Kuppan T. Heat Exchanger Design Handbook
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I54
Chapter
3
opment), surface temperature, maldistribution, fouling, manufacturing imperfections, fluid
physical properties, etc.
[34].
Thermal performance degradation due to uncertainties in heat
transfer will be felt more in the case of highly viscous fluids and units in which phase change
takes place. Temperature effects and thermal entry length effect are significant in lamina
flows; the latter effect is generally not significant in turbulent flow except for low Prandtl
number fluids. Approximate methods to account for specific variations in heat-transfer coeffi-
cient for counterflow are analyzed by Colburn
[35]
and Butterworth
[36],
for crossflow by
Sider-Tate
[37]
and Roetzel
[38],
and for
1-2N
shell flow by Bowman et al.
[39].
These
methods are summarised in Refs.
33
and
34.
The state of the
art
on nonuniform heat transfer
coefficient is reviewed
in
Ref.
34.
Bypass Path on the Air Side of Compact Tube-Fin Exchangers
Owing to the construction requirements, there are various clearances on the shell side of a
shell and tube exchanger leading to various bypass paths. Modem procedures for shell-side
heat-transfer calculations do take care of various leakages and bypass streams while evaluating
shell-side performance. In the case of finned-tube banks, the bypass paths are inevitable
he-
tween
(1
)
the sidesheet assembly and the outermost tubes, and
(2)
the core assembly and the
housing
in
which the core is housed. The thermal performance deterioration due to these clear-
ances can be overcome by the following means:
1.
Attach seals to the sidesheet assembly to block the clearance between the sidesheet assem-
bly and the outermost tubes.
2.
Permanently weld strips to the housing (without hindering the fitment of the core), which
will block the bypass path between the core assembly and the housing
in
which the core
is housed.
These measures will be discussed
in
Chapter
4.
Uncertainty in Fouling
The influence of uncertainties inherent in fouling factors is generally greater than that of uncer-
tainties
in
physical properties, flow rates, or temperatures, such as in heat exchange between
dirty aqueous fluids, in which fouling resistances can completely dominate the thermal design
[40].
Planned fouling prevention, maintenance, and cleaning schedules make
it
possible to
allow lower resistance values.
Miscellaneous Effects
Depending upon the individual desigdconstructiond features, there exist certain miscellaneous
effects that add uncertainties on thermal performance. Such effects include stagnant regions,
radiation effects. allowance for in-service tube plugging due to leakages that cannot be corrected,
influence
of
brazingholdering, etc. Compact soldered finned-tube cores and brazed PFHEs will
suffer from solderinghrazing-induced surface roughness/partial blockage due to melting
of
braz-
ing filler metal. This may reduce the
j
factor slightly but increase the
f
factor substantially.
8.2
Determination
of
Uncertainties
The method usually used by heat exchanger designers is to ignore in the original calculations
uncertainties
in
the design parameters. After the area has been calculated, it is multiplied by a
safety factor assigned by the designer to ensure that the exchanger will perform adequately.
The safety factor is based mostly upon the designer’s experience and judgment and can vary
from
15
to 100%. Such methods can unnecessarily add to the cost of the equipment
in
capital
investment
[24].
Heat Exchanger The rma
1
Design
I55
Computational Procedures
Buckley
[41]
was the first to use a statistical approach to the sizing of process equipment. His
approach was to first size the unit with nominal values of design parameters. Then, based on
the assumption that uncertainties follow the normal distribution, he determined the standard
deviation for each variable. From the individual uncertainty (standard deviation), its effect on
the overall uncertainty of the area was determined. Once the effects of all uncertain parameters
on the overall heat transfer area are known, the oversizing can be determined according to the
desired confidence level.
Mahbub Uddin and Bell
[26]
presents a Monte Carlo procedure for dealing with the effect
of uncertainties on the design, performance, and operation of systems of process heat ex-
changers.
Cho [25] presents a simple method of assessing the uncertainties
in
the design
of
heat
exchangers assuming
a
Gaussian form
of
data distribution for “uncertain” parameters, which
leads to the root sum square
(RSS)
method
of
establishing the probability, or confidence level,
that the heat exchanger design will meet its performance requirements. This method is briefly
discussed next.
Cho’s
Method
of
Uncertainty Analysis
[25].
