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hermal design of shell-and-tube
heat exchangers (STHEs) is
done by sophisticated computer
software. However, a good un-
derstanding of the underlying principles
of exchanger design is needed to use this
software effectively.
This article explains the basics of ex-
changer thermal design, covering such
topics as: STHE components; classifica-
tion of STHEs according to construction
and according to service; data needed for
thermal design; tubeside design; shellside
design, including tube layout, baffling,
and shellside pressure drop; and mean
temperature difference. The basic equa-
tions for tubeside and shellside heat
transfer and pressure drop are well-
known; here we focus on the application
of these correlations for the optimum de-
sign of heat exchangers. A followup arti-
cle on advanced topics in shell-and-tube
heat exchanger design, such as allocation
of shellside and tubeside fluids, use of
multiple shells, overdesign, and fouling,
is scheduled to appear in the next issue.
Components of STHEs
It is essential for the designer to have a
good working knowledge of the mechani-
cal features of STHEs and how they in-
fluence thermal design. The principal
components of an STHE are:
• shell;
• shell cover;
• tubes;
• channel;
• channel cover;
• tubesheet;
• baffles; and
• nozzles.
Other components include tie-rods and
spacers, pass partition plates, impinge-
ment plate, longitudinal baffle, sealing
strips, supports, and foundation.
The Standards of the Tubular Ex-
changer Manufacturers Association
(TEMA) (1) describe these various com-
ponents in detail.
An STHE is divided into three parts:
the front head, the shell, and the rear
head. Figure 1 illustrates the TEMA
nomenclature for the various construction
possibilities. Exchangers are described by
the letter codes for the three sections —
for example, a BFL exchanger has a bon-
net cover, a two-pass shell with a longitu-
dinal baffle, and a fixed-tubesheet rear
based on construction
Fixed tubesheet. A fixed-tubesheet
heat exchanger (Figure 2) has straight
tubes that are secured at both ends to
tubesheets welded to the shell. The con-
struction may have removable channel
covers (e.g., AEL), bonnet-type channel
covers (e.g., BEM), or integral tubesheets
(e.g., NEN).
The principal advantage of the fixed-
tubesheet construction is its low cost be-
cause of its simple construction. In fact,
the fixed tubesheet is the least expensive
construction type, as long as no expan-
sion joint is required.
Other advantages are that the tubes can
be cleaned mechanically after removal of
Copyright 1997 American Institute of Chemical Engineers. All rights reserved. Copying and downloading permitted with restrictions.
Effectively Design
Heat Exchangers
Rajiv Mukherjee,
Engi neers Indi a Lt d.
To make the most
of exchanger
design software,
one needs to
understand STHE
components, tube
layout, baffling,
pressure drop, and
mean temperature
I Figure 1. TEMA designations for shell-and-tube heat exchangers.
One-Pass Shell
Two-Pass Shell
with Longitudinal Baffle
Split Flow
Double Split Flow
Divided Flow
Cross Flow
Kettle-Type Reboiler
Removable Channel and Cover
Bonnet (Integral Cover)
Integral With Tubesheet
Removable Cover
Special High-Pressure Closures
U-Tube Bundle
Pull-Through Floating Head
Floating Head with Backing Device
Outside Packed Floating Head
Fixed Tube Sheet
Like "C"Stationary Head
Fixed Tube Sheet
Like "B"Stationary Head
Externally Sealed
Floating Tubesheet
Fixed Tube Sheet
Like "A"Stationary Head
Stationary Head Types Shell Types Rear Head Types
Channel Integral With Tubesheet
and Removable Cover
the channel cover or bonnet, and that
leakage of the shellside fluid is mini-
mized since there are no flanged joints.
A disadvantage of this design is
that since the bundle is fixed to the
shell and cannot be removed, the out-
sides of the tubes cannot be cleaned
mechanically. Thus, its application is
limited to clean services on the shell-
side. However, if a satisfactory chem-
ical cleaning program can be em-
ployed, fixed-tubesheet construction
may be selected for fouling services
on the shellside.
In the event of a large differential
temperature between the tubes and
the shell, the tubesheets will be un-
able to absorb the differential stress,
thereby making it necessary to incor-
porate an expansion joint. This takes
away the advantage of low cost to a
significant extent.
U-tube. As the name implies, the
tubes of a U-tube heat exchanger
(Figure 3) are bent in the shape of a
U. There is only one tubesheet in a U-
tube heat exchanger. However, the
lower cost for the single tubesheet is
offset by the additional costs incurred
for the bending of the tubes and the
somewhat larger shell diameter (due
to the minimum U-bend radius), mak-
ing the cost of a U-tube heat ex-
changer comparable to that of a fixed-
tubesheet exchanger.
The advantage of a U-tube heat
exchanger is that because one end is
free, the bundle can expand or con-
tract in response to stress differen-
tials. In addition, the outsides of the
tubes can be cleaned, as the tube bun-
dle can be removed.
The disadvantage of the U-tube
construction is that the insides of the
tubes cannot be cleaned effectively,
since the U-bends would require flex-
ible-end drill shafts for cleaning.
Thus, U-tube heat exchangers should
not be used for services with a dirty
fluid inside tubes.
Floating head. The floating-head
heat exchanger is the most versatile
type of STHE, and also the costliest.
In this design, one tubesheet is fixed
relative to the shell, and the other is
free to “float” within the shell. This
permits free expansion of the tube
bundle, as well as cleaning of both
the insides and outsides of the tubes.
Thus, floating-head SHTEs can be
used for services where both the
shellside and the tubeside fluids are
dirty — making this the standard con-
struction type used in dirty services,
such as in petroleum refineries.
There are various types of float-
ing-head construction. The two most
common are the pull-through with
backing device (TEMA S) and pull-
through (TEMAT) designs.
The TEMA S design (Figure 4) is
the most common configuration in
the chemical process industries (CPI).
The floating-head cover is secured
against the floating tubesheet by bolt-
ing it to an ingenious split backing
ring. This floating-head closure is lo-
cated beyond the end of the shell and
contained by a shell cover of a larger
diameter. To dismantle the heat ex-
changer, the shell cover is removed
first, then the split backing ring, and
then the floating-head cover, after
which the tube bundle can be re-
moved from the stationary end.
In the TEMA T construction (Fig-
ure 5), the entire tube bundle, includ-
ing the floating-head assembly, can
be removed from the stationary end,
since the shell diameter is larger than
the floating-head flange. The floating-
head cover is bolted directly to the
floating tubesheet so that a split back-
ing ring is not required.
The advantage of this construction
is that the tube bundle may be re-
moved from the shell without remov-
ing either the shell or the floating-
head cover, thus reducing mainte-
nance time. This design is particular-
ly suited to kettle reboilers having a
dirty heating medium where U-tubes
cannot be employed. Due to the en-
larged shell, this construction has the
highest cost of all exchanger types.
Baffles Tie Rods
and Spacers
I Figure 2. Fixed-tubesheet heat exchanger.
Tubeplate Shell Tubes Baffles Header
I Figure 3. U-tube heat exchanger.
There are also two types of packed
floating-head construction — outside-
packed stuffing-box (TEMA P) and
outside-packed lantern ring (TEMA
W) (see Figure 1). However, since
they are prone to leakage, their use is
limited to services with shellside flu-
ids that are nonhazardous and non-
toxic and that have moderate pres-
sures and temperatures (40 kg/cm
and 300°C).
based on service
Basically, a service may be single-
phase (such as the cooling or heating
of a liquid or gas) or two-phase (such
as condensing or vaporizing). Since
there are two sides to an STHE, this
can lead to several combinations of
Broadly, services can be classified
as follows:
• single-phase (both shellside and
• condensing (one side condens-
ing and the other single-phase);
• vaporizing (one side vaporizing
and the other side single-phase); and
• condensing/vaporizing (one side
condensing and the other side
The following nomenclature is
usually used:
Heat exchanger: both sides single-
phase and process streams (that is,
not a utility).
