ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
TABLE OF CONTENTS
Page
List of Figures ............................................................................................................................................... ii
List of Tables ............................................................................................................................................... iii
Enabling Objectives ..................................................................................................................................... iv
Introduction ................................................................................................................................................ 3-1
Conduction ................................................................................................................................................. 3-1
Conduction Through Composite Bodies........................................................................................ 3-6
Conduction in Cylindrical Geometry ............................................................................................. 3-9
Convection ................................................................................................................................................. 3-9
Forced Convection ....................................................................................................................... 3-11
Radiation .................................................................................................................................................. 3-11
Heat Exchangers ...................................................................................................................................... 3-14
Classification of Heat Exchangers ............................................................................................... 3-16
Overall Heat Transfer Coefficient (U) ......................................................................................... 3-18
Log Mean Temperature Difference.............................................................................................. 3-19
Counter Flow and Parallel Flow Heat Exchanger Calculations................................................... 3-20
Comparison of Counterflow Versus Parallel Flow Heat Exchangers.......................................... 3-24
General Energy Equation for Heat Exchangers ........................................................................... 3-24
Summary .................................................................................................................................................. 3-27
Definitions................................................................................................................................................ 3-28
Exercises .................................................................................................................................................. 3-29
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ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
LIST OF FIGURES
Page
Figure 3.1
Section of a Plane Wall
3.2
Figure 3.2
Glass Window Pane
3.5
Figure 3.3
Temperature versus Distance in a Composite Path
3.7
Figure 3.4
Shell-and-Tube Design Heat Exchanger
3.15
Figure 3.5
Parallel and Counterflow Heat Exchangers
3.17
Figure 3.6
Cross Flow Heat Exchanger
3.17
Figure 3.7
Parallel Flow and Counterflow Heat Exchangers
3.21
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ESP100.30 Rev. 4
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Chapter 3
LIST OF TABLES
Page
Table 3.1
Conductivity Constants
Table 3.2
Heat Transfer Coefficients
3.4
3.23
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Heat Transfers and Heat Exchangers
Chapter 3
Enabling Objectives
1.0
Summarize the following modes of heat transfer:
•
Conduction
•
Convection
•
Radiation
2.0
Explain how the physical integrity of a heat source is affected by the uncovering of the heat
source. Include in your explanation heat transfer principles.
3.0
Differentiate between regenerative and non-regenerative heat exchangers.
4.0
Summarize the characteristics and effectiveness of parallel flow, counter flow, cross flow, and
combination heat exchangers.
5.0
Given the equations for heat transfer rate
and the expression for TLMTD, calculate the value of any unknown for parallel flow, counter
flow, and cross flow combinations of heat exchangers.
6.0
7.0
Given the expressions:
a)
Describe how the factors in each equation can change due to operational changes in the
plant.
b)
Identify which equation should be used for a given set of conditions as applicable to heat
transfer in heat exchangers.
c)
Calculate the value of any unknown in the expressions when given values for the other
variables.
Summarize the effect of corrosion, plugging, and fouling on heat exchanger performance.
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Chapter 3
3.0
Introduction
Heat exchangers transfer heat from one substance to another by three basic mechanisms:
conduction, convection, and radiation. While all three contribute to any heat-transfer process in
varying degrees, radiation plays a relatively minor role in most of the shell-and-tube heat
exchangers found in the Nuclear Steam Supply System (NSSS).
A cursory look at the underlying principles of conduction, convection, and radiation is presented
here. It should be emphasized, however, that designing a heat exchanger requires both a
comprehensive understanding of each basic mechanism and detailed engineering analysis.
3.1
Conduction
Conduction is heat transfer from molecule to molecule in a stationary substance. The heat flows
from a higher temperature location to a lower temperature location.
In most heat exchangers, a metal wall separates two fluids having different temperatures. Heat
from the hotter fluid passes through the separating wall to the cooler fluid by a mechanical
molecular process.
Molecules are the fundamental building blocks of any substance. Those that make up a solid
material – such as the metal wall separating two fluids – act on each other through two kinds of
force – attraction and repulsion. When the molecules of a solid are spaced just the right way, as in
their normal lattice structure, all forces are in balance; the molecules remain fixed in place, with
nothing but space separating them.
It is only at absolute zero, minus 460°F, that they are absolutely motionless. Above that
temperature, they vibrate in place, stimulated by the heat energy they absorb.
Gas molecules, unlike those of a solid, are perfectly free to move. They shoot about in random
paths, moving faster at higher temperatures. In some exchangers, swiftly moving molecules of hot
gas strike surface molecules of the tube wall, releasing part of their energy during impact. The
effect is to intensify vibration of the surface molecules. Then, under mutual attractive and
repulsive forces, this stepped-up activity is passed along to other molecules of the tube wall.
Since even the smallest surface area comprises billions of molecules, and since billions of
collisions occur each second between gas and solid molecules, we will be concerned only with the
total effect of all collisions in solving heat-transfer calculations.
A block or wall transfers heat from the hot side to the cold side.
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Consider a block or section of a plane wall of area A, thickness x, with a higher temperature T1 on
one side and a lower temperature T2 on the other side, as shown by Figure 3.1.
FIGURE 3.1 SECTION OF A PLANE WALL
Heat is represented by the symbol Q (BTU). Heat flow rate is represented by superimposing a dot
over the Q to represent per unit of time. As shown in the figure, the temperature decrease from the
hot temperature T1 to the lower or cold temperature is represented as a straight line.
The heat transfer rate through the block depends on the material composition. Certain materials
such as metals have a high thermal conductivity, (k), while other materials, such as air or cork,
have a low thermal conductivity, (k).
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The heat transfer rate depends on the area A. Greater heat transfer rate occurs for a larger area.
The heat transfer rate depends on the temperature difference (T1 – T2) between the two sides.
Greater heat transfer rate occurs for a larger temperature difference.
The thickness of material (x) offers a resistance to heat flow. A greater thickness (x) will reduce
the heat flow rate . The heat transfer rate is, therefore, inversely dependent on the thickness (x).
The ratio of the temperature difference to the thickness can be expressed as: (T1 – T2)/x, and is
called the temperature gradient.
The foregoing is mathematically expressed by the conduction law:
The units of the terms are those required to make the equation dimensionally unit-consistent.
Note:
is normally expressed in BTU/hr; however, other time units are valid if used consistently.
Where:
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Chapter 3
Table 3.1 Thermal Conductivity Values
Material
Cork
0.025
Fiber Insulating Board
0.028
Maple or Oak Wood
0.096
Building Brick
0.4
Window Glass
0.45
Concrete
0.79
1% Carbon Steel
25
1% Chrome Steel
35
Aluminum
118
Copper
223
Silver
235
Saturated Steam (at 600°F)
Water (at 600°F)
0.030
0.3
Example A
A 3’ x 4’ glass window pane, 1/8” thick, as shown in Figure 3.2, is installed in a home. On a cold
day in winter the outside surface temperature is 0°F and the inside surface temperature is 68°F.
Find (1) the rate of heat flow out of the pane, and (2) the temperature in the glass 3/32” from the
inside surface.
(1)
Given:
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Chapter 3
Find:
68°F
0°F
FIGURE 3.2 GLASS WINDOW PANE
Solution
The rate of heat flow is assumed constant throughout the pane.
