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eat exchangers serve a straightforward purpose

:
controlling a system’s or substance’s temperature
by adding or removing thermal energy. Although there
are many different sizes, levels of sophisti-
cation, and types of heat exchangers, they
all use a thermally conducting element—
usually in the form of a tube or plate—to
separate two
fl ui ds, such
that one can
transfer ther-
mal energy to
the other.
Home heating
systems use a
heat exchang-
er to transfer
c o m b u s t i o n -
gas heat to water or air,
whi ch is circul at ed
through the house. Power
plants use locally available
water or ambi ent air i n
quite large heat exchang-
er s t o condense steam
from the turbines. Many
industrial applications use
small heat exchangers to
establ ish or maintain a
required temperature. In
industry, heat exchangers
perform many tasks, rang-
ing from cooling lasers to
establishing a controlled
sample temperature prior
to chromatography.
Anyone who wants to use a heat exchanger faces a
fundamental challenge: fully defining the problem to be
solved, which requires an understanding of the thermo-
dynamic and transport properties of fluids. Such knowl-
edge can be combined with some simple calculations to
define a specific heat-transfer problem and select an
appropriate heat exchanger.
Fluid fundamentals
How heat gets transferred from one fluid to another
depends largely on the physical characteristics of the
fluids involved, especially their density, specific heat,
thermal conductivity, and dynamic viscosity.
D e n s i t y ( ) is a fluid’s mass per unit volume, mea-
sured as lb
m
/ft
3
(where lb
m
represents pounds of mass)
or kg/m
3
. Density can be used to convert a measure-
ment from a mass-flow rate, such as lb
m
/hr, to the more
common volumetric units, such as gallons per minute
for liquids, or cubic feet per minute for gases. Through-
out a heat exchanger, the
mass-flow rate remains con-
stant, but changes in tem-
perature and pressure can
change the volumetric flow
rate, particularly for a gas.
So a gas flow should be stat-
ed as a mass flow, a volu-
metric flow at standard con-
ditions, or as a volumetric
flow including temperature
and pressure. In any case,
the operati ng pressure
should always be specified.
Specific heat (c or c
p
for a
gas, where p represents a
constant pressure) is the
amount of heat required to
raise the temperature of one
unit of fluid mass by one
degree. Its unit s are
B T U / ( l b
m
°C) or J/(kg °C).
Specifi c heat relates the
quantity of transferred heat
to the temperature change
of the fluid while passing
through the heat exchanger.
Thermal conductivity (k)
represents the ability of a fluid to conduct heat. It is
measured in BTU/[ft
2
hr (°F/ft)], BTU/(ft hr °F), or
W/(m °C).
Dynamic viscosity ( ) indicates a fluid’s resistance to
flow. A fluid with high dynamic viscosity produces a
high pressure loss because of the shear resistance, pri-
marily along the heat exchanger surfaces. Its units are
l b
m
/(ft hr), (lb
f
h r ) / f t
2
(where lb
f
is pounds of force),
kg/(m s), (N s)/m
2
, Pa s, and many others. The selection
of units usually depends on the industry, but they
can be converted to one of the above forms. In most
cases, viscosity is given in centipoise [1 centipoise =
1,000 Pa s= 2.42 lb
m
/(ft hr)].
The Fundamentals
of Heat Exchangers
18
The Industrial Physicist
by Dean A. Bartlett
© 1996 American Institute of Physics
To control the tempera-
ture of a system or sub-
stance, pick one of
three types of heat
e x c h a n g e rs and use
these equations to esti-
mate the size you need
F e a t u r e F E A T U R E
Figure 1. Coil heat exchangers are capable of
handling high pressures and wide temperature
differences.
Fluid flow
Inside a heat exchanger, the fluid flow is either turbu-
lent or laminar. Turbulent flow produces better heat
transfer, because it mixes the fluid. Laminar-flow heat
transfer relies entirely on the thermal conductivity of the
fluid to transfer heat from inside a stream to a heat-
exchanger wall.
An exchanger’s fluid flow can be determined from its
Reynolds number (N
Re
):
where is flow velocity and D is the diameter of the
tube in which the fluid flows. The units cancel each
other, making the Reynolds number dimensionless. If
the Reynolds number is less than 2,000, the fluid flow
will be laminar; if the Reynolds number is greater than
6,000, the fluid flow will be fully turbulent. The transi-
tion region between laminar and turbulent flow pro-
duces rapidly increasing thermal performance as the
Reynolds number increases.