Cooler: one stream a process fluid
and the other cooling water or air.
Heater: one stream a process fluid
and the other a hot utility, such as
steam or hot oil.
Condenser: one stream a condens-
ing vapor and the other cooling water
or air.
Chiller: one stream a process
fluid being condensed at sub-atmo-
spheric temperatures and the other a
boiling refrigerant or process stream.
Reboiler: one stream a bottoms
stream from a distillation column and
the other a hot utility (steam or hot
oil) or a process stream.
This article will focus specifically
on single-phase applications.
Design data
Before discussing actual thermal
design, let us look at the data that
must be furnished by the process li-
censor before design can begin:
1. flow rates of both streams.
2. inlet and outlet temperatures of
both streams.
3. operating pressure of both
streams. This is required for gases,
especially if the gas density is not
furnished; it is not really necessary
for liquids, as their properties do not
vary with pressure.
4. allowable pressure drop for
both streams. This is a very important
parameter for heat exchanger design.
Generally, for liquids, a value of
0.5–0.7 kg/cm
is permitted per shell.
Ahigher pressure drop is usually war-
ranted for viscous liquids, especially
in the tubeside. For gases, the allowed
value is generally 0.05–0.2 kg/cm
with 0.1 kg/cm
being typical.
5. fouling resistance for both
streams. If this is not furnished, the
designer should adopt values speci-
fied in the TEMA standards or based
on past experience.
6. physical properties of both
streams. These include viscosity,
thermal conductivity, density, and
specific heat, preferably at both inlet
and outlet temperatures. Viscosity
data must be supplied at inlet and
outlet temperatures, especially for
liquids, since the variation with tem-
perature may be considerable and is
irregular (neither linear nor log-log).
7. heat duty. The duty specified
should be consistent for both the
shellside and the tubeside.
8. type of heat exchanger. If not
furnished, the designer can choose
this based upon the characteristics of
the various types of construction de-
scribed earlier. In fact, the designer is
normally in a better position than the
process engineer to do this.
9. line sizes. It is desirable to
match nozzle sizes with line sizes to
avoid expanders or reducers. Howev-
er, sizing criteria for nozzles are usu-
ally more stringent than for lines, es-
pecially for the shellside inlet. Conse-
quently, nozzle sizes must sometimes
be one size (or even more in excep-
tional circumstances) larger than the
corresponding line sizes, especially
for small lines.
10. preferred tube size. Tube size
is designated as O.D. × thickness ×
length. Some plant owners have a
preferred O.D. × thickness (usually
based upon inventory considerations),
and the available plot area will deter-
mine the maximum tube length.
Many plant owners prefer to stan-
dardize all three dimensions, again
based upon inventory considerations.
11. maximum shell diameter. This
is based upon tube-bundle removal re-
quirements and is limited by crane ca-
pacities. Such limitations apply only to
exchangers with removable tube bun-
dles, namely U-tube and floating-head.
For fixed-tubesheet exchangers, the
only limitation is the manufacturer’s
fabrication capability and the avail-
ability of components such as dished
ends and flanges. Thus, floating-head
heat exchangers are often limited to a
shell I.D. of 1.4–1.5 m and a tube
length of 6 m or 9 m, whereas fixed-
tubesheet heat exchangers can have
shells as large as 3 m and tubes
lengths up to 12 m or more.
12. materials of construction. If
the tubes and shell are made of iden-
tical materials, all components should
be of this material. Thus, only the
shell and tube materials of construc-
tion need to be specified. However, if
the shell and tubes are of different
metallurgy, the materials of all princi-
pal components should be specified
to avoid any ambiguity. The principal
components are shell (and shell
cover), tubes, channel (and channel
cover), tubesheets, and baffles.
Tubesheets may be lined or clad.
13. special considerations. These
include cycling, upset conditions, al-
ternative operating scenarios, and
whether operation is continuous or
Tubeside design
Tubeside calculations are quite
straightforward, since tubeside flow
represents a simple case of flow
through a circular conduit. Heat-trans-
fer coefficient and pressure drop both
vary with tubeside velocity, the latter
more strongly so. A good design will
make the best use of the allowable
pressure drop, as this will yield the
highest heat-transfer coefficient.
If all the tubeside fluid were to
flow through all the tubes (one tube
pass), it would lead to a certain veloc-
ity. Usually, this velocity is unaccept-
ably low and therefore has to be in-
creased. By incorporating pass parti-
tion plates (with appropriate gasket-
ing) in the channels, the tubeside fluid
is made to flow several times through
a fraction of the total number of tubes.
Thus, in a heat exchanger with 200
tubes and two passes, the fluid flows
through 100 tubes at a time, and the
velocity will be twice what it would
be if there were only one pass. The
number of tube passes is usually one,
two, four, six, eight, and so on.
Heat-transfer coefficient
The tubeside heat-transfer coeffi-
cient is a function of the Reynolds
number, the Prandtl number, and
the tube diameter. These can be bro-
ken down into the following funda-
mental paramet ers: physi cal
propert i es (namely viscosity, ther-
mal conductivity, and specific heat);
tube diameter; and, very important-
ly, mass velocity.
The variation in liquid viscosity is
quite considerable; so, this physical
property has the most dramatic effect
on heat-transfer coefficient.
The fundamental equation for tur-
bulent heat-transfer inside tubes is:
Nu = 0.027 (Re)
(hD/k) =
0.027 (DG/µ)
h = 0.027(DG/µ)
(k/D) (1c)
Viscosity influences the heat-trans-
fer coefficient in two opposing ways
— as a parameter of the Reynolds
number, and as a parameter of Prandtl
number. Thus, from Eq. 1c:
h α (µ)
h α (µ)
In other words, the heat-transfer
coefficient is inversely proportional
to viscosity to the 0.47 power. Simi-
larly, the heat-transfer coefficient is
directly proportional to thermal con-
ductivity to the 0.67 power.
These two facts lead to some inter-
esting generalities about heat transfer.
Ahigh thermal conductivity promotes
a high heat-transfer coefficient. Thus,
cooling water (thermal conductivity
of around 0.55 kcal/h•m•°C) has an
extremely high heat-transfer coeffi-
cient of typically 6,000 kcal/h•m
followed by hydrocarbon liquids
(thermal conductivity between 0.08
and 0.12 kcal/h•m•°C) at 250–1,300
•°C, and then hydrocarbon
gases (thermal conductivity between
0.02 and 0.03 kcal/h•m•°C) at
50–500 kcal/h•m
Hydrogen is an unusual gas, be-
cause it has an exceptionally high
thermal conductivity (greater than
that of hydrocarbon liquids). Thus,
its heat-transfer coefficient is to-
ward the upper limit of the range
for hydrocarbon liquids.
The range of heat-transfer coeffi-
cients for hydrocarbon liquids is
Tubesheet Shell
Tie Rods
and Spacers
I Figure 4. Pull-through floating-head exchanger with backing device (TEMA S).
Saddle Baffles
Tie Rods
and Spacers
I Figure 5. Pull-through floating-head exchanger (TEMA T).
rather large due to the large variation
in their viscosity, from less than 0.1
cP for ethylene and propylene to more
than 1,000 cP or more for bitumen.
The large variation in the heat-transfer
coefficients of hydrocarbon gases is
attributable to the large variation in
operating pressure. As operating pres-
sure rises, gas density increases. Pres-
sure drop is directly proportional to
the square of mass velocity and in-
versely proportional to density. There-
fore, for the same pressure drop, a
higher mass velocity can be main-
tained when the density is higher. This
larger mass velocity translates into a
higher heat-transfer coefficient.