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Chapter 3
(2)
Given:
Find:
Solution
3.1.1 Conduction Through Composite Bodies
If more than one material is present, as in a multi-layered wall, each substance has a different
thermal conductivity constant. The resulting temperature versus distance graph would be as seen
in Figure 3.3
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Chapter 3
XA XB
XC
XD
FIGURE 3.3 TEMPERATURE VERSUS DISTANCE IN A COMPOSITE PATH
Notice that the rate of heat flow is steady; therefore, the same amount of heat is conducted through
each individual layer per unit of time.
So:
Solving these equations simultaneously yields:
for “n” layers where ΔT is the total temperature drop across the “n” layers.
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Example B
Consider that a side panel of a refrigerator 6 ft. x 3 ft. is made of an inside sheet of aluminum
1/16” thick, a layer of cork insulation, and a 1/8” sheet of 1% carbon steel. The interior surface
temperature of the refrigerator is kept at 40°F and the outside at 68°F. How thick must the cork
layer be to limit the flow of heat through the wall to 50 BTU/hr?
Given:
Find:
Solution
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Chapter 3
Isolating xc
3.1.2 Conduction in Cylindrical Geometry
Although conduction through flat plates and walls is the most direct application of the
conductivity equation, in the PWR a great deal of heat transfer takes place across cylindrical walls.
In this type of geometry, where heat is moving from a small diameter to a larger diameter, the
cross-sectional can no longer be assumed constant, thus complicating the problem. For this
application, the conductivity expression takes on a different form.
ro = outside radius of pipe
ri = inside radius of pipe
3.2
Convection
Convection is generally listed as a mode of heat transfer along with conduction and radiation.
Strictly speaking, however, convection is really conduction combined with mass transfer. This
motion of coolant mass is the characteristic feature of convection, whether the coolant is a gas,
liquid or liquid metal.
There are two types of convection, forced and natural. In the latter, currents result from heating or
cooling effects and the natural tendency for hot fluids to rise above cold fluids. In the former,
fluid is moved by a pump, fan or other device. By forcing fluid to flow over a heat source at
higher speed, the rate of heat transfer can be increased – within limits.
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As an example, consider a heating element submerged in a container of water. Heat is generated
within the element by electrical resistance, and the temperature of the element increases. When
the temperature of the surface becomes greater than that of the water contacting it, the potential
exists for heat transfer.
However, as soon as some thermal energy is transferred to the water, that water undergoes a
decrease in density and is promptly displaced by water of greater density. The warmer water rises
because of natural buoyant forces acting on it. The rising water contacts cooler water, and its
slightly higher temperature causes the extra heat energy to be dissipated in the bulk coolant. The
heater element, meanwhile, is still surrounded by cooler water, and will be until the whole bulk
temperature gradually increases. This increase in bulk temperature is caused mostly by the heat
energy carried by moving fluid, as opposed to pure conduction.
A close look at the water immediately adjacent to the heater surface would show a temperature
gradient form the surface into the water, just as exists in conduction. A thin layer of water
remains in contact with the surface because of adhesive forces, and heat is transferred through this
relatively stable boundary layer. Because of the variables affecting this layer (surface roughness,
shape, size, fluid viscosity, temperatures and temperature differences), it is extremely difficult to
quantify,. Rather, the rate of heat transfer through the layer is determined for a range of
conditions, and this heat transfer coefficient is used for design purposes. The coefficient,
designated h, expresses the amount of heat (BTU) which can be transferred across a liquid
interface per unit area (ft2) per unit time (hr), per degree difference between the surface and the
bulk coolant (°F). The equation for the rate of convective heat transfer is similar to that for
conduction:
The equation works for heat transfer in either direction, from surface-to-liquid, or from liquid-tosurface.
Notice that the units of the convective heat transfer coefficient (h) and thermal conductivity (k) are
different. Thermal conductivity is in BTUs per hr per °F per ft. of thickness (BTU/hr °F ft) while
convective heat transfer coefficient is BTU per hr per °F per ft2 of area (BTU/hr °F ft2).
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Chapter 3
3.2.1 Forced Convection
The initial discussion on convection emphasized the fact that heat energy was transported and
dispersed because of fluid movement. In that case the movement was caused by buoyant forces,
and the fluid motion was inherently slow and diffuse. The amount of heat which can be removed
from (or added to) a surface can be significantly increased by forcing the fluid to move past the
surface with some controlled velocity. This is analogous to the difference between a hot radiator
depending on natural circulation of air to heat a room and having a fan move air across the radiator
to speed and improve the process. Just as in natural convection, many factors affect heat removal
capability, including flow characteristics (i.e., laminar or turbulent flow patterns). Is the flow
being forced along the length of a heated surface, or is it perpendicular to the surface? Is the flow
contained inside a pipe channel (pipe, duct), or is it flowing outside heated surfaces? For many of
these different conditions, special correlations have been developed which yield the appropriate
heat transfer coefficient. The empirical correlations generally require information about fluid
properties and flow conditions as well as the solid surface properties.
In heat exchangers, convection is an important adjunct to conduction. Under the convective
effect, a fluid heated at a surface mixes with nearby cooler fluid, and in turn, imparts some of its
heat. Also, movement of heated fluid away from the heating surface allows a steady flow of
cooler fluid to make contact and extract heat.
3.3
Radiation
Radiation, or radiant heat transfer, involves the transfer of heat by electromagnetic radiation which
arises due to the temperature of a body. Most energy of this type is in the infra-red region,
although some is visible. The term thermal radiation is frequently used to distinguish this form of
electromagnetic radiation from other forms, such as radio waves, x-rays or gamma rays. The
transfer of heat from a fireplace across a room in the line of sight is an example of radiant heat
transfer.
Radiant heat transfer depends on only a few factors. A perfect radiator is a material that absorbs
all of the radiant energy striking its surface and emits the maximum amount of radiant energy for a
given temperature. Most materials only partially absorb, reflect and/or transmit radiant energy. A
perfect radiator is called a black body. Josef Stefan was the first to empirically determine that the
energy (E) per unit are of a black body is directly proportional to the fourth power of its absolute
temperature:
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Ludwig Boltzman later derived the same proportionality using a thermodynamic analysis. The
constant of proportionality (σ), named the Stefan-Boltzman constant, was later derived; its value is
The rate of radiant heat transfer from a black body taking into account its surface area is
An insulator resists heat transfer. Most materials are not perfect insulators. To determine the
radiant heat transfer from a material which is not a perfect insulator, a correction factor must be
added. The emissivity of a material takes into account the non-black or gray nature of such
material surfaces. In addition, the geometric view factor also determines the amount of radiant
heat transfer. With these considerations, the formula now becomes
where:
In most heat transfer processes, all three (3) modes of heat transfer occur simultaneously.
Generally, one or more primary modes are dominant. We also need to realize that as long as a
temperature difference exists between two (2) objects, heat will be transferred by one or more of
the primary modes. Under normal operations in the plant, the dominant modes of heat transfer are
conduction and convection. Conduction occurs through the fuel rod and clad; convection occurs
from clad surface into primary coolant. Under an accident condition which leaves the fuel rod
blanketed with steam, however, the convective transfer process can no longer as effectively
remove the heat being generated in the fuel. One reason for this is due to the thermal conductivity
of the steam being much less than the thermal conductivity of the water at the same temperature
(Table 3.1). Since the convective transfer process is no longer adequate, radiant heat transfer must
take over. This results in serious consequences for the fuel rod, because in order for the radiant
heat transfer to equal the heat being generated, the temperature of the rod must increase
dramatically. This increase in temperature must occur since the Stefan-Boltzman constant is so
small.