The type of flow determines how much pressure a
fluid loses as it moves through a heat exchanger. This is
important because higher pressure drops require more
pumping power. Although a manufacturer will normally
determine the pressure drop, it is useful to predict the
pressure drops that can occur with changing rates of
flow. Laminar flow produces the smallest loss, which
increases linearly with flow velocity. For example, dou-
bling the flow velocity doubles the pressure loss. For
Reynolds numbers beyond the laminar region, the pres-
sure loss is a function of flow velocity raised to a power
in the range 1.6–2.0. In other words, doubling the flow
could increase the pressure loss by a factor of four.
Balance and effectiveness
The characteristics of fluids contribute to a funda-
mental property of heat exchangers—the heat-transfer
rate ( ). The heat transferred to the colder fluid must
equal that transferred from the hotter fluid, according to
the following equation:
where represents the mass flow per unit time. So the
heat transferred per unit time equals the product of mass
flow per unit time, specific heat, and the temperature
change. This quick calculation should be done before
specifying any heat exchanger. Although heat exchangers
are commonly specified only with desired temperatures,
m
Q
V
19
The Industrial Physicist
Figure 2 (left).
Thermal perfor-
mance of shell-
and-tube exchang-
ers is high.
Figure 3 (right).
Plate heat
exchangers have
high heat-transfer
coefficients and
area.
N
Re
=
× × D V
Q= [ × c
p
× (T
out
– T
in
)]
cold
m
= – [ × c
p
× (T
out
– T
in
)]
hot
m
the heat-transfer rate is the prime criterion.
An exchanger’s effectiveness ( ) is the ratio of the actu-
al heat transferred to the heat that could be transferred by
an exchanger of infinite size. Effectiveness is the best way
to compare different types of heat exchangers.
For example, Figure 4 shows a hot-fluid stream being
cooled by a cold-fluid stream in a counterflow heat
exchanger. When the hot stream exits the exchanger, it
must be warmer than the inlet temperature of the cold
stream. In an ideal heat exchanger, with = 1, the out-
going hot stream’s temperature equals the incoming
cold stream’s temperature. In additi on, this heat
exchanger’s cold stream exits at a temperature lower
than the inlet temperature of the hot stream.
The heat-balance equation can be applied to this
problem as:
where the denominator, or maximum possible rate of
heat transfer, is based on the stream with the smallest
(mass-flow rate)(specific heat) product, also known as
the minimum thermal-capacity rate and indicated by the
subscript “min”. Given that the temperature drop on the
hot stream is greater than the temperature gain in the
cold stream in this example, the product of the mass-
flow rate and the specific heat of the hot stream must be
less than that of the cold stream, because of the required
heat-transfer rate balance.
Exchanger equation
The heat-transfer rate ( ) of a given exchanger
depends on its design and the properties of the two fluid
streams. This characteristic can be defined as:
where U is the overall heat-transfer coefficient, or the
ability to transfer heat between the fluid streams, A i s
the heat-transfer area of the heat exchanger, or in other
words the total area of the wall that separates the two
fluids, and ∆T
log mean
is the average effective temperature
difference between the two fluid streams over the length
of the heat exchanger.
A heat exchanger’s performance is predicted by calcu-
lating the overall heat transfer coefficient U and the area
A. The inlet temperatures of the two streams can be
measured, which leaves three unknowns—the two exit
temperatures and the heat- tr ansfer r ate. These
unknowns can be determined from three equations (the
one above using an arithmetic average for T
log mean
plus
the heat-balance equation for each stream):
Solving these equations si mul taneously usually
requires iteration. In any case, a heat exchanger’s manu-
facturer usually completes them.
Types of exchangers
Heat exchangers come in a wide variety of types and
sizes. Here are a few of the most common ones.
Coil heat exchangers (Figure 1) have a long, small-
diameter tube placed concentrically within a larger tube,
the combined tubes being wound or bent in a helix. One
fluid passes through the inner tube, and the other fluid
passes through the outer tube. Thi s type of heat
exchanger is robust—capable of handling high pressures
and wide temperature di fferences. Although these
exchangers tend to be inexpensive, they provide rather
poor thermal performance because of a small heat-trans-
fer area. Nevertheless, a coil heat exchanger may be the
best choice for low-flow situations, because the single-
tube passage creates higher flow velocity and a higher
Reynolds number. These exchangers are commonly used
to establish a fixed temperature for a process-stream
sample prior to taking measurements. These exchangers
can also be used to condense high-temperature stream
samples.
Plate heat exchangers (Figure 3) consist of a stack of
parallel thin plates that lie between heavy end plates.