Pressure drop
Mass velocity strongly influences
the heat-transfer coefficient. For tur-
bulent flow, the tubeside heat-transfer
coefficient varies to the 0.8 power of
tubeside mass velocity, whereas tube-
side pressure drop varies to the square
of mass velocity. Thus, with increas-
ing mass velocity, pressure drop in-
creases more rapidly than does the
heat-transfer coefficient. Consequent-
ly, there will be an optimum mass ve-
locity above which it will be wasteful
to increase mass velocity further.
Furthermore, very high velocities
lead to erosion. However, the pres-
sure drop limitation usually becomes
controlling long before erosive veloc-
ities are attained. The minimum rec-
ommended liquid velocity inside
tubes is 1.0 m/s, while the maximum
is 2.5–3.0 m/s.
Pressure drop is proportional to
the square of velocity and the total
length of travel. Thus, when the num-
ber of tube passes is increased for a
given number of tubes and a given
tubeside flow rate, the pressure drop
rises to the cube of this increase. In
actual practice, the rise is somewhat
less because of lower friction factors
at higher Reynolds numbers, so the
exponent should be approximately
2.8 instead of 3.
Tubeside pressure drop rises steeply
with an increase in the number of tube
passes. Consequently, it often happens
that for a given number of tubes and
two passes, the pressure drop is much
lower than the allowable value, but
with four passes it exceeds the allow-
able pressure drop. If in such circum-
stances a standard tube has to be em-
ployed, the designer may be forced to
accept a rather low velocity. However,
if the tube diameter and length may be
varied, the allowable pressure drop can
be better utilized and a higher tubeside
velocity realized.
The following tube diameters are
usually used in the CPI: w, , e, ,
1, 1, and 1 in. Of these, in. and
1 in. are the most popular. Tubes
smaller than in. O.D. should not be
used for fouling services. The use of
small-diameter tubes, such as in.,
is warranted only for small heat ex-
changers with heat-transfer areas less
than 20–30 m
It is important to realize that the
total pressure drop for a given stream
must be met. The distribution of pres-
sure drop in the various heat exchang-
ers for a given stream in a particular
circuit may be varied to obtain good
heat transfer in all the heat exchang-
ers. Consider a hot liquid stream flow-
ing through several preheat exchang-
ers. Normally, a pressure drop of 0.7
per shell is permitted for liq-
uid streams. If there are five such pre-
heat exchangers, a total pressure drop
of 3.5 kg/cm
for the circuit would be
permitted. If the pressure drop
through two of these exchangers turns
out to be only 0.8 kg/cm
, the balance
of 2.7 kg/cm
would be available for
the other three.
Example 1:
Optimizing tubeside design
Consider the heat exchanger ser-
vice specified in Table 1. A TEMA
Type AES exchanger (split-ring pull-
through floating-head construction)
was to be employed. Tubes were to
be either 25 mm O.D. (preferred) or
20 mm O.D., 2 mm thick, and 9 m
long (but could be shorter).
A first design was produced using
25-mm-O.D. × 9-m tubes (Case A in
Table 2). The tubeside pressure drop
was only 0.17 kg/cm
even though
0.7 kg/cm
was permitted. Further,
the tubeside heat-transfer resistance
was 27.71% of the total, which meant
that if the allowable pressure drop
were better utilized, the heat-transfer
area would decrease. However, when
the number of tube passes was in-
creased from two to four (keeping the
shell diameter the same and decreas-
ing the number of tubes from 500 to
480 due to the extra pass-partition
lanes), the tubeside pressure drop in-
creased to 1.06 kg/cm
, which was
unacceptable. (The shellside design
was satisfactory, with the allowable
pressure drop quite well utilized.)
Shellside Tubeside
Fluid Crude oil Heavy gas oil circulating reflux
Flow rate, kg/h 399,831 277,200
Temperature in/out, °C 227 / 249 302 / 275
Operating pressure, kg/cm
(abs.) 28.3 13.0
Allowable pressure drop, kg/cm
1.2 0.7
Fouling resistance, h•m
•°C/kcal 0.0007 0.0006
Heat duty, MM kcal/h 5.4945 5.4945
Viscosity in/out, cP 0.664 / 0.563 0.32 / 0.389
Design pressure, kg/cm
(gage) 44.0 17.0
Line size, mm (nominal) 300 300
Material of construction Carbon steel Tubes: Type 410 stainless steel
Other: 5CrMo
Table 1. Heat exchanger service for Example 1.
Since the overdesign in the four-
pass configuration was 28.1%, an at-
tempt was made to reduce the tube-
side pressure drop by decreasing the
tube length. When the tube length
was reduced to 7.5 m, the overdesign
was 5.72%, but the tubeside pressure
drop was 0.91 kg/cm
, which was
still higher than that permitted.
Next, a design with 20-mm-O.D.
tubes was attempted (Case B in Table
2). The shell diameter and heat-trans-
fer surface decreased considerably,
from 925 mm to 780 mm, and from
343 m
to 300 m
, respectively. The
tubeside velocity (2.17 m/s vs. 1.36
m/s earlier), pressure drop (0.51
vs. 0.17 kg/cm
), and heat-
transfer coefficient (1,976 vs. 1,285
•°C) were all much higher.
The overall heat-transfer coefficient
for this design was 398 kcal/h•m
vs. 356 for Case A.
Stepwise calculations
for viscous liquids
When the variation in tubeside vis-
cosity is pronounced, a single-point
calculation for the tubeside heat-
transfer coefficient and pressure drop
will give unrealistic results. This is
particularly true in cases where a
combination of turbulent (or transi-
tion) flow and laminar flow exist,
since the thermal performance is very
different in these two regimes.
In such cases, it will be necessary
to perform the calculations stepwise
or zone-wise. The number of steps or
zones will be determined by the vari-
ation in the tubeside viscosity and
thus the Reynolds number.
Example 2:
Stepwise calculations
The principal process parameters
for a kettle-type steam generator in a
refinery are shown in Table 3. The
viscosity of the heavy vacuum gas oil
varies from 1.6 cP at the inlet to 6.36
cP at the outlet.
A design was produced without
performing the calculations stepwise
— that is, on the basis of a single av-
erage temperature and corresponding
physical properties. Details of this de-
sign are shown in Table 4.
Performing the tubeside calcula-
tions stepwise, in ten equal heat duty
steps, revealed that the original ex-
changer was undersurfaced. The rele-
vant performance parameters for the
single-point and stepwise calculations
are compared in Table 5.
The main reason for the difference
was the variation in Reynolds num-
ber, from 9,813 in the first zone to
2,851 in the last zone. In addition,
the mean temperature difference
(MTD) decreased drastically, from
138.47°C in the first zone to a mere
Case A Case B
Shell I.D., mm 925 780
Tube O.D. × Number of tubes × 25 × 500 × 2 20 × 540 × 2
Number of tube passes
Heat-transfer area, m
343 300
Tube pitch × Tube layout angle 32 × 90° 26 × 90°
Baffle type Single-segmental Single-segmental
Baffle spacing, mm 450 400
Baffle cut, percent of diameter 25 30
Velocity, m/s
Shellside 1.15 1.52
Tubeside 1.36 2.17
Heat-transfer coefficient, kcal/h•m
Shellside 2,065 2,511
Tubeside 1,285 1,976
Pressure drop, kg/cm
Shellside 0.86 1.2
Tubeside 0.17 0.51
Resistance, %
Shellside film 17.24 15.84
Tubeside film 27.71 21.14
Fouling 50.35 57.66
Metal wall 4.69 4.87
Overdesign 8.29 4.87
Table 2. Details of two designs for Example 1.
Shellside Tubeside
Fluid Boiler feedwater, Steam Heavy vacuum gas oil
Flow rate, kg/h 23,100 (fully vaporized) 129,085
Temperature in/out, °C 154 / 154 299 / 165
Allowable pressure drop, kg/cm
Negligible 1.4
Fouling resistance, h•m
•°C/kcal 0.0002 0.0006
Viscosity in/out, cP 0.176 / 0.176 1.6 / 6.36
Design pressure, kg/cm
(gage) 6.5 21.3
Heat duty, kcal/h 11,242,000 11,242,000
Table 3. Process parameters for Example 2.