The degree
of
data spread around the mean value
may be quantified using the concept of standard deviation,
O.
Suppose that the distribution of
data points for
a
certain parameter has a Gaussian or normal distribution. Then the procedure
to incorporate the effect
of
data spread into the design of
a
heat exchanger is as follows. For
example, consider the convective heat-transfer coefficient,
11,
which has a data spread as shown
in Fig.
1
l(a). The probability of the value
of
h
falling below the mean value is of concern.
Therefore. if one takes
or
21
=-Z
and
Z2=-
then the probability that
h
will attain a value greater than
-
2
o,,
is
AIR
IN
-
WATER
OUT
+-E
t
t
+J
WATER
IN
Figure
8
Maldistribution due to nozzle location
is
corrected
by
relocating the nozzles.
156
Chapter
3
1
Figure
9
Nonuniform flow due
to
flow
turning in a header.
Figure
10
Nonuniform
flow
passages of
a
compact heat exchanger.
f
t
Figure
11
Normal
hstribution
of
(a) heat transfer coefficient,
h;
and (b) tube wall thickness,
t.
Heat
Exchanger
Thermal
Design
157
(33)
where
This probability is known as the cumulative probability
or
one-sided confidence level and
the numerical values are given in Table
7.
Here,
2
indicates the degree of the design confidence
level; for example, if one desires a
90%
confidence level, the value of
2
becomes 1.282. This
means the value of
h
should be reduced to
A
-
1.282
Oh
to obtain a
90%
level of design
confidence. Due to the reduction in the heat-transfer coefficient, the surface area is to be
increased to get the desired thermal performance. These equations (32 and
33)
are applicable
to uncertain parameters whose lower values are
of
design concern, like heat-transfer coeffi-
cients and tube-wall thermal conductivity.
Now consider the effect of tube wall thickness,
t,
which has a data spread as shown in
Fig. ll(b). The value of
t
greater than the mean value is of concern here. Therefore, if one
takes
or
then the probability that
r
will attain a value less than
t
+
Z
o,
is
Again,
Z
indicates the degree
of
the design confidence level. The numerical values are
given in Table
7.
A
90%
level of design confidence requires the use of an increased thickness,
t
+
1.2820,
in the sizing calculation. The reduction in heat-transfer rate due to increased thick-
ness is to be compensated by increase in heat-transfer surface area. These equations (35 and
36) are applicable to uncertain parameters whose upper values are of design concern, like tube-
wall thickness and fouling resistance.
The effects of data spreads have been discussed for individual parameters. These individ-
ual effects usually take place simultaneously, and the combined effect can be assessed for
normally distributed parameters, using the root sum square
(RSS)
method
[25]:
AX
=
4
f
(AX,)’
(37)
I=I
Additional Surface Area Required Due to Uncertainty
The effects of data spread have been discussed for individual parameters. These individual
effects usually take place simultaneously and the combined effect is assessed using the RSS
method. The total additional surface area
AA,
required to obtain a certain level of design confi-
dence is calculated from
[25]:
158
Chapter
3
Additional Pressure Drop Due to Uncertainty
Equation
37
can also be applied
to
determine the additional pressure drop,
A(&)
required to
obtain
a
certain level of design confidence,
as
given by the following equation
[25]:
I
Table
7
Cumulative Probability Function
[25]
Z
0
1
2
3
4
5
6
7
8 9
0.0
0.5000
0.5040
0.5080
0.5 120
0.5
160
0.5
199
0.5239
0.5279
0.53 19
0.5359
0.1 0.5398
0.5438
0.5478
0.5517
0.5557 0.5596
0.5636
0.5675
0.57
14
0.5753
0.2 0.5793
0.5832
0.587
1
0.59
10