Each fluid stream passes alternately between adjoining
plates in the stack, exchanging heat through the
Q
= [ × c
p
× (T
out
– T
in
)]
cold
m
20
The Industrial Physicist
ε =
( c
p
)
hot
(T
in
– T
out
)
hot
m
=
( c
p
)
cold
(T
out
– T
in
)
cold
m
( c
p
)
min
(T
in hot
– T
in cold
) m
Q
= – [ × c
p
× (T
out
– T
in
)]
hot
m
( c
p
)
min
(T
in hot
– T
in cold
) m
=U A
(T
in hot
– T
out cold
) + (T
out hot
– T
in cold
)
2
Q
e < 1(actual)
e = 1(ideal)
T
in(hot)
T
out(cold)
T
out(hot)
Cold fluid
Hot fluid
T
in(cold)
Figure 4.
Stream temper-
atures through
a heat exchang-
er in counter-
current flow.
Length
Q=UA∆T
log mean
21
The Industrial Physicist
plates. The plates
ar e cor rugated
for strength and
to enhance heat
transfer by direct-
ing the flow and
increasing turbu-
l ence. These
exchangers have high heat-transfer coefficients and
area, the pressure drop is also typically low, and they
often provide very high effectiveness. However, they
have relatively low pressure capability.
Shell-and-tube heat exchangers (Figures 2 & 5) consist
of a bundle of parallel tubes that provide the heat-trans-
fer surface separating the two fluid streams. The tube-
side fluid passes axially through the inside of the tubes;
the shell-side fluid passes over the outside of the tubes.
Baffles external and perpendicular to the tubes direct the
fl ow across the tubes and provide tube support.
Tubesheets seal the ends of the tubes, ensuring separa-
tion of the two streams. The process fluid is usually
placed inside the tubes for ease of cleaning or to take
advantage of the higher pressure capability inside the
tubes. The thermal performance of such an exchanger
usually surpasses a coil type but is less than a plate type.
Pressure capability of shell-and-tube exchangers is gen-
erally higher than a plate type but lower than a coil type.
Technical tips
For any heat-exchanger application, a user will profit
from the following pointers:
• Consider heat exchangers early in system design.
• Avoid being overly safe in specifying performance cri-
teria. Asking for more temperature change, higher
flow capability, and other just-in-case possibilities
can easily double an exchanger’s size and cost. Con-
sider the required effectiveness values, but remember
that an exchanger’s size approaches infinity asymp-
totically as effectiveness approaches 1. So it takes
considerably more heat-exchanger area to raise the
effectiveness from 0.8 to 0.9 than it does to go from
0.7 to 0.8. High effectiveness—greater than 0.9—can
be very expensive.
• Consider increasing pumping power rather than
increasing an exchanger’s size. Higher velocity flow
can produce or increase turbulence, which leads to
an increased pressure drop and the need for more
pumping power. Neverthel ess, turbulence al so
increases the heat-transfer coeffici ent, thereby
decreasing the required heat-exchanger size. Accept-
ing the increased pressure drop may be a more viable
option than increasing size.
• Remember that the prime criterion is the product of
the overall heat-transfer coefficient and the transfer
area (U A)—not just the transfer area. For laminar-
flow tubes, the total tube length, not the transfer
area, is usually the important factor; so 10 feet of 1/4-
inch tubing works as well as 10 feet of 1-inch tubing.
• Specify the smallest possible tubing for tube-type heat
exchangers, because it gives the maximum thermal
performance with the minimum volume. However,
be aware of the effects of fouling or particulates that
may clog small tubes.
• Strive for turbulent flow to enhance heat transfer,
even though that can be difficult with viscous fluids
and low flow rates.
• Be aware of fluid thermal conductivity when specify-
ing the cooling or heating fluid. Perhaps surprisingly,
water usually works the best.
• Match the inlet-port size to the piping sizes expected
for the rest of the system.
• Consider an exchanger’s lifetime and maintenance
requirements. Choose the type and thickness of
material that will reduce failure caused by corrosion
and erosion. Also consider a system’ s ease of
mechanical or chemical cleaning as well as filtration
of the fluid streams.
• Provide the heat-exchanger vendor with as much
information on the total system as possible.
These technical tips, basic concepts, and equations
should give you the tools for defining a heat-exchange
problem and considering the possible heat-exchanger
solutions. For information on specific exchangers, look
at manufacturers’ catalogs, which provide more details
about what can be accomplished with different types of
heat exchangers.
Dean A. Bartlett has an M.S. in mechanical
engineering and is founder, president, and
technical director of Exergy Inc., Hanson,
Massachusetts, heat transfer specialists.
Shell side
flow
Shell
Tube
Tube sheet
Tube
side
flow
Baffle
Figure 5. Shell-
and-tube heat
exchanger with
counter-current
flow.