17.04°C in the last. Thus, while the
initial zones (the hot end) had both a
high heat-transfer coefficient and a
high MTD, these decreased progres-
sively toward the outlet (cold) end of
the exchanger. Consequently, while
the first zone required a length of
only 2.325 m, the last zone required
a length of 44.967 m, even though
the heat duties were the same. The
tubeside pressure drop was only
marginally higher by the stepwise
method, because the tubeside is en-
tirely in the transition regime (Re be-
tween 2,851 and 9,813).
Shellside design
The shellside calculations are far
more complex than those for the
tubeside. This is mainly because on
the shellside there is not just one flow
stream but one principal cross-flow
stream and four leakage or bypass
streams. There are various shellside
flow arrangements, as well as various
tube layout patterns and baffling de-
signs, which together determine the
shellside stream analysis.
Shell configuration
TEMA defines various shell pat-
terns based on the flow of the shell-
side fluid through the shell: E, F, G,
H, J, K, and X (see Figure 1).
In a TEMAE single-pass shell, the
shellside fluid enters the shell at one
end and leaves from the other end.
This is the most common shell type
— more heat exchangers are built to
this configuration than all other con-
figurations combined.
A TEMA F two-pass shell has a
longitudinal baffle that divides the
shell into two passes. The shellside
fluid enters at one end, traverses the
entire length of the exchanger
through one-half the shell cross-sec-
tional area, turns around and flows
through the second pass, then finally
leaves at the end of the second pass.
The longitudinal baffle stops well
short of the tubesheet, so that the
fluid can flow into the second pass.
The F shell is used for tempera-
ture-cross situations — that is, where
the cold stream leaves at a tempera-
ture higher than the outlet tempera-
ture of the hot stream. If a two-pass
(F) shell has only two tube passes,
this becomes a true countercurrent ar-
rangement where a large temperature
cross can be achieved.
A TEMA J shell is a divided-flow
shell wherein the shellside fluid en-
ters the shell at the center and divides
into two halves, one flowing to the
left and the other to the right and
leaving separately. They are then
combined into a single stream. This is
identified as a J 1–2 shell. Alterna-
tively, the stream may be split into
two halves that enter the shell at the
two ends, flow toward the center, and
leave as a single stream, which is
identified as a J 2–1 shell.
A TEMA G shell is a split-flow
shell (see Figure 1). This construction
is usually employed for horizontal
thermosyphon reboilers. There is only
a central support plate and no baffles.
A G shell cannot be used for heat ex-
changers with tube lengths greater
than 3 m, since this would exceed the
limit on maximum unsupported tube
length specified by TEMA — typical-
ly 1.5 m, though it varies with tube
O.D., thickness, and material.
When a larger tube length is need-
ed, a TEMA H shell (see Figure 1) is
used. An H shell is basically two G
shells placed side-by-side, so that
there are two full support plates. This
is described as a double-split config-
uration, as the flow is split twice and
recombined twice. This construction,
too, is invariably employed for hori-
zontal thermosyphon reboilers. The
advantage of G and H shells is that
the pressure drop is drastically less
and there are no cross baffles.
A TEMA X shell (see Figure 1) is
a pure cross-flow shell where the
shellside fluid enters at the top (or
bottom) of the shell, flows across the
tubes, and exits from the opposite
side of the shell. The flow may be
introduced through multiple nozzles
Number of kettles 2 (in parallel)
Kettle/port I.D., mm 1,825 / 1,225
Tubes per kettle 790 tubes
Type 316 stainless steel
25 mm O.D. × 2 mm thick × 9 m long
Number of tube passes 12
Tube pitch 32 mm square (90°)
Baffling Full support plates only
Connections, mm (nominal) Shellside: inlet 75, outlet 3 × 200
Tubeside: 150
Heat-transfer area, m
1,104 (2 × 552)
Table 4. Design produced for Example 2
without stepwise calculations.
Single-point Stepwise
Calculations Calculations
Tubeside heat-transfer coefficient, kcal/h•m
•°C 347.9 229.2
Overall heat-transfer coefficient, kcal/h•m
•°C 244.7 179.3
Tubeside pressure drop, kg/cm
1.28 1.35
Overdesign, % 24.03 –9.11
Table 5. Performance parameters for Example 2 using
single-point and stepwise calculations.
located strategically along the length
of the shell in order to achieve a bet-
ter distribution. The pressure drop
will be extremely low — in fact,
there is hardly any pressure drop in
the shell, and what pressure drop
there is, is virtually all in the noz-
zles. Thus, this configuration is em-
ployed for cooling or condensing va-
pors at low pressure, particularly
vacuum. Full support plates can be
located if needed for structural in-
tegrity; they do not interfere with the
shellside flow because they are par-
allel to the flow direction.
A TEMA K shell (see Figure 1) is
a special cross-flow shell employed
for kettle reboilers (thus the K). It
has an integral vapor-disengagement
space embodied in an enlarged shell.
Here, too, full support plates can be
employed as required.
Tube layout patterns
There are four tube layout pat-
terns, as shown in Figure 6: triangular
(30°), rotated triangular (60°), square
(90°), and rotated square (45°).
A triangular (or rotated triangular)
pattern will accommodate more tubes
than a square (or rotated square) pat-
tern. Furthermore, a triangular pat-
tern produces high turbulence and
therefore a high heat-transfer coeffi-
cient. However, at the typical tube
pitch of 1.25 times the tube O.D., it
does not permit mechanical cleaning
of tubes, since access lanes are not
available. Consequently, a triangular
layout is limited to clean shellside
services. For services that require
mechanical cleaning on the shellside,
square patterns must be used. Chemi-
cal cleaning does not require access
lanes, so a triangular layout may be
used for dirty shellside services pro-
vided chemical cleaning is suitable
and effective.
A rotated triangular pattern sel-
dom offers any advantages over a
triangular pattern, and its use is
consequently not very popular.
For dirty shellside services, a
square layout is typically employed.
However, since this is an in-line
pattern, it produces lower turbu-
lence. Thus, when the shellside
Reynolds number is low (< 2,000),
it is usually advantageous to em-
ploy a rotated square pattern be-
cause this produces much higher
turbulence, which results in a high-
er efficiency of conversion of pres-
sure drop to heat transfer.
As noted earlier, fixed-tubesheet
construction is usually employed for
clean services on the shellside, U-
tube construction for clean services
on the tubeside, and floating-head
construction for dirty services on
both the shellside and tubeside. (For
clean services on both shellside and
tubeside, either fixed-tubesheet or
U-tube construction may be used, al-
though U-tube is preferable since it
permits differential expansion be-
tween the shell and the tubes.)
Hence, a triangular tube pattern may
be used for fixed-tubesheet exchang-
ers and a square (or rotated square)
pattern for floating-head exchangers.
For U-tube exchangers, a triangular
pattern may be used provided the
shellside stream is clean and a
square (or rotated square) pattern if
it is dirty.
Tube pitch
Tube pitch is defined as the shortest
distance between two adjacent tubes.
For a triangular pattern, TEMA
specifies a minimum tube pitch of
1.25 times the tube O.D. Thus, a 25-
mm tube pitch is usually employed
for 20-mm O.D. tubes.
For square patterns, TEMA addi-
tionally recommends a minimum
cleaning lane of in. (or 6 mm) be-
tween adjacent tubes. Thus, the mini-
mum tube pitch for square patterns is
either 1.25 times the tube O.D. or the
tube O.D. plus 6 mm, whichever is
larger. For example, 20-mm tubes
should be laid on a 26-mm (20 mm +
6 mm) square pitch, but 25-mm tubes
should be laid on a 31.25-mm (25
mm × 1.25) square pitch.
Designers prefer to employ the
minimum recommended tube pitch,
because it leads to the smallest shell
diameter for a given number of tubes.