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The following example gives one a quantitative idea of how much the rod temperature must
increase if radiant heat transfer is dominant.
Example C
The reactor is shutdown producing 5 percent of rated thermal power (0.27 kw/ft of rod) due to
decay heat. The fuel rod is 12.5 ft long and 0.40 inches in diameter. The temperature of the
coolant and the reactor vessel wall is 550°F. The convective heat transfer coefficient for these
conditions is 970 BTU/hr-ft2-°F. The emissivity of the fuel rod is 0.035. What is the temperature
of the fuel rod cladding under normal, and Loss of Coolant Accident conditions?
Solution
Under normal conditions, heat transfer from the clad surface to the coolant is by convection.
Under Loss of Coolant Accident conditions, radiant heat transfer dominates.
Note: Since heat is also being transferred from the wall to the clad, the net rate at which heat is
transferred from the clad is proportional to the difference in T4.
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Chapter 3
Although this temperature is lower than the actual temperature (since we assumed ideal
geometries and did not take into account the emissivity of the wall), the fact that radiant heat
transfer results in significantly higher clad temperatures than does convection is a valid
conclusion.
Typical cladding material used for reactor fuel is a zirconium based alloy, zircalloy. Zircalloy
becomes brittle at 2800°F, and melts at 3375°F. And when in contact with water, it is subject to a
rapid zirconium-water reaction at 1800°F. This reaction rapidly oxidizes the zirconium, resulting
in the production of hydrogen gas, which is explosive. When the clad temperature reaches
2300°F, the zirconium-water reaction is accelerated to the point where the reaction is completely
self-sustaining. From this we can conclude that even under decay heat conditions, the physical
integrity of the clad is subject to degradation.
3.4
Heat Exchangers
A heat exchanger is a device designed to allow a controlled transfer of heat from one fluid to
another fluid. The heat transfer is controlled by designing heat exchangers with specific
characteristics for specific applications.
A major design consideration for heat exchangers at the nuclear plant is the necessity for
separation of systems. System separation is used to control radiation exposure by isolating
radioactivity to specific plant locations, and minimizing the spread of radioactive contamination.
Separation of individual systems also allows better corrosion control. For these reasons, most heat
exchangers used are of a nonmixing-fluid design. In a nonmixing-fluid heat exchanger, the fluids
are physically separated from one another. In a shell-and-tube heat exchanger, one fluid passes
through a bundle of tubes. The bundle of tubes is enclosed within a shell containing the other
fluid. The fluid within the tubes, illustrated in Figure 3.4, is referred to as the tube-side fluid. The
fluid outside the tubes is the shell-side fluid. At the end of the tubes, the tube side is physically
separated from the shell side by a structural support plate called the tubesheet.
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SHELL-SIDE
FLUID
TUBE-SIDE
FLUID
TUBE
SHEET
SHEL
L
FIGURE 3.4 SHELL-AND-TUBE DESIGN HEAT EXCHANGER
Another major consideration in heat exchanger design is achieving the maximum heat transfer
surface area within the volume of a particular heat exchanger. The shell-and-tube design also
addresses this concern. For example, if heat transfer occurs across a single flat plate, only a small
percentage of either heat-exchanging fluid is in contact with the heat transfer surface area. Using
tubes increases the heat transfer surface area and allows more of the heat-exchanging fluid to be in
contact with this surface area. Furthermore, the relatively low cost of tube construction allows the
shell-and-tube design to provide this optimum heat transfer surface area in a very cost-effective
way.
Perhaps one of the most critical design considerations for a power plant heat exchanger is that it
must be able to withstand the pressures and high temperatures of the fluids. The shell-and-tube
design meets this requirement. In a bundle of tubes, the pressure forces inside each tube are
exerted uniformly outward in all directions. Normally, material for a tube is selected to allow the
tube to be capable of withstanding higher pressures on the inside than on the outside. As a result,
higher-pressure, higher temperature fluid is normally inside the tubes.
The material selected for shell-and-tube heat exchangers must also be ductile and strong. Ductility
allows the material to expand or contract during pressure transients. A strong material is needed
in order to improve heat transfer by decreasing the required thickness of the heat transfer material.
However, the selection of a strong, ductile material is limited by the corrosive nature of the fluids
used in a reactor plant. Carbon steel, for example, is a strong, ductile material with good heat
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transfer capabilities. Carbon steel is also very susceptible to corrosion when exposed to oxygen
and must be used with chemical corrosion inhibitors. Where corrosion inhibitors cannot be used,
as in the primary system, carbon steel cannot be used.
Another example of a strong, ductile material with good heat transfer properties is stainless steel.
At high pressures and temperatures, however, stainless steel rapidly corrodes, particularly in the
presence of chloride impurities. As a result, early steam generators manufactured with stainless
steel required very strict chemistry control. Inconel, a strong material with good heat transfer
properties and high resistance to corrosion, is used in many PWR components, including later
design steam generator tubes.
3.4.1 Classification of Heat Exchangers
Operationally, heat exchangers can be divided into two major categories, single-phase and twophase. In single-phase heat exchangers, both the cooling (heating) fluid and the cooled (heated)
fluid remain in their initial gaseous or liquid state. In two-phase heat exchangers either the
cooling (heating) fluid or the cooled (heated) fluid changes phase.
The two most important two-phase heat exchangers in a nuclear power plant are the steam
generator and the main condenser. The gland exhaust condenser and the feedwater heaters are
other two-phase heat exchangers.
Recall from our earlier discussion, single phase heat exchangers normally consist of a set of tubes
in a container called a shell; at the ends of the heat exchanger, the tube-side fluid is separated from
the shell-side fluid by the tube sheet. The tubes are rolled and press fitted or welded into the tube
sheet to prevent leakage from one side to the other. If a tube should begin leaking, it may be
plugged or blocked off during its next maintenance outage. Two-phase heat exchangers are
similar in design to single-phase heat exchangers. The steam generator tube sheets are extra thick
(approximately two feet) to prevent leakage of primary fluid into the secondary fluid; the main
condenser has a double tube sheet on each end with a drain between the two. Construction being
similar, the primary different between single phase and two-phase heat exchangers occurs in their
operation.
In addition to the operational categories stated above, it is also necessary to classify heat
exchangers by the direction of flows within the heat exchanger. The three basic designs based on
flow directions are parallel flow, counter flow, and cross flow heat exchangers. The most
common arrangements for flowpaths within a heat exchanger are the counterflow and parallel flow
heat exchangers. A counterflow heat exchanger is one in which the direction of flow of one of the
working fluids is opposite to the direction of flow of the other fluid. In a parallel flow heat
exchanger, both fluids in the heat exchanger flow in the same direction. Figure 3.5 represents the
direction of flows in the parallel and counterflow heat exchangers.
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Chapter 3
PARALLEL-FLOW
COUNTER-FLOW
FIGURE 3.5 PARALLEL AND COUNTERFLOW HEAT EXCHANGERS
In cross flow heat exchangers, the two heat-exchanging fluids flow perpendicular to each other as
illustrated in Figure 3.6.
CROSS FLOW
FIGURE 3.6 CROSS FLOW HEAT EXCHANGER
Heat exchangers are also classified by whether they are regenerative or non-regenerative.