0.5948
0.5987
0.6026
0.6064
0.6 103
0.6141
0.3 0.6179
0.62 17
0.6255
0.6293
0.633
1
0.6368
0.6406
0.6443
0.6480
0.65 17
0.4 0.6554
0.659
1
0.6628
0.6664
0.6700
0.6736
0.6772
0.6808
0.6844
0.6879
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7 123
0.7 157
0.7 190
0.7224
0.6 0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.75
17
0.7549
0.7 0.7580
0.761
1
0.7642
0.7673
0.7703
0.7734
0.7764
0.7794 0.7823
0.7852
0.8 0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.805
1
0.8078
0.8 106
0.8 133
0.9 0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
1.0 0.8413
0.8438
0.846
1
0.8485
0.8508
0.853
1
0.8554
0.8577
0.8599
0.862
1
1.1
0.8643
0.8665
0.8686
0.8708
0.8729
0.8749
0.8770
0.8790
0.88 10
0.8830
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.8980
0.8997
0.9015
1.3 0.9032
0.9049
0.9066
0.9082
0.9099
0.91 15
0.9131
0.9 147 0.9 162
0.9
177
1.4 0.9192
0.9207
0.9222
0.9236
0.925
1
0.9265
0.9278
0.9292
0.9306
0.93 19
1.5 0.9332
0.9345
0.9357
0.9370
0.9382
0.9394
0.9406
0.94
1
8
0.9430
0.944
1
1.6 0.9452
0.9463
0.9474
0.9484
0.9495
0.9505
0.95 15
0.9525
0.9535
0.9545
1.7 0.9554
0.9564
0.9573
0.9582
0.959
1
0.9599
0.9608
0.96 16
0.9625
0.9633
1.8 0.9641
0.9648
0.9656
0.9664
0.967
1
0.9678
0.9686
0.9693
0.9700
0.9706
1.9 0.9713
0.97 19
0.9726
0.9732
0.9738
0.9744
0.9750
0.9756
0.9762
0.9767
2.0
0.9772
0.9778
0.9783
0.9788
0.9793
0.9798
0.9803
0.9808
0.98
12
0.98 17
2.1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842
0.9846
0.9850
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.987
1
0.9874
0.9878
0.988
1
0.9884
0.9887
0.9890
2.3
0.9893
0.9896
0.9898
0.9901
0.9904
0.9906
0.9909
0.991
1
0.99 13
0.99 16
2.4 0.9918
0.9920
0.9922
0.9925
0.9927
0.9929
0.993
1
0.9932
0.9934
0.9936
2.5 0.9938
0.9940
0.994
1
0.9943
0.9945
0.9946
0.9948
0.9949
0.995
1
0.9952
2.6 0.9953
0.9955
0.9956
0.9957
0.9959
0.9960
0.996
1
0.9962
0.9963
0.9964
2.7 0.9965
0.9966
0.9967
0.9968
0.9969
0.9970
0.997
1
0.9972
0.9973
0.9974
2.8 0.9974
0.9975
0.9976
0.9977
0.9977
0.9978
0.9979
0.9979
0.9980
0.998
1
2.9 0.9981
0.9982
0.9982
0.9983
0.9984
0.9984
0.9985
0.9985
0.9986
0.9986
3.0 0.9987
0.9990
0.9993
0.9995
0.9997
0.9998
0.9998
0.9999
0.9999
0.1000
4
Compact
Heat
Exchangers
1
CLASSIFICATION AND CONSTRUCTION DETAILS OF
TUBE-FIN COMPACT HEAT EXCHANGERS
Compact heat exchangers are used in a wide variety of applications. Typical among them are
the heat exchangers used in automobiles, air conditioning, electronics cooling, waste and pro-
cess heat recovery, cryogenics, aircraft and spacecraft, ocean thermal energy conservation,
solar, and geothermal systems. The need for light-weight, space-saving, and economical heat
exchangers has driven the development
of
compact surfaces.
1
.I
Characteristics
of
Compact Heat Exchangers
Specific characteristics of compact heat exchangers are discussed by Shah
[
1-41
and include
the following:
Usually with extended surfaces.
A
high heat-transfer surface area per unit volume
of
the core, usually in excess of
700
m2/m3 on at least one of the fluid sides, which usually has gas flow.
Small hydraulic diameter.
Usually at least one of the fluids is a gas.
Fluids must be clean and relatively nonfouling because of small hydraulic diameter
(Dh)
flow passages and difficulty in cleaning; plain uninterrupted fins are used when “moder-
ate” fouling is expected.
The fluid pumping power (i.e., pressure drop) consideration is as important as the heat-
transfer rate.
Operating pressures and temperatures are limited to a certain extent compared to shell
and tube exchangers due to thin fins and/or joining of the fins to plates or tubes by
brazing, mechanical expansion, etc.
