Figure
22
Six tube
rows,
six passes, Both fluids unmixed throughout; fluid
1
inverted coupling between passes.
F
as
a function
of
P
for
constant
R
(solid lines) and constant
NTU
(dashed lines).
68
Chapter
2
I
I
I
I
I
Figure
23
Tube rows multiples arrangement; (a) four rows-two pass; (b)
six
rows-two pass.
Values of F for four rows, two passes, and six rows, two passes are shown in Figs.
24
and
2
5,
re spec ti vel
y
.
6.4.
Thermal Relations for Various TEMA Shells and Others
The thermal effectiveness relations for various
TEMA
shells and others are presented next,
using the following simplifying assumptions given at the beginning of this section and the
additional assumption of perfect transverse mixing of the shell fluid. Since the shell-side flow
arrangement is unique with each shell type, the exchanger effectiveness is different for each
shell even though the number of tube passes may be the same. The P-NTU, or LMTD method
is commonly used for the thermal analysis of shell and tube exchangers. Therefore, thermal
relation formulas and effectiveness charts are presented as for the P-NTU, method.
E
Shell
The basic case of the
E
shell, one shell pass and one tube pass with parallel flow and counter-
flow arrangement, is shown in Fig. 26. For the counterflow case with more than five baffles,
the
F
value can be taken as
1.
Thermal effectiveness charts shown in Fig. 6 can be used for
parallel flow arrangement and Fig. 7 for counterflow arrangement.
Multipassing
on
the
Tube
Side.
On the tube side, any number of odd or even passes is
possible. Increasing the even number of tube passes from two to four, six, etc., decreases the
exchanger effectiveness slightly, and in the limit when the number of tube passes approaches
infinity with one shell pass, the exchanger effectiveness approaches that for a single-pass cross-
flow exchanger with both fluids mixed. The odd number of tube passes per shell has slightly
better effectiveness when the shell fluid flows countercurrent to the tube fluid for more than
half the tube passes. However, this is an uncommon design and may result in structural and
thermal problems in manufacturing and design. Common tube-side multipass arrangements for
TEMA El.?,
El-3,
and
El..,
shells are shown in Fig. 27.
Even Number
of
Tube Passes. One shell pass and two tube passes as shown in Fig. 4 using
a U-tube bundle is one of the most common flow arrangements used in the single-pass TEMA
E
shell. The heat exchanger with this arrangement is also simply referred to as a conventional
1-2 heat exchanger. If the shell fluid is idealized as well mixed, its temperature is constant at
any cross section. In this case, reversing the tube fluid flow direction will not change the
idealized temperature distribution and the exchanger thermal effectiveness. Possible flow pat-
terns of the
E,.:
shell were already shown in Fig.
4.
This is referred as “stream symmetric.”
The 1-2 and
1-4
cases were solved long ago by Bowman
[
111, Underwood
[
121, and
Nagle
[30].
The 1-N geometry for even number of passes was solved by Back
[31].
Thermal
effectiveness formula for the El.: case is given by
Eq.
T13 in Table 6 and the thermal effective-
ness chart is given in Fig.
28
along with the
Fmln
curve. Thermal effectiveness formulas for
4
and N tube-side passes are given by
Eqs.
T14 and
T15,
respectively, in Table 6. The thermal
69
Heat Exchanger Themtohydraulic Fundamentals
e,
Thermal effectiveness
Figure
24
Four rows-two passes with two rows per pass. One fluid is unmixed throughout; Tubeside fluid mixed between passes
and in each pass unmixed; fluid
1
inverted coupling between
passes.
F
as
a
function of
P
for constant
R
(solid lines) and constant
NTU (dashed lines).
70
Chapter
2
Thermal
effectiveness
Figure
25
Six Rows-two passes with three rows
per
pass. One fluid is unmixed throughout; tubeside
fluid
mixed between
passes
and in each pass unmixed; fluid
1
inverted coupling between passes.
F
as
a
function of
P
for
constant R (solid lines) and constant
NTU
(dashed lines).
Heat Exchanger Thennohydraulic Fundamentals
71
4
Figure
26
E
shell single pass arrangement: parallel flow; counterflow. (Note: for a large number
of
segmental baffles, the flow approaches true parallel and counterflow.)
effectiveness chart for the
E,.,,
case is shown in Fig.
29,
and this figure may be used for even
N
2
6
cases also without loss
of
much accuracy.
Odd Number
of
Tube Passes.
With the TEMA
E
shell, an odd number of tube passes can
have both parallel flow and counterflow arrangements. Thermal effectiveness relations for
overall parallel flow and counterflow arrangements are discussed next.
A
I
4kt
+
!
Figure
27
Common tubepass arrangement for
El.?,
El-4
and shells.
_____
1
72
Chapter 2
Table
6
E,.Shell (N Even) (Refened to Tubeside)
Eq.
no./
Value for
R
=
1
Flow arrangement Ref.
General formula
and special cases
~13[301
p=
2
1
+
R
+A
coth (A NTU/2)
P=
1
+
coth (NTU/+)/fi
A=l/-iTi?
12
T1
3MA El.? shell: she
!ll
fluid mixed, tube
fluid mixed be-
tween passes;
stream symmetric
Same as Jl.l shell
Same as Jl.l shell
&ifl
‘2
El.z shell. shell fluid
divided into two
streams, individu-
ally mixed; tube
fluid mixed be-
tween passes
A
T14 [30]
PI
=
[
y=
4-j
(’
+
R,
+
4
)
+
M[
4
[4
+
$A
+
B]
P=
I]
A
=
coth (GNTU/4)
B
=
tanh (NTU/4)
t2
TEMA
E14
shell: shell
fluid mixed, tube
fluid mixed be-
tween passes
T15 [31]
2
PI
=
A+B+C
Same as Eqn. T15 with
R
:
1.
A
=
1
+
R
+
coth(NTU/2)
I
I2
-1
NTU
NI
B
=
-
coth/
2~,
1
TEMA E,+, (even N)
shell: shell fluid
mixed; and tube
fluid mixed be-
tween passes
N
N1
=-
2
N
+
=
results in well known single pass cross-
flow exchanger with both fluids mixed.
73
Heat Exchanger Thennohydraulic Fundamentals