A regenerative heat exchanger is one in which the same fluid is used as both the cooling fluid and
the cooled fluid. A good example of a regenerative heat exchanger is the regenerative heat
exchanger in the letdown line of the Chemical and Volume Control System (CVCS). Here, the
hot letdown flow is cooled in the regenerative heat exchanger by colder charging water as it is
returned to the reactor loops.
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In a non-regenerative heat exchanger, the hot fluid is cooled by a colder fluid which is supplied by
another system where the heat is eventually transferred to a sink.
Heat exchangers may also be classified as closed or open.
A closed heat exchanger is one in which heat exchanger internals are constructed so that there is
separation between the two fluids. Examples are tube and shell types and plate and shell types. A
plate type heat exchanger has thin, hollow plates (rather than tubes), thus maximizing heat transfer
surface area while limiting the volume of space that a heat exchanger occupies.
An open heat exchanger, on the other had, is one in which there is no barrier between the two
fluids (i.e., no tubes, simply a tank or vessel where two fluids with different temperatures meet).
Fluids heat/cool by direct contact and mixing. Usually one fluid is sprayed into another to
increase surface contact.
Heat transfer within a heat exchanger involves both the conductive and convective methods of
heat transfer. Conduction takes place across the heat exchanger tubes. Convection takes place in
both fluid flow paths. One fluid convectively transfers heat to the tube wall; conduction takes
place across the tube wall. Then, heat is once again convectively transferred to the second fluid in
the heat exchanger.
3.4.2 Overall Heat Transfer Coefficient (U)
In discussing combined heat transfer by conduction and convection, the basic relationships are
combined to define the overall heat transfer coefficient U.
Where:
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The difficulty in applying the relationship for combined heat transfer by conduction and
convection to real heat exchangers is that the overall temperature different T0 is not constant.
For example, the temperature difference between the reactor coolant and the feedwater or steam in
a steam generator varies along the length of the steam generator tubes. In order to apply the
relationship, an average temperature difference which accurately reflects the overall process must
be used.
3.4.3 Log Mean Temperature Difference
The effective temperature difference, TLMTD, between the two fluid across the heat exchanger is
defined by the following relationship.
Where:
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For many real heat exchangers, the log mean temperature difference TLMTD accurately reflects
the overall heat transfer process. The use of the log mean temperature difference TLMTD
requires that the temperature of one fluid is continuously changing from inlet to outlet while the
temperature of the other fluid is either constant or also continuously changing. Under these
conditions, the heat transfer rate equals the product of the overall heat transfer coefficient U, the
overall cross-sectional area for heat transfer A, and the log mean temperature difference TLMTD:
Where:
3.4.4 Counter Flow and Parallel Flow Heat Exchanger Calculations
We can apply the equation above to the analysis of the performance of parallel flow and
counterflow heat exchangers. If we consider two heat exchangers with the same inlet and outlet
temperatures except that one is parallel flow and the other is counterflow, we can compare their
respective heat transfer capabilities.
Figure 3.7 represents the inlet and outlet temperature conditions of both types of heat exchangers.
For purposes of our example, both heat exchangers are considered to have the same value of U:
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80 F
PARALLEL-FLOW
200 F
145 F
120 F
120 F
COUNTER-FLOW
200 F
145 F
80 F
FIGURE 3.7 PARALLEL FLOW AND COUNTERFLOW HEAT EXCHANGERS
Example C
Calculate the ΔTLMTD for both exchangers in Figure 3.7.
For parallel flow:
For counterflow:
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The difference in the values of TLMTD for the parallel and counterflow flow paths can be used to
show that the counterflow heat exchanger is more efficient. If the overall heat transfer rate was the
same across each heat exchanger, then
Since:
or,
That is,
The difference in the values of TLMTD guarantees that the tube area needed for the counterflow
heat exchanger is less than the area required by a parallel flow exchanger transferring the same
amount of heat. Therefore, the counterflow exchanger is more efficient.
The analysis of heat exchanger operation just presented is a simplified representation of heat
exchanger operation. In actuality, analysis of heat exchanger operation is significantly more
detailed. In our examples we stated that the temperature differential in the heat exchanger was
continuously changing. In a two-phase heat exchanger, this may not be true. Additionally, we
assumed that the value of U was the same throughout the heat exchanger. In actuality the value of
U varies throughout the heat exchanger due to heat exchanger geometry, and changes in the nature
of fluid flow or fluid properties. U also changes as heat transfer surfaces become fouled. Table
3.2 shows a range of values of U for different combinations of fluids. The table values cover a
range for different heat exchanger designs.
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The value of U for a given heat exchanger design decreases as the heat transfer surface becomes
fouled. An acceptable method to monitor heat exchanger operation is to lump U and A as a single
value:
and use the result as a figure of merit that can be compared to the design value. A running plot of
UA can predict when a heat exchanger needs to be removed from service and cleaned.
Table 3.2 Heat Transfer Coefficients
U
Fluid
Oil to Oil
Organics to Organics
Steam to:
Aqueous Solutions
Fuel Oil, Heavy
Fuel Oil, Light
Gases
Water
Water to:
Alcohol
Brine
Compressed Air
Condensing Alcohol
Condensing Ammonia
Condensing Freon-12
Condensing Oil
Gasoline
Lubricating Oil
Organic Solvents
Water
30-55
10-60
100-600
10-30
30-60
5-50
175-600
50-150
100-200
10-30
45-120
150-250
80-150
40-100
60-90
20-60
50-150
150-300
3-23
Chapter 3
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
3.4.5 Comparison of Counterflow Versus Parallel Flow Heat Exchangers
3.4.5.1 Parallel Flow
A parallel flow heat exchanger is advantageous when two fluids are required to be brought to the
same temperature. However, this is not usually the goal of a heat exchanger in a power plant.
Thus, this type of heat exchanger is not typically used in a power plant. Two major disadvantages
of this type of heat exchanger are the large thermal stress due to large T at the inlet and the
inability to raise the temperature of the cold fluid above the lowest temperature of the hot fluid.
3.4.5.2 Counter Flow
Counter flow heat exchangers create a small thermal stress, due to a more uniform T overall. A
more uniform temperature difference gives a more uniform heat transfer rate. The cold fluid at the
outlet is able to approach the highest hot fluid temperature.
3.4.6 General Energy Equation for Heat Exchangers
In addition to the previous methods of analyzing the processes in a heat exchanger, we can also
use the general energy equation. The general energy equation can be expressed as follows for heat
exchangers:
where:
If we consider that the heat in one fluid is transferred to the secondary fluid with no external
losses, the equation can be written to express the heat transfer rate between the two fluids:
3-24
Chapter 3
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
The above equation can be used to represent the heat transfer rate between two fluids which are
changing phase. As discussed previously, whenever a change of phase occurs, the enthalpy
change must be used. However, in most heat exchangers, either one fluid or both do not change
phase. If one fluid is changing phase, such as in the steam generator, the following equation
represents the heat transfer rate between the fluids:
If both fluids remain in the same phase, as is the case with most heat exchangers, then the
following equation is used to represent the heat transfer rate between the fluids:
The equation
can be used to calculate the heat transfer rate, as was used to
calculate the heat transfer rate for heat exchangers in general, except care must be taken to use the
proper value for U. The value of U changes depending upon the phase or state of the water, as
well as with other factors such as geometry.
Example D
In the regenerative heat exchanger, the heat removed from 40 gpm of reactor coolant as it
decreases in temperature from 552°F to 264°F us recovered by being transferred to 44 gpm of
water entering at 120°F and rising in temperature. Calculate (a) heat
removed from the hot
water, and (b) temperature of the relatively colder water returning to the RCS. Assume the density
of the letdown flow is 54.5 lbm/ft3 and the density of the charging flow is 60.0 lbm/ft3.
Solution
Since the value of cp is not provided, the heat transfer rate in terms of enthalpy difference is used:
(a)
3-25
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
(b)
Solving for hout:
This corresponds to a temperature of 378°F.
3.4.7 Conditions Heat Exchanger Performance
Several factors affect the efficient of heat exchangers. Specifically:
•
Corrosion
Corrosion on tubes creates oxides which have different k values, and increase tube thickness.
This tends to reduce conduction through the tube, decreasing the overall heat transfer
coefficient and heat efficiency.
•
Tube Plugging
Tubes which leak must be repaired or plugged. Plugged tubes represent a reduction in heat
transfer surface area. This decreases heater efficiency.
•
Tube Fouling
Foreign matter which flows in the tube side fluid can become trapped on the inlet tube sheet.
This blocks flow (or reduces flow) in some tubes.
•
Reducing the heat transfer surface area.
•
Also can result in a decrease in flowrate, thereby causing hc to decrease.
Overall, fouling decreases efficiency.
3-26
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.5
Summary
Heat exchangers transfer heat from one substance to another by three basic mechanisms:
conduction, convection, and radiation. While all three contribute to any heat-transfer process in
varying degrees, radiation plays a relatively minor role in most of the shell-and-tube heat
exchangers found in nuclear power plants.
We took a look at the underlying principles of conduction, convection, and radiation.
3-27
Chapter 3
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Definitions
Conduction – Transfer of heat energy from molecule to molecule in a stationary substance as a
result of a temperature differential.
Convection – Transfer of heat energy between a surface and a fluid moving past the surface.
Convection is conduction and energy storage combined with mass transfer.
Radiation – Transfer of heat energy by electromagnetic radiation which arises due to the
temperature of a body.
3-28
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
EXERCISES
3-29
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.1
The basic mode of heat transfer that involves the transfer of heat by interaction between
adjacent molecules of a material is called ___________________ heat transfer.
A.
B.
C.
D.
3.1.2
The basic mode of heat transfer that involves the transfer of heat by motion and mixing of
macroscopic portions of a fluid is called __________________ heat transfer.
A.
B.
C.
D.
3.1.3
Conduction
Convection
Radiant
Two-phase
Convection heat transfer can be described as the transfer of heat by:
A.
B.
C.
D.
3.1.6
Conduction
Convection
Radiation
Molecular
The basic mode of heat transfer that involves the transfer of heat due to the differential
temperature of two separated bodies in a vacuum in called _______________ heat transfer.
A.
B.
C.
D.
3.1.5
Conduction
Convection
Radiation
Molecular
Interaction and mixing of molecules of a solid material
Electromagnetic radiation that arises due to the temperature of a body
Interaction between adjacent molecules without macroscopic interaction of the
material through which the heat is being transferred
Motion and mixing of macroscopic portions of a fluid
Refer to the drawing of a fuel rod and coolant flow channel at beginning of core life (see
Figure 3.7-1). What is the primary method of heat transfer in the gap between the reactor
fuel and the fuel clad?
A.
B.
C.
D.
Conduction
Convection
Radiant
Molecular
3-30
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.7
The transfer of heat through a solid piece of material would be considered______________
heat transfer.
A.
B.
C.
D.
3.1.8
During a loss-of-coolant accident, which of the following heat transfer mechanisms
provides the most core cooling when fuel elements are not in contact with the coolant?
A.
B.
C.
D.
3.1.9
Conduction
Convection
Radiation
Natural circulation
Which phrase illustrates radiation heat transfer?
A.
B.
C.
D.
3.1.11
Radiation
Emission
Convection
Conduction
Helium gas is used to fill the gap between the fuel pellet and the cladding to improve the
heat transferred by _________________ from the pellet to the cladding.
A.
B.
C.
D.
2.1.10
Conduction
Convection
Radiant
Molecular
Heat transfer from the fuel cladding to the core barrel within a voided reactor vessel
Heat transfer from the center to the edge of a fuel pellet
Heat transfer from the reactor coolant to the feedwater in a steam generator
Heat transfer from the fuel cladding to the reactor coolant via subcooled nucleate
boiling
The transfer of heat from the reactor fuel to the fuel cladding during normal operations is an
example of ________________ heat transfer.
A.
B.
C.
D.
Conduction
Convection
Radiant
Two-phase
3-31
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.12
The basic mode of heat transfer that involves the transfer of heat due to the differential
temperature of two separated bodies in a vacuum is best described as:
A.
B.
C.
D.
3.1.13
The transfer of heat energy through a solid material as a result of a temperature difference
across the material is best described as:
A.
B.
C.
D.
3.1.14
Conduction, forced convection
Conduction, conduction
Conduction, natural convection
Convection, conduction
Complete the following statement: Heat transfer from the centerline to the edge of the fuel
pellet is _______________ heat transfer, and heat transfer from the fuel clad wall to the
bulk liquid is ________________ heat transfer.
A.
B.
C.
D.
3.2.1
Conduction heat transfer
Convection heat transfer
Radiation heat transfer
Decay heat
The method of heat transfer from the centerline of the fuel pellet to the outside surface of
the fuel rod is _____________. Across the laminar layer the method is _____________.
A.
B.
C.
D.
3.1.15
Conduction heat transfer
Convection heat transfer
Radiation heat transfer
Molecular heat transfer
Radiative, convective
Convective, convective
Convective, conductive
Conductive, convective
A feedwater heat exchanger tube has a restriction in it which reduces the flow rate of the
feedwater so that feedwater flashes to steam halfway along the tube. This restriction causes
the heat transfer rate of the tube to _______________ and the overall heat transfer rate of
the heat exchanger to _________________.
A.
B.
C.
D.
Decrease, decrease
Decrease, remain the same
Increase, increase
Increase, remain the same
3-32
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.2.2
As fluid rate increases through the tubes of a shell-and-tube heat exchanger, the laminar
film thickness ________________, which causes heat transfer rate to ________________.
A.
B.
C.
D.
3.3.1
Which of the following describes the difference between a regenerative and a nonregenerative heat exchanger?
A.
B.
C.
D.
3.3.2
Increases, increase
Increases, decrease
Decreases, increase
Decreases, decrease
A non-regenerative heat exchanger uses its own system’s rejected heat to heat the
system.
A regenerative heat exchanger uses its own system’s heat to heat the system.
A non-regenerative heat exchanger can only be a “U” tube type heat exchanger.
A regenerative heat exchanger can only be “U” tube type heat exchanger.
From the diagram below, select the heat exchanger(s) that is (are) regenerative.
A.
B.
C.
D.
A
C
B
D
A and B
A only
A and D
D only
3-33
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.4.1
In a single-phase heat exchanger, heat transfer can be affected by several factors, one of
which is gases entrained in the fluid. Excessive amounts of gases passing through the heat
exchanger are undesirable because:
A.
B.
C.
D.
3.4.2
Which of the following best represents what is included in the overall heat transfer
coefficient for a heat exchanger?
A.
B.
C.
D.
3.4.3
Parallel-flow heat exchanger
Counter-flow heat exchanger
Cross-flow heat exchanger
Mixing-fluid heat exchanger
When comparing a parallel and counter-flow exchanger with identical inlet and outlet
temperatures of both fluids, which of the below is true?
A.
B.
C.
D.
3.4.5
Properties of the fluids in the heat exchanger
Operating conditions of heat exchanger
Geometry of heat exchanger
All of the above
Which types of exchanger is described by the following? “The two heat exchanging fluids
flow in opposite directions in a parallel path.”
A.
B.
C.
D.
3.4.4
Flow blockage can occur in the heat exchanger
Gases will break up the laminar layer in the heat exchanger
The heat transfer coefficient will increase in the heat exchanger
The DT will decrease across the tubes in the heat exchanger
The counter-flow HE has a higher DT mean
The parallel-flow HE has a higher DT mean
Both heat exchangers have the same DT mean
None of the above are true
Which of the following best describes why a counter-flow heat exchanger is generally more
efficient than an parallel-flow heat exchanger?
A.
B.
C.
D.
The counter-flow heat exchanger’s outlet temperature of the cold fluid approaches
the highest temperature of the hot fluid
The counter-flow heat exchanger has a more even heat transfer rate
The counter-flow heat exchanger generally can support a higher flow rate due to its
design
Both A and B
3-34
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.4.6
Which of the following statements is true regarding adding baffles to a counter-flow heat
exchanger?
A.
B.
C.
D.
3.4.7
Select the best choice which describes the types of flow which can be utilized in a U-tube
heat exchanger.
A.
B.
C.
D.
3.4.8
Parallel flow
Counter flow
Cross flow
All of the above
A heat engine receives heat from a source at 535°F and rejects the unused heat energy to a
reservoir at 80°F. What is the maximum thermal efficiency of this engine?
A.
B.
C.
D.
3.4.10
Parallel flow
Counter flow
Cross flow
Any of the above
A U-tube heat exchanger is an example of:
A.
B.
C.
D.
3.4.9
Baffles decrease fluid velocity which increases heat transfer
A higher convective heat transfer coefficent results
Baffles decrease heat transfer but increase mechanical strength
A lower amount of turbulent flow will increase heat transfer
26%
36%
46%
56%
Select the choice which best indicates the advantage of a U-tube heat exchanger.
A.
B.
C.
D.
Less turbulent flow within the tubes
More turbulent flow within the tubes
Ability of tubes to expand lengthwise, reducing thermal stresses
None of the above in an advantage
3-35
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.4.11
The plant is at 8% and increasing when the unit operator inadvertently trips the # 1 RCP.
Which of the following best describes the initial impact on S/G level, Tave, and S/G
pressure for the affected loop?
A.
B.
C.
D.
3.6.1
A heat engine receive heat from a source of 535°F and rejects the unused heat energy to a
reservoir at 80°F. What is the maximum thermal efficiency of this engine?
A.
B.
C.
D.
3.6.2
Less turbulent flow within the tubes
More turbulent flow within the tubes
Ability of tubes to expand lengthwise, reducing thermal stresses
None of the above is an advantage
Which of the following best explains the effects of steam formation on heat transfer in
single-phase (liquid) heat exchangers?
A.
B.
C.
D.
3.6.4
26%
36%
46%
56%
Select the choice which best indicates the advantage of a U-tube heat exchanger.
A.
B.
C.
D.
3.6.3
S/G level increases, Tave increases, and S/G pressure increases
S/G level increases, Tave decreases, and S/G pressure increases
S/G level decreases, Tave decreases, and S/G pressure decreases
S/G level decreases, Tave increases, and S/G pressure decreases
The T across the tubes will decrease in the heat exchanger
Steam voids will increase the heat transfer coefficient of the heat exchanger
A small amount of steam will reduce the amount of heat transfer
Steam voids can accumulate and cause blockage
If a reduction of reactor coolant flow occurs during power operation, what affect will this
have on core T, assuming no change in reactor power level?
A.
B.
C.
D.
Increases
Decreases
Remains unchanged
Temporarily decreases, then returns to previous value
3-36
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.5
Assuming the reactor power remains constant, steady-state to steady-state, as reactor
coolant flow increases, fuel temperature will:
A.
B.
C.
D.
3.6.6
Assuming that reactor power remains constant at 30 percent, if reactor coolant flow
decreases by 10 percent, fuel temperature will:
A.
B.
C.
D.
3.6.7
Overall heat transfer coefficient of the RCS
Reactor coolant flow rate
Pressurizer temperature
Fuel centerline temperature
Which of the following explains the effects of steam formation on heat transfer in singlephase (liquid) heat exchangers?
A.
B.
C.
D.
3.6.9
Increase, then stabilize at a higher value
Decrease, then stabilize at a lower value
Increase, then return to the original steady-state value
Decrease, then return to the original steady-state value
Which of the following parameters, when changed, would not directly affect the heat
transfer rate tot he reactor coolant system? (Evaluate each change separately).
A.
B.
C.
D.
3.6.8
Increase
Decrease
Remain the same, steady-state to steady-state
Increase, then return to the original steady-state value
The temperature difference across the tubes will decrease through the heat
exchanger
Steam voids will increase the heat transfer coefficient of the heat exchanger
A small amount of steam will reduce the amount of heat transfer
Steam voids can accumulate and cause flow blockage
In a single-phase (liquid) heat exchanger, heat transfer can be affected by several factors,
one of which is gases entrained in the fluid. Excessive amounts of gases passing through
the heat exchanger are undesirable because:
A.
B.
C.
D.
Flow blockage can occur in the heat exchanger
Gases will break up the laminar layer in the heat exchanger
The heat transfer coefficient will increase in the heat exchanger
The temperature difference across the tubes will decrease through the heat
exchanger
3-37
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.10
Using the diagram below select which of the following is correct.
105°
105°
90°
D
#1
#2
C
90°
A
A.
B.
C.
D.
3.6.11
B
“C” is closer to 105 degrees than “D”
“D” is closer to 105 degrees than “C”
Heat exchanger #1 is more efficient than heat exchanger #2
None of the above
A counter-flow heat exchanger (HE) transfer 2 x 109 BTY/hr with a Log Mean temperature
difference of 55°F. The HE has 15,000 tubes measuring 5/8” (OD) by 10’ long. What is
the heat transfer coefficient for this HE?
A.
B.
C.
D.
123.5 BTU/hr-°F-ft2
387.8 BTU/hr-°F-ft2
1235.3 BTU/hr-°F-ft2
1481.6 BTU/hr-°F-ft2
3-38
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.12
Why can temperature NOT be used to calculate the heat transfer in a heat exchanger in
which a phase change occurs?
A.
B.
C.
D.
3.6.13
The reactor coolant enters the core at 548°F and exits at 596°F. If the reactor coolant flow
rate is 8.36 x 107 lbm/hr and the specific heat of water at core conditions has a magnitude of
1.3, what is the core thermal power?
A.
B.
C.
D.
3.6.14
755 MWt
1509 MWt
3018 MWt
3411 MWt
The reactor coolant enters the core at 545 degrees F and leaves at 595 degrees F. If the
reactor coolant flow rate is 6.6 x 107 lbm/hr and the specific heat of water at core conditions
is 1.3 BTY/lbm-degree F, what is the core thermal power? (1 Kwatt = 3.4127 x 103
BTU/hr)
A.
B.
C.
D.
3.6.16
522 MWt
1176 MWt
1528 MWt
1592 MWt
In a two-loop pressurized water reactor, feedwater flow to each steam generator is 3.3 x 106
lbm/hr at an enthalpy of 419 BTU/lbm. The steam existing each steam generator is at 800
psia with 100% steam quality. Ignoring blowdown and pump heat, what is the core thermal
power?
A.
B.
C.
D.
3.6.15
At constant pressure, temperature does not change during phase changes
At constant pressure, temperature changes radically during phase changes
Changes in temperature during phase changes are not easily measured
Temperature CAN be used to measure heat transfer during phase changes
967 MWt
1160 MWt
1257 MWt
1508 MWt
Which of the below statements is NOT true regarding the rate of heat transfer through a
solid material?
A.
B.
C.
D.
Heat transfer rate increases with an increase in T.
Heat transfer rate decreases with an increase in thickness.
Heat transfer rate decreases with an increase in surface area.
Heat transfer rate increases with an increase in thermal conductivity.
3-39
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.18
The mass flow rate of circulating water through the tubes of the main condenser 3.0 x 108
lbm/hr with an inlet temperature of 72°F. The heat being discharged is 6.98 x 109 BTU/hr.
What is the outlet temperature? (Assume cp = 1.0)
A.
B.
C.
D.
3.7.1
87.8°F
93.2°F
95.3°F
102.8°F
Tube scaling in a parallel-flow heat exchanger will cause heat transfer to decrease because:
A.
B.
C.
D.
Flow through the heat exchanger increases
Surface area of the tubes decreases
Heat transfer coefficient decreases
Inlet temperature of the cooling fluid increases
3-40
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.1
The basic mode of heat transfer that involves the transfer of heat by interaction between
adjacent molecules of a material is called ___________________ heat transfer.
A.
B.
C.
D.
3.1.2
The basic mode of heat transfer that involves the transfer of heat by motion and mixing of
macroscopic portions of a fluid is called __________________ heat transfer.
A.
B.
C.
D.
3.1.3
Conduction
Convection
Radiation
Molecular
The transfer of heat from the reactor to the fuel cladding during normal operations is an
example of __________________heat transfer.
A.
B.
C.
D.
3.1.5
Conduction
Convection
Radiation
Molecular
The basic mode of heat transfer that involves the transfer of heat due to the differential
temperature of two separated bodies in a vacuum in called _______________ heat transfer.
A.
B.
C.
D.
3.1.4
Conduction
Convection
Radiation
Molecular
Conduction
Convection
Radiation
Two-phase
Convection heat transfer can be described as the transfer of heat by:
A.
B.
C.
D.
Interaction and mixing of molecules of a solid material
Electromagnetic radiation that arises due to the temperature of a body
Interaction between adjacent molecules without macroscopic interaction of the
material through which the heat is being transferred
Motion and mixing of macroscopic portions of a fluid
3-41
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.6
Refer to the drawing of a fuel rod and coolant flow channel at beginning of core life (see
Figure 3.7-1). What is the primary method of heat transfer in the gap between the reactor
fuel and the fuel clad?
A.
B.
C.
D.
3.1.7
The transfer of heat through a solid piece of material would be considered______________
heat transfer.
A.
B.
C.
D.
3.1.8
Radiation
Emission
Convection
Conduction
Helium gas is used to fill the gap between the fuel pellet and the cladding to improve the
heat transferred by _________________ from the pellet to the cladding.
A.
B.
C.
D.
3.1.10
Conduction
Convection
Radiant
Molecular
During a loss-of-coolant accident, which of the following heat transfer mechanisms
provides the most core cooling when fuel elements are not in contact with the coolant?
A.
B.
C.
D.
3.1.9
Conduction
Convection
Radiation
Natural circulation
Conduction
Convection
Radiation
Natural circulation
Which phrase illustrates radiation heat transfer?
A.
B.
C.
D.
Heat transfer from the fuel cladding to the core barrel within a voided reactor
vessel
Heat transfer from the center to the edge of a fuel pellet
Heat transfer from the reactor coolant to the feedwater in a steam generator
Heat transfer from the fuel cladding to the reactor coolant via subcooled nucleate
boiling
3-42
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.1.11
The transfer of heat from the reactor fuel to the fuel cladding during normal operations is an
example of ________________ heat transfer.
A.
B.
C.
D.
3.1.12
The basic mode of heat transfer that involves the transfer of heat due to the differential
temperature of two separated bodies in a vacuum is best described as:
A.
B.
C.
D.
3.1.13
Conduction, forced convection
Conduction, conduction
Conduction, natural convection
Convection, conduction
Complete the following statement: Heat transfer from the centerline to the edge of the fuel
pellet is _______________ heat transfer, and heat transfer from the fuel clad wall to the
bulk liquid is ________________ heat transfer.
A.
B.
C.
D.
3.2.1
Conduction heat transfer
Convection heat transfer
Radiation heat transfer
Decay heat
The method of heat transfer from the centerline of the fuel pellet to the outside surface of
the fuel rod is _____________. Across the laminar layer the method is _____________.
A.
B.
C.
D.
3.1.15
Conduction heat transfer
Convection heat transfer
Radiation heat transfer
Molecular heat transfer
The transfer of heat energy through a solid material as a result of a temperature difference
across the material is best described as:
A.
B.
C.
D.
3.1.14
Conduction
Convection
Radiant
Two-phase
Radiative, convective
Convective, convective
Convective, conductive
Conductive, convective
A feedwater heat exchanger tube has a restriction in it which reduces the flow rate of the
feedwater so that feedwater flashes to steam halfway along the tube. This restriction causes
the heat transfer rate of the tube to _______________ and the overall heat transfer rate of
the heat exchanger to _________________.
3-43
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
A.
B.
C.
D.
3.2.2
As fluid rate increases through the tubes of a shell-and-tube heat exchanger, the laminar
film thickness ________________, which causes heat transfer rate to ________________.
A.
B.
C.
D.
3.3.1
Decrease, decrease
Decrease, remain the same
Increase, increase
Increase, remain the same
Increases, increase
Increases, decrease
Decreases, increase
Decreases, decrease
Which of the following describes the difference between a regenerative and a nonregenerative heat exchanger?
A.
B.
C.
D.
A non-regenerative heat exchanger uses its own system’s rejected heat to heat the
system.
A regenerative heat exchanger uses its own system’s heat to heat the system.
A non-regenerative heat exchanger can only be a “U” tube type heat exchanger.
A regenerative heat exchanger can only be “U” tube type heat exchanger.
3-44
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.3.2
From the diagram below, select the heat exchanger(s) that is (are) regenerative.
A.
B.
C.
D.
3.4.1
C
B
D
A and B
A only
A and D
D only
In a single-phase heat exchanger, heat transfer can be affected by several factors, one of
which is gases entrained in the fluid. Excessive amounts of gases passing through the heat
exchanger are undesirable because:
A.
B.
C.
D.
3.4.2
A
Flow blockage can occur in the heat exchanger
Gases will break up the laminar layer in the heat exchanger
The heat transfer coefficient will increase in the heat exchanger
The DT will decrease across the tubes in the heat exchanger
Which of the following best represents what is included in the overall heat transfer
coefficient for a heat exchanger?
A.
B.
C.
D.
Properties of the fluids in the heat exchanger
Operating conditions of heat exchanger
Geometry of heat exchanger
All of the above
3-45
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.4.3
Which types of exchanger is described by the following? “The two heat exchanging fluids
flow in opposite directions in a parallel path.”
A.
B.
C.
D.
3.4.4
When comparing a parallel and counter-flow exchanger with identical inlet and outlet
temperatures of both fluids, which of the below is true?
A.
B.
C.
D.
3.4.5
B.
C.
D.
The counter-flow heat exchanger’s outlet temperature of the cold fluid approaches
the highest temperature of the hot fluid
The counter-flow heat exchanger has a more even heat transfer rate
The counter-flow heat exchanger generally can support a higher flow rate due to its
design
Both A and B
Which of the following statements is true regarding adding baffles to a counter-flow heat
exchanger?
A.
B.
C.
D.
3.4.7
The counter-flow HE has a higher DT mean
The parallel-flow HE has a higher DT mean
Both heat exchangers have the same DT mean
None of the above are true
Which of the following best describes why a counter-flow heat exchanger is generally more
efficient than an parallel-flow heat exchanger?
A.
3.4.6
Parallel-flow heat exchanger
Counter-flow heat exchanger
Cross-flow heat exchanger
Mixing-fluid heat exchanger
Baffles decrease fluid velocity which increases heat transfer
A higher convective heat transfer coefficent results
Baffles decrease heat transfer but increase mechanical strength
A lower amount of turbulent flow will increase heat transfer
Select the best choice which describes the types of flow which can be utilized in a U-tube
heat exchanger.
A.
B.
C.
D.
Parallel flow
Counter flow
Cross flow
Any of the above
3-46
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.4.8
A U-tube heat exchanger is an example of:
A.
B.
C.
D.
3.4.9
A heat engine receives heat from a source at 535°F and rejects the unused heat energy to a
reservoir at 80°F. What is the maximum thermal efficiency of this engine?
A.
B.
C.
D.
3.4.10
26%
36%
46%
56%
Select the choice which best indicates the advantage of a U-tube heat exchanger.
A.
B.
C.
D.
3.4.11
Parallel flow
Counter flow
Cross flow
All of the above
Less turbulent flow within the tubes
More turbulent flow within the tubes
Ability of tubes to expand lengthwise, reducing thermal stresses
None of the above in an advantage
The plant is at 8% and increasing when the unit operator inadvertently trips the # 1 RCP.
Which of the following best describes the initial impact on S/G level, Tave, and S/G
pressure for the affected loop?
A.
B.
C.
D.
3.6.1
S/G level increases, Tave increases, and S/G pressure increases
S/G level increases, Tave decreases, and S/G pressure increases
S/G level decreases, Tave decreases, and S/G pressure decreases
S/G level decreases, Tave increases, and S/G pressure decreases
A heat engine receive heat from a source of 535°F and rejects the unused heat energy to a
reservoir at 80°F. What is the maximum thermal efficiency of this engine?
A.
B.
C.
D.
26%
36%
46%
56%
3-47
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.2
Select the choice which best indicates the advantage of a U-tube heat exchanger.
A.
B.
C.
D.
3.6.3
Which of the following best explains the effects of steam formation on heat transfer in
single-phase (liquid) heat exchangers?
A.
B.
C.
D.
3.6.4
Increases
Decreases
Remains unchanged
Temporarily decreases, then returns to previous value
Assuming the reactor power remains constant, steady-state to steady-state, as reactor
coolant flow increases, fuel temperature will:
A.
B.
C.
D.
3.6.6
The T across the tubes will decrease in the heat exchanger
Steam voids will increase the heat transfer coefficient of the heat exchanger
A small amount of steam will reduce the amount of heat transfer
Steam voids can accumulate and cause blockage
If a reduction of reactor coolant flow occurs during power operation, what affect will this
have on core T, assuming no change in reactor power level?
A.
B.
C.
D.
3.6.5
Less turbulent flow within the tubes
More turbulent flow within the tubes
Ability of tubes to expand lengthwise, reducing thermal stresses
None of the above is an advantage
Increase
Decrease
Remain the same, steady-state to steady-state
Increase, then return to the original steady-state value
Assuming that reactor power remains constant at 30 percent, if reactor coolant flow
decreases by 10 percent, fuel temperature will:
A.
B.
C.
D.
Increase, then stabilize at a higher value
Decrease, then stabilize at a lower value
Increase, then return to the original steady-state value
Decrease, then return to the original steady-state value
3-48
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.7
Which of the following parameters, when changed, would not directly affect the heat
transfer rate tot he reactor coolant system? (Evaluate each change separately).
A.
B.
C.
D.
3.6.8
Which of the following explains the effects of steam formation on heat transfer in singlephase (liquid) heat exchangers?
A.
B.
C.
D.
3.6.9
Overall heat transfer coefficient of the RCS
Reactor coolant flow rate
Pressurizer temperature
Fuel centerline temperature
The temperature difference across the tubes will decrease through the heat
exchanger
Steam voids will increase the heat transfer coefficient of the heat exchanger
A small amount of steam will reduce the amount of heat transfer
Steam voids can accumulate and cause flow blockage
In a single-phase (liquid) heat exchanger, heat transfer can be affected by several factors,
one of which is gases entrained in the fluid. Excessive amounts of gases passing through
the heat exchanger are undesirable because:
A.
B.
C.
D.
Flow blockage can occur in the heat exchanger
Gases will break up the laminar layer in the heat exchanger
The heat transfer coefficient will increase in the heat exchanger
The temperature difference across the tubes will decrease through the heat
exchanger
3-49
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.10
Using the diagram below select which of the following is correct.
105
°
105
°
90
D
#1
#2
C
90
A
A.
B.
C.
D.
3.6.11
B
“C” is closer to 105 degrees than “D”
“D” is closer to 105 degrees than “C”
Heat exchanger #1 is more efficient than heat exchanger #2
None of the above
A counter-flow heat exchanger (HE) transfer 2 x 109 BTY/hr with a Log Mean temperature
difference of 55°F. The HE has 15,000 tubes measuring 5/8” (OD) by 10’ long. What is
the heat transfer coefficient for this HE?
A.
B.
C.
D.
123.5 BTU/hr-°F-ft2
387.8 BTU/hr-°F-ft2
1235.3 BTU/hr-°F-ft2
1481.6 BTU/hr-°F-ft2
3-50
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.12
Why can temperature NOT be used to calculate the heat transfer in a heat exchanger in
which a phase change occurs?
A.
B.
C.
D.
3.6.13
The reactor coolant enters the core at 548°F and exits at 596°F. If the reactor coolant flow
rate is 8.36 x 107 lbm/hr and the specific heat of water at core conditions has a magnitude of
1.3, what is the core thermal power?
A.
B.
C.
D.
3.6.14
755 MWt
1509 MWt
3018 MWt
3411 MWt
The reactor coolant enters the core at 545 degrees F and leaves at 595 degrees F. If the
reactor coolant flow rate is 6.6 x 107 lbm/hr and the specific heat of water at core conditions
is 1.3 BTY/lbm-degree F, what is the core thermal power? (1 Kwatt = 3.4127 x 103
BTU/hr)
A.
B.
C.
D.
3.6.16
522 MWt
1176 MWt
1528 MWt
1592 MWt
In a two-loop pressurized water reactor, feedwater flow to