The use
of
highly compact surfaces results in an exchanger with a large frontal area and
159
160
Chapter
4
a short flow length; therefore, the header design of a compact heat exchanger is important
for a uniform flow distribution.
9.
Fluid contamination
is
generally
not
a problem.
10.
Variety of surfaces are available having different order of magnitudes of surface area
density.
11. Flexibility in distributing surface area on the hot or cold side as desired by the designer.
Other features of compact heat exchangers are:
Materials for the manufacture of fins are limited by the operating temperature of certain appli-
cations. For low- to moderate-temperature applications, fins can be made from aluminum,
copper, or brass and thus maintain high fin efficiency. For high-temperature applications,
stainless steel and heat-resistant alloys may be used with possibly a reduction in the fin
efficiency. Consequently, suitable high-performance surfaces may be selected to offset the
reduction in fin efficiency or the fin thickness should be reduced.
Manufacture
is
by brazing or welding. For low- or moderate-temperature applications, the fins
can be mechanically bonded. Low-fin tubes are extruded.
Flow arrangements: Compact exchangers are mostly used as single-pass crossflow or multipass
cross-counterflow exchangers.
1.2
Construction Types
of
Compact Heat Exchangers
Basic construction types of compact heat exchangers are
1. Tube-fin
2.
Plate-fin
3.
Regenerators
Tube-fin and plate-fin heat exchangers are discussed in this chapter. Regenerators, exclu-
sively used in gas-to-gas applications, could have more compact surface area density compared
to plate-fin or tube-fin surfaces. They are covered in detail in a separate chapter. The unique
characteristics of compact extended-surface plate-fin and tube-fin exchangers that favor them
as compared with the conventional shell and tube exchangers include the following
[
1,3,4]:
1.
Many surfaces are available having different orders
of
magnitude of surface area density.
2.
Flexibility in distributing surface area on the hot and cold sides as warranted by design
considerations.
3.
Generally substantial cost, weight, or volume savings.
The following factors mainly determine the choice among the three types of compact heat
exchangers:
1.
Operating pressure and temperature
2.
Phases of the fluids dealt with
3.
Fouling characteristics of the fluid
4.
Allowable pressure drop
5.
Strength and ruggedness
6.
Restrictions on size and/or weight
7.
Acceptable intermixing of the fluids dealt with
1.3
Tube-Fin Heat Exchangers
Tube-fin heat exchangers are widely used throughout the industry in a variety of applications.
They are employed when one fluid stream is at a higher pressure and/or has a significantly
161
Compact
Heat
Exchangers
higher heat-transfer coefficient compared to the other fluid stream. For example, in a gas-to-
liquid exchanger, the heat-transfer coefficient on the liquid side is generally very high com-
pared to the gas side. Fins are used on the gas side to increase surface area. In
a
tube-fin
exchanger, round and rectangular tubes are most commonly used (although elliptical tubes are
also
used), and fins are employed either on the outside
or
on the inside, or on both sides of
the tubes, depending upon the application. Fins on the outside of the tubes (Fig. 1) may be
categorized as follows:
1. Normal fins on individual tubes (Fig. la), referred to as individually finned tubes.
2.
Longitudinal fins
on
individual tubes (Fig. lb), which are generally used in condensing
applications and for viscous fluids in double-pipe heat exchangers.
3.
Flat or continuous (plain, wavy, or interrupted) external fins on an array of tubes (Fig. lc).
Since interrupted fins are more prone to fouling, many users prefer plain continuous fins
in situations where fouling, particularly by fibrous matter, is a serious problem.
Specific Qualitative Considerations for Tube-Fin Surfaces
Specific qualitative considerations for the tube-fin surfaces include the following:
Tube-fin exchangers usually have lower compactness than plate-fin units.
A
tube-fin exchanger may be designed for a wide range of tube fluid operating pressures, with
the other fluid being at low pressure.
Reasonable fouling can be tolerated on the tube side if the tubes can be cleaned.
OlRECflON
OF
___c
(c)
AIR
FLOW
Figure
1
Tube-fin exchanger: (a) normal fin;
(b)
longitudinal fin;
(c)
continuous fins on an array of
straight tubes fin;
and
(d)
continuous fins on
an
array of wavy
tubes
fin.