However, in exceptional circum-
stances, the tube pitch may be in-
creased to a higher value, for exam-
ple, to reduce shellside pressure drop.
This is particularly true in the case of
a cross-flow shell.
Type of baffles. Baffles are used to
support tubes, enable a desirable ve-
locity to be maintained for the shell-
side fluid, and prevent failure of tubes
due to flow-induced vibration. There
are two types of baffles: plate and rod.
Plate baffles may be single-segmental,
double-segmental, or triple-segmen-
tal, as shown in Figure 7.
Baffle spacing. Baffle spacing is
the centerline-to-centerline distance
between adjacent baffles. It is the
most vital parameter in STHE design.
The TEMA standards specify the
minimum baffle spacing as one-fifth
of the shell inside diameter or 2 in.,
whichever is greater. Closer spacing
will result in poor bundle penetration
by the shellside fluid and difficulty in
mechanically cleaning the outsides of
the tubes. Furthermore, a low baffle
spacing results in a poor stream dis-
tribution as will be explained later.
(30 ˚)
I Figure 6. Tube layout patterns.
The maximum baffle spacing is
the shell inside diameter. Higher baf-
fle spacing will lead to predominantly
longitudinal flow, which is less effi-
cient than cross-flow, and large un-
supported tube spans, which will
make the exchanger prone to tube
failure due to flow-induced vibration.
Optimum baffle spacing. For tur-
bulent flow on the shellside (Re >
1,000), the heat-transfer coefficient
varies to the 0.6–0.7 power of veloci-
ty; however, pressure drop varies to
the 1.7–2.0 power. For laminar flow
(Re < 100), the exponents are 0.33 for
the heat-transfer coefficient and 1.0
for pressure drop. Thus, as baffle
spacing is reduced, pressure drop in-
creases at a much faster rate than
does the heat-transfer coefficient.
This means that there will be an
optimum ratio of baffle spacing to
shell inside diameter that will result
in the highest efficiency of conver-
sion of pressure drop to heat transfer.
This optimum ratio is normally be-
tween 0.3 and 0.6.
Baffle cut. As shown in Figure 8,
baffle cut is the height of the segment
that is cut in each baffle to permit the
shellside fluid to flow across the baffle.
This is expressed as a percentage of
the shell inside diameter. Although
this, too, is an important parameter for
STHE design, its effect is less pro-
found than that of baffle spacing.
Baffle cut can vary between 15%
and 45% of the shell inside diameter.
Both very small and very large
baffle cuts are detrimental to effi-
cient heat transfer on the shellside
due to large deviation from an ideal
situation, as illustrated in Figure 9. It
is strongly recommended that only
baffle cuts between 20% and 35% be
employed. Reducing baffle cut
below 20% to increase the shellside
heat-transfer coefficient or increas-
ing the baffle cut beyond 35% to de-
crease the shellside pressure drop
usually lead to poor designs. Other
aspects of tube bundle geometry
should be changed instead to achieve
those goals. For example, double-
segmental baffles or a divided-flow
shell, or even a cross-flow shell,
may be used to reduce the shellside
pressure drop.
For single-phase fluids on the
shellside, a horizontal baffle cut (Fig-
ure 10) is recommended, because this
minimizes accumulation of deposits
at the bottom of the shell and also
prevents stratification. However, in
the case of a two-pass shell (TEMA
F), a vertical cut is preferred for ease
of fabrication and bundle assembly.
Baffling is discussed in greater de-
tail in (2) and (3).
Equalize cross-flow
and window velocities
Flow across tubes is referred to as
cross-flow, whereas flow through the
window area (that is, through the baffle
cut area) is referred to as window flow.
The window velocity and the
cross-flow velocity should be as close
as possible — preferably within 20%
I Figure 8. Baffle cut.
I Figure 7. Types of baffles.
Double Segmental
Triple Segmental
Single Segmental
Rod Baffle No-Tubes-in-Window Segmental Baffles
of each other. If they differ by more
than that, repeated acceleration and
deceleration take place along the
length of the tube bundle, resulting in
inefficient conversion of pressure
drop to heat transfer.
Shellside stream analysis
On the shellside, there is not just
one stream, but a main cross-flow
stream and four leakage or bypass
streams, as illustrated in Figure 11.
Tinker (4) proposed calling these
streams the main cross-flow stream
(B), a tube-to-baffle-hole leakage
stream (A), a bundle bypass stream
(C), a pass-partition bypass stream
(F), and a baffle-to-shell leakage
stream (E).
While the B (main cross-flow)
stream is highly effective for heat
transfer, the other streams are not as
effective. The A stream is fairly effi-
cient, because the shellside fluid is
in contact with the tubes. Similarly,
the C stream is in contact with the
peripheral tubes around the bundle,
and the F stream is in contact with
the tubes along the pass-partition
lanes. Consequently, these streams
also experience heat transfer, al-
though at a lower efficiency than the
B stream. However, since the E
stream flows along the shell wall,
where there are no tubes, it encoun-
ters no heat transfer at all.
The fractions of the total flow rep-
resented by these five streams can be
determined for a particular set of ex-
changer geometry and shellside flow
conditions by any sophisticated heat-
exchanger thermal design software.
Essentially, the five streams are in
parallel and flow along paths of vary-
ing hydraulic resistances. Thus, the
flow fractions will be such that the
pressure drop of each stream is iden-
tical, since all the streams begin and
end at the inlet and outlet nozzles.
Subsequently, based upon the effi-
ciency of each of these streams, the
overall shellside stream efficiency
and thus the shellside heat-transfer
coefficient is established.
Since the flow fractions depend
strongly upon the path resistances,
varying any of the following con-
struction parameters will affect
stream analysis and thereby the shell-
side performance of an exchanger:
• baffle spacing and baffle cut;
• tube layout angle and tube
• number of lanes in the flow di-
rection and lane width;
• clearance between the tube and
the baffle hole;
• clearance between the shell I.D.
and the baffle; and
• location of sealing strips and
sealing rods.
Horizontal Cut
Vertical Cut
I Figure 10. Baffle cut orientation.
I Figure 11. Shellside flow distribution.
I Figure 9. Effect of small and large baffle cuts.
Main Flow
a. Small Baffle Cut
b. Large Baffle Cut
c. Ideal Baffle Cut and Baffle Spacing
Using a very low baffle spacing
tends to increase the leakage and by-
pass streams. This is because all five
shellside streams are in parallel and,
therefore, have the same pressure
drop. The leakage path dimensions
are fixed. Consequently, when baffle
spacing is decreased, the resistance of
the main cross-flow path and thereby
its pressure drop increases. Since the
pressure drops of all five streams must
be equal, the leakage and bypass
streams increase until the pressure
drops of all the streams balance out.
The net result is a rise in the pressure
drop without a corresponding increase
in the heat-transfer coefficient.
The shellside fluid viscosity also
affects stream analysis profoundly. In
addition to influencing the shellside
heat transfer and pressure drop per-
formance, the stream analysis also
affects the mean temperature differ-
ence (MTD) of the exchanger. This
will be discussed in detail later. First,
though, let’s look at an example that
demonstrates how to optimize baffle
design when there is no significant
temperature profile distortion.
Example 3:
Optimizing baffle design
Consider the heat exchanger ser-
vice specified in Table 6. Since there
are two independent variables — baf-
fle spacing and baffle cut — we will
first keep the baffle cut constant at
25% and vary the baffle spacing
(Table 7). Later, the baffle spacing
will be kept constant and the baffle
cut varied (Table 8). In real practice,
both parameters should be varied si-
multaneously, but keeping one pa-
rameter constant and varying the
other will more vividly demonstrate
the influence of each parameter.
The first design developed is des-
ignated Design A in Table 7. Here,
the baffle cut is 25% and the baffle
spacing is 300 mm. In Designs B and
C, the baffle spacing was changed to
350 mm and 400 mm, respectively.
There is no temperature profile dis-
tortion problem with these designs.
Notice that as the baffle spacing is
increased from 300 mm to 400 mm,
the main cross-flow, bundle bypass,
and pass-partition bypass streams in-
crease progressively, whereas the
tube-to-baffle-hole leakage and baf-
fle-to-shell leakage streams decrease
progressively. The overall heat-trans-
fer efficiency of the shellside stream
increases progressively. Neverthe-
less, since the shellside velocity and
the Reynolds number decrease, both
the shellside heat-transfer coefficient
and the shellside pressure drop de-
crease, but the former at a much
lower rate than the latter. Since the
allowable shellside pressure drop is
1.0 kg/cm
, Design A is ruled out, as
its shellside pressure drop far ex-
Shellside Tubeside
Fluid Crude oil Heavy gas oil circulating reflux
Flow rate, kg/h 367,647 105,682
Temperature in/out, °C 209 / 226 319 / 269
Heat duty, MM kcal/h 4.0 4.0
Density in/out, kg/m
730 / 715 655 / 700
Viscosity in/out, cP 0.52 / 0.46 0.27 / 0.37
Specific heat in/out, kcal/kg•°C 0.63 / 0.65 0.78 / 0.73
Thermal conductivity in/out, kcal/h•m•°C 0.087 / 0.085 0.073 / 0.0795
Allowable pressure drop, kg/cm
1.0 0.7
Fouling resistance, h•m
•°C/kcal 0.0006 0.0006
Design pressure, kg/cm
(gage) 36.6 14.0
Design temperature, °C 250 340
Line size, mm (nominal) 300 150
Material of construction Carbon steel 5CrMo
Table 6. Process parameters for Example 3.
Design A Design B Design C
Baffle spacing, mm 300 350 400
Tube-to-baffle-hole leakage (A), fraction 0.157 0.141 0.13
Main cross-flow stream (B), fraction 0.542 0.563 0.577
Bundle bypass stream (C), fraction 0.113 0.116 0.119
Baffle-to-shell leakage stream (E), fraction 0.12 0.109 0.1
Pass-partition bypass stream (F), fraction 0.069 0.072 0.075
Overall shellside heat-transfer efficiency, % 71.3 73.4 74.9
Shellside velocity, m/s
Cross-flow 2.5 2.15 1.87
Window flow 2.34 2.34 2.34
Shellside pressure drop, kg/cm
1.34 1.03 0.79
Heat-transfer coefficient, kcal/h•m
Shellside 2,578 2,498 2,372
Tubeside 1,402 1,402 1,402
Overall 401.8 399.8 396.5
Overdesign, % 7.58 7.08 6.21
Table 7. Effects of varying baffle spacing for a constant 25%
baffle cut for Example 3.
ceeds this limit. Designs B and C are
both acceptable. The overdesign
varies marginally. Thus, it would be
prudent to adopt Design C, since it
has a lower pressure drop and a bet-
ter stream analysis.
Now consider the effect of varying
the baffle cut while keeping the baffle
spacing constant at 400 mm, as
shown in Table 8. As the baffle cut is
progressively increased from 25% in
Design D to 36% in Design G, the
following changes are observed:
• the main cross-flow stream (B)
fraction increases appreciably;
• the tube-to-baffle-hole (A), baf-
fle-to-shell (E), and pass-partition (F)
stream fractions decrease steadily;
• the bundle bypass (C) stream
fraction remains steady;
• the overall heat-transfer effi-
ciency of the shellside stream first de-
creases and then increases; and
• as the window velocity decreas-
es, the shellside heat-transfer coeffi-
cient falls; the pressure drop also de-
creases, but not as fast as the heat-
transfer coefficient.
These observations are reflected in
the overdesign values. Design E ap-
pears to be the best choice, since De-
sign D cannot be accepted because of
the excessive shellside pressure drop.
Reducing ∆P
by modifying baffle design
Single-pass shell and single-seg-
mental baffles. The first baffle alter-
native is the single-segmental baffle
in a single-pass (TEMA E) shell.
However, in many situations, the
shellside pressure drop is too high
with single-segmental baffles in a sin-
gle-pass shell, even after increasing
the baffle spacing and baffle cut to the
highest values recommended. Such a
situation may arise when handling a
very high shellside flow rate or when
the shellside fluid is a low-pressure
gas. In these cases, the next alterna-
tive that should be considered is the
double-segmental baffle (Figure 7).
Single-pass shell and double-seg-
mental baffles. By changing the baf-
fling from single-segmental to double-
segmental at the same spacing in an
otherwise identical heat exchanger,
the cross-flow velocity is reduced ap-
proximately to half, because the shell-
side flow is divided into two parallel
streams. This greatly reduces the
cross-flow pressure drop. However,
the window velocity and therefore the
window pressure drop cannot be re-
duced appreciably (assuming that the
maximum recommended baffle cut
was already tried with single-segmen-
tal baffles before switching to double-
segmental baffles). Nevertheless,
since cross-flow pressure drop is in-
variably much greater than window
pressure drop, there is an appreciable
reduction in the total pressure drop.
There is also a decrease in the shell-
side heat-transfer coefficient, but this
is considerably less than the reduction
in the pressure drop. The use of dou-
ble-segmental baffles is covered in
depth in (3).
Divided-flow shell and single-seg-
mental baffles. If the allowable shell-
side pressure drop cannot be satisfied
even with double-segmental baffles at
a relatively large spacing, a divided-
flow shell (TEMA J) with single-seg-
mental baffles (Figure 1) should be in-
vestigated next. Since pressure drop is
proportional to the square of the veloc-
ity and to the length of travel, a divid-
ed-flow shell will have approximately
Design D Design E Design F Design G Design H
Baffle cut, percent of diameter 25 30 33 36 20
Tube-to-baffle-hole leakage (A), fraction 0.13 0.106 0.093 0.08 0.159
Main cross-flow stream (B), fraction 0.577 0.612 0.643 0.674 0.54
Bundle bypass stream (C), fraction 0.119 0.122 0.118 0.117 0.126
Baffle-to-shell leakage stream (E), fraction 0.1 0.091 0.085 0.078 0.114
Pass-partition bypass stream (F), fraction 0.075 0.069 0.062 0.052 0.061
Overall shellside heat-transfer efficiency, % 74.9 73.0 75.7 78.6 72.7
Shellside velocity, m/s
Cross-flow 1.87 1.87 1.87 1.87 1.87
Window flow 2.34 1.86 1.65 1.48 3.09
Shellside pressure drop, kg/cm
0.79 0.69 0.65 0.6 0.98
Heat-transfer coefficient, kcal/h•m
Shellside 2,372 2,200 2,074 1,929 2,406
Tubeside 1,402 1,402 1,402 1,402 1,402
Overall 396.5 391.4 387.3 381.9 397.4
Overdesign, % 6.21 4.86 3.76 2.33 6.43
Table 8. Effects of varying baffle cut for a constant 400-mmbaffle spacing for Example 3.
one-eighth the pressure drop in an oth-
erwise identical single-pass exchanger.
The advantage of a divided-flow
shell over double-segmental baffles is
that it offers an even larger reduction
in pressure drop, since not only cross-
flow velocity but even window veloc-
ity can be reduced. The disadvantage
is the increase in cost due to the addi-
tional piping required.
Divided-flow shell and double-
segmental baffles. If even a divided-
flow shell with single-segmental baf-
fles is unable to meet the allowable
shellside pressure drop limit, it will
be necessary to adopt a combination
of a divided-flow shell and double-
segmental baffles. With such a com-
bination, a very large reduction in
shellside pressure drop is possible —
to as low as 4% of the pressure drop
in a single-pass exchanger with the
same baffle spacing and baffle cut. In
sharp contrast, the heat-transfer coef-
ficient will reduce to about 40%.
No-tubes-in-window segmental
baffles. As baffle spacing is increased
to reduce the shellside pressure drop,
an exchanger becomes more prone to
tube failure due to flow-induced vi-
bration. Exchangers with double-seg-
mental baffles are less likely to expe-
rience such problems than those with
single-segmental baffles.
However, a vibration problem may
persist even with double-segmental
baffles. In such cases, a no-tubes-in-
window design (Figure 7) should be
adopted. Here, each tube is supported
by every baffle, so that the unsupport-
ed tube span is the baffle spacing. In
exchangers with normal single-seg-
mental baffles, the unsupported tube
span is twice the baffle spacing.
Should it become necessary to use
a very large baffle spacing to restrict
the shellside pressure drop to the per-
mitted value, intermediate supports
may be used to increase the natural
frequency of the tubes, thus produc-
ing a design that is safe against tube
failure due to flow-induced vibration.
The no-tubes-in-window design
requires a larger shell diameter for a
given number of tubes. This esclates
its cost, typically by about 10%. The
higher cost is offset to some extent by
the higher shellside heat-transfer co-
efficient, since pure cross-flow is
more efficient than the combination
of cross-flow and window flow in
conventional designs.
Cross-flow shell. There are some
services where the pressure drop limi-
tation is so severe that none of the
above shell/baffling configurations can
yield a satisfactory design. A steam
ejector condenser operating at a pres-
sure of 50 mm Hg and having an al-
lowable pressure drop of 5 mm Hg is
an example. Such situations require the
use of a cross-flow shell (TEMAX).
Here, pure cross-flow takes place at
a very low velocity, so there is virtually
no pressure drop in the shell. Whatever
pressure drop occurs is almost entirely
in the nozzles. Support plates will be
needed to meet TEMA requirements
and prevent any possible flow-induced
tube vibration. Since the shellside flow
is parallel to these support plates, shell-
side pressure drop is not increased.
Increasing tube pitch
For a given number of tubes, the
smaller the tube pitch, the smaller the
shell diameter, and therefore the
lower the cost. Consequently, design-
ers tend to pack in as many tubes as
mechanically possible.
As noted earlier, designers gener-
ally set the tube pitch at 1.25 times
the tube O.D. For square or rotated
square pitch, a minimum cleaning
lane of in. or 6 mm is recommend-
ed by TEMA.
As far as thermal-hydraulics are
concerned, the optimum tube-pitch-
to-tube-diameter ratio for conversion
of pressure drop to heat transfer is
typically 1.25–1.35 for turbulent flow
and around 1.4 for laminar flow.
Increasing the tube pitch to re-
duce pressure drop is generally not
recommended for two reasons. First,
it increases the shell diameter and,
thereby, the cost. Second, reducing
pressure drop by modifying the baf-
fle spacing, baffle cut, or shell type
will result in a cheaper design.
However, in the case of X shells, it
may be necessary to increase the tube
pitch above the TEMA minimum to
meet pressure drop limitations, since
there are no other parameters that can
be modified.
Mean temperature difference
Temperature difference is the driv-
ing force for heat transfer.
When two streams flow in op-
posing directions across a tube wall,
there is true countercurrent flow
(Figure 12). In this situation, the
only limitation is that the hot
stream should at all points be hotter
than the cold stream. The outlet
temperature of the cold stream may
be higher than the outlet tempera-
ture of the hot stream, as shown in
Figure 12.
I Figure 13. Cocurrent flow.
Exchanger Length
I Figure 12. Countercurrent flow.
Exchanger Length
Since the temperature difference
varies along the length of the heat
exchanger, it has to be weighted to
obtain a mean value for single-point
determination of heat-transfer area.
The logarithmic mean temperature
difference (LMTD) represents this
weighted value.
If the hot and cold streams flow in
the same direction, flow is cocurrent
(Figure 13). The mean temperature
difference is still represented by the
LMTD. However, the LMTD for
cocurrent flow is lower than that for
countercurrent flow for the same ter-
minal differences. This is because al-
though one terminal temperature dif-
ference is very high, the other is far
too low — that is, the temperature
differences along the path of heat
transfer are not balanced.
What is even more serious with
cocurrent flow is that the outlet tem-
perature of the cold stream must be
somewhat lower than the outlet tem-
perature of the hot stream, which is a
serious limitation. Consequently,
countercurrent flow is always pre-
ferred to cocurrent flow.
These principles apply only to sin-
gle-pass exchangers. However, as
noted earlier, shell-and-tube heat ex-
changers invariably have two or more
tube passes. Since the shellside fluid
flows in one direction, half the tube
passes experience countercurrent
flow and the other half experience
cocurrent flow. The MTD for this sit-
uation is neither the LMTD for coun-
tercurrent flow nor that for cocurrent
flow, but a value between the two.
A correction factor, F
, which de-
pends on the four terminal tempera-
tures and the shell style can be deter-
mined from charts in the TEMA stan-
dards. The LMTD for countercurrent
flow is multiplied by this factor to ob-
tain the corrected MTD.
An important limitation for 1-2
shells (one shell pass and two or more
tube passes) is that the outlet tempera-
ture of the cold stream cannot exceed
the outlet temperature of the hot
stream. This is because of the presence
of one or more cocurrent passes. In re-
ality, a very small temperature differ-
ence is possible, but this represents an
area of uncertainty and the credit is
very small, so it is usually ignored.
When there is a temperature cross
(that is, the outlet temperature of the
cold stream is higher than the outlet
temperature of the hot stream), and
pure countercurrent flow is not possi-
ble, multiple shells in series must be
used. This will be discussed in detail
in the followup article scheduled to
be published in the next issue.
An F shell has two passes, so if there
are two tube passes, this is a pure coun-
tercurrent situation. However, if an F
shell has four or more tube passes, it is
no longer a true countercurrent situation
and, hence, the F
correction has to be
applied. An F shell having four or more
tube passes is represented as a 2-4 shell.
The F
factor for a 2-4 shell is identical
to that for two 1-2 shells in series or two
shell passes. The TEMA F
factor chart
for three shell passes really represents
three shells in series, that for four shell
passes four shells in series, and so on.
It is important to realize that the
LMTD and F
factor concept assumes
that there is no significant variation in
the overall heat-transfer coefficient
along the length of the shell. Howev-
er, there are some services where this
is not true. An example of this is the
cooling of a viscous liquid — as the
liquid is cooled, its viscosity increas-
es, and this results in a progressive
reduction in the shellside heat-trans-
fer coefficient. In this case, the sim-
plistic overall MTD approach will be
inaccurate, and the exchanger must
be broken into several sections and
the calculations performed zone-wise.
Temperature profile distortion
An important issue that has not
been considered so far is the tempera-
ture profile distortion. As noted earli-
er, the leakage and bypass streams are
less efficient for heat transfer than the
main cross-flow stream.
Consider a case where the shellside
stream is the cold fluid. Since the
main cross-flow stream encounters a
very large fraction of the total heat-
transfer surface, it has to pick up a
very large part of the total heat duty.
Assume that the cross-flow stream is
58% of the total shellside stream, but
that it comes in contact with 80% of
the tubes. As a result, its temperature
rises more rapidly than if the entire
shellside stream were to pick up the
entire heat duty. Therefore, its temper-
I Figure 14. Temperature profile distortion factor due to bypass and leakage.
E Stream

Exchanger Length
Apparent Temperature Profile
C =Bundle-to-Shell Bypass
E =Baffle-to-Shell Leakage
ature profile will be steeper than that
of the total stream (the apparent tem-
perature profile) without considering
the various flow fractions (Figure 14).
The temperature profiles of the
baffle-hole-to-tube leakage, shell-to-
bundle leakage, and pass-partition by-
pass streams will depend on their re-
spective flow fractions and the frac-
tional heat-transfer area encountered.
However, since the shell-to-baffle
leakage stream does not experience
any heat transfer, the remaining four
streams must pick up the entire heat
duty, so that these four streams to-
gether will have a temperature profile
steeper than that of the apparent
stream. Consequently, the temperature
difference between the hot and the
cold streams will be lower all along
the length of the heat exchanger,
thereby resulting in the reduction of
the MTD. This reduction in the MTD
is known as the temperature profile
distortion (or correction) factor.
The temperature profile distortion
factor is more pronounced when the
leakage and bypass streams are high,
especially the shell-to-baffle leakage
stream, and the ratio of shellside tem-
perature difference to the temperature
approach at the shell outlet is high.
The latter is because the closer the
temperature approach at the shell out-
let, the sharper the reduction in MTD. The leakage and bypass streams
tend to be high when the shellside
viscosity is high and when the baffle
spacing is very low. Thus, care has to
be exercised in the design of viscous
liquid coolers such as a vacuum
residue cooler in a crude oil refinery.
The minimum recommended tem-
perature profile distortion factor is
0.75. Below this, two or more shells
in series must be employed. By using
multiple shells in series, the ratio of
shellside temperature difference to
the temperature approach at the shell
outlet is reduced. The mixing of the
main cross-flow stream with the by-
pass and leakage streams after each
shell reduces the penalty due to the
distortion of the temperature profile
and hence increases the temperature
profile distortion factor.
In many situations, a temperature
profile distortion factor is unavoid-
able, such as when cooling a viscous
liquid over a large temperature
range, and there is no alternative to
the use of multiple shells in series.
However, in many other situations,
improper baffle spacing unnecessar-
ily imposes such a penalty where it
is easily avoidable. Designers nor-
mally tend to pack baffles as close
as possible to get the maximum
shellside heat-transfer coefficient,
pressure drop permitting. In many
such cases, the use of somewhat
higher baffle spacing will reduce the
shell-to-baffle leakage stream (the
principal culprit) and hence improve
the MTD correction factor appre-
ciably, thereby producing a much
better design.
Shell I.D. 500 mm
Tubes 188 tubes, 20 mm O.D. × 2 mm thick × 6 m long
Number of tube passes 2
Tube pitch 26 mm square (90°)
Baffling Single-segmental, 140 mm spacing, 21% cut (diameter)
Connections 75 mm on shellside, 150 mm on tubeside
Heat-transfer area 70 m
Table 10. Construction parameters for Example 4.
c = stream specific heat, kcal/kg•°C
D = tube inside diameter, m
= LMTD correction factor,
G = stream mass velocity, kg/m
h = stream heat-transfer coefficient,
k = stream thermal conductivity,
Nu = Nusselt number = hD/k,
Pr = Prandtl number = cµ/k,
Re = Reynolds number = DG/µ,
Greek Letter
µ = stream viscosity, kg/m•h
Shellside Tubeside
Fluid Naphtha Cooling water
Flow rate, kg/h 9,841 65,570
Temperature in/out, °C 114 / 40 33 / 40
Heat duty, MM kcal/h 0.46 0.46
Specific gravity in/out 0.62 / 0.692 1.0 / 1.0
Viscosity in/out, cP 0.254 / 0.484 0.76 / 0.66
Average specific heat, kcal/kg•°C 0.632 1.0
Thermal conductivity in/out, kcal/h•m•°C 0.092 / 0.101 0.542 / 0.546
Allowable pressure drop, kg/cm
0.7 0.7
Fouling resistance, h•m
•°C/kcal 0.0002 0.0004
Design pressure, kg/cm
(gage) 12.0 6.5
Design temperature, °C 150 60
Material of construction Carbon steel Admirality brass
Table 9. Process parameters for Example 4.
Example 4: Temperature
distortion and baffle spacing
Consider an existing naphtha
cooler in a refinery and petrochemi-
cal complex. The process parameters
are listed in Table 9, and the con-
struction parameters in Table 10.
The existing design was undersur-
faced by 21%, mainly because the
temperature profile distortion factor
was 0.6, which is lower than the
minimum recommended value of
0.75. The existing design had a baf-
fle spacing of 140 mm and a baffle
cut of 21% (of the diameter). The
shell-to-baffle leakage stream frac-
tion was 0.24.
To improve the design, the baffle
spacing was progressively increased.
The undersurfacing decreased with
increasing baffle spacing, up to a
spacing of 190 mm; thereafter, per-
formance again started to deteriorate.
Thus, 190 mm is the optimum baffle
The detailed results of the vari-
ous iterations are compared in
Table 11.
Existing Design Alternative No. 1 Alternative No. 2 Alternative No. 3 Alternative No. 4
Baffle spacing, mm 140 160 175 190 210
Stream analysis, fraction of stream
Baffle-hole-to-tube leakage (A) 0.189 0.173 0.163 0.154 0.143
Main cross-flow (B) 0.463 0.489 0.506 0.521 0.539
Shell-to-bundle leakage (C) 0.109 0.113 0.116 0.118 0.121
Shell-to-baffle leakage (E) 0.24 0.225 0.215 0.207 0.196
Pass-partition bypass stream (F) 0 0 0 0 0
Overall shellside heat-transfer 62 64.7 66.4 67.9 69.7
efficiency, %
Temperature profile distortion factor 0.6 0.692 0.735 0.766 0.794
Shellside velocity, m/s 0.15 0.14 0.13 0.13 0.12
Shellside heat-transfer coefficient, 614 570 562 550 512
Shellside pressure drop, kg/cm
0.034 0.029 0.027 0.026 0.023
Overall heat-transfer coefficient,
•°C 380 362 359 354 338
Mean temperature difference, °C 13.73 15.9 16.87 17.58 18.22
Overdesign, % –21.1 –12.8 –8.26 –5.73 –6.61
Table 11. Detailed results of Example 4 iterations.
Literature Cited
1. Tubular Exchanger Manufacturers
Association, “Standards of the Tubular
Exchanger Manufacturers Associa-
tion,” 7th ed., TEMA, New York
2. Mukherjee, R., “Don’t Let Baffling
Baffle You,” Chem. Eng. Progress, 92
(4), pp. 72–79 (Apr. 1996).
3. Mukherjee, R., “Use Double-Segmen-
tal Baffles in Shell-and-Tube Heat Ex-
changers,” Chem. Eng. Progress, 88
(11), pp. 47–52 (Nov. 1992).
4. Tinker, T., “Shellside Characteristics of
Shell-and-tube Heat Exchangers: A
Simplified Rating System for Commer-
cial Heat Exchangers,” Trans. ASME,
80, pp. 36–52 (1958).
Further Reading
Kakac, S., et al., “Heat Exchangers: Ther-
mal-Hydraulic Fundamentals and De-
sign,” Hemisphere Publishing Corp.,
New York (1981).
Schlunder, E.V., et al., eds., “Heat Ex-
changer Design Handbook,” Hemi-
sphere Publishing Corp., New York
R. MUKHERJ EE is assistant chief consultant in
the Heat and Mass Transfer Dept. of Engineers
India Ltd., New Delhi (011-91-11-371-6171;
Fax: 011-91-11-371-5059l; e-mail:, where he has
been employed since 1971. He has over 26
years of experience in the design, revamping,
and troubleshooting of air-cooled and shell-
and-tube heat exchangers (especially for oil
refineries, gas processing plants, and
petrochemical plants), and also has
considerable experience in heat-exchanger-
network synthesis and optimization. He has
written several articles in technical journals
and has presented two papers in the Industrial
Session of the 10th International Heat Transfer
Conference at Brighton in August 1994.
He has served as faculty for several courses in
heat exchanger design, energy conservation,
and heat exchanger network optimization.
He is an honors graduate in chemical
engineering fromJ adavpur Univ., Calcutta,
and is a member of the Indian Institute of
Chemical Engineers and the Indian Society
for Heat and Mass Transfer.
The author is grateful to the management of
Engineers India, Ltd., for permission to publish
this article and acknowledges the use of Heat
Transfer Research, Inc.’s software for the
worked-out examples and their design