I62
Chapter
4
Applications
Tube-fin exchangers are extensively used as condensers and evaporators in air-conditioning
and refrigeration applications, for cooling of water or oil
of
vehicular or stationary internal
combustion engines, and as air-cooled exchangers in the process and power industries. The
ususal arrangement is that water, oil, or refrigerant flows in the tubes, while air flows across
the finned tubes.
Individually Finned Tubes
Individually finned tube geometry is much more rugged than the continuous fin geometry, but
has lower compactness. The most common individual finned tubes are with plain circular,
helical, or annular enhanced fin geometries like segmented, spine, studded, slotted, or wire-
loop fins
[5].
Figure
2
shows some of the fin geometries that have been used on circular tubes.
They are attached to the tubes by a tight mechanical fit, tension winding, adhesive bonding,
soldering, brazing, welding, or extrusion. Figure 3 shows common circular tube-fin classifica-
tion and manufacturing techniques. Details
of
various geometries are discussed next.
Plain Circular Fins.
Plain circular fins are the simplest and most common. They are manu-
factured by tension wrapping the fin strip around a tube, forming a continuous helical fin, or
by mounting circular
fin
disks on the tube. Helically wrapped and extruded fins on circular
tubes are frequently used in the process industries and in heat recovery applications. Classifica-
tion of plain circular fin tubes in terms of fin height is discussed next.
Fin
Height and Classification
of
Finned Tubes.
Fin height and classification of finned tubes
are discussed by Wen-Jei Yan
[6].
According to fin height, the finned tubes are called low-fin
tubes, medium-fin tubes, and high-fin tubes, as follows:
1.
In low-fin tubes, fins are extruded from the tube material with fin heights on the order of
1-2
mm. Fins of nominal
1.6
mm
(i
in) height have become standard for the low-fin
type
of duty usually required in shell and tube exchangers. The integral type eliminates all the
uncertainty concerning the tube-fin bond contact resistance,
2.
Fins of approximately 3.2 mm
(i
in) are referred to as medium fins and are usually em-
ployed in shell and tube exchangers.
3.
Air-cooled exchangers require high fins, which have the height of
6.4-25
mm ($-1.0 in).
Heat recovery systems prefer medium to high fins in tube banks of in-line arrangement.
Studded
Wire
Coop
Sbttad
haltcal
Figure
2
Forms
of
individually finned
tubes.
Compact Heat Exchangers
I63
Circular finned tube
9
Spiral fin
Annular fin
I I
Fabrication
by
Wound fins
extrusion
Figure
3
Tube-fin manufacturing techniques.
However, Rabas and Taborek [7] low-fin tubes as having a fin height less than
6.35
mm
(0.25
in). The major reasons for using low-finned tubes in various types of heat exchangers
are
[7]:
1.
To balance heat-transfer resistance
2.
To maintain fin bond integrity
3.
To reduce fouling
4.
To satisfy the tube material specification
Enhanced Fin Geometries.
Segmented or Spine Fins. Segmented
or
spine fins are made by helically winding a
continuous strip of metal that has been partially cut into narrow sections. Upon winding, the
narrow sections separate and form the narrow strip fins that are connected at the base.
Studded Fins. A studded fin is similar to the segmented fin, but individual studs are
welded to the tubes.
Slotted Fins. Slotted fins have slots in the radial direction; when radially slitted material
is wound on a tube, the slits open.
Wire Loops Around the Tube. The wire loops are held in the tube by a tensioned wire
within the helix or by soldering. The enhancement characteristic
of
small-diameter wires is
important at low flows where the enhancement of other interrupted fins diminishes.
All of these geometries provide enhancement by the periodic development
of
thin bound-
ary
layers on small-diameter wires or flat strips, followed by their dissipation
in
the wake
region between elements
[8].
Construction Materials.
The materials to be used for the tubes, headers, and water tanks
depend on the specific requirements of the application. The most common materials for tubes
and fins are copper, aluminum, and steel. For open-circuit installations, the tubes are made
from copper, phosphorus-deoxidized copper, aluminum, brass, and copper-nickel-iron alloys,
that is, cupronickels, and carbon steel for heat recovery applications. Fins are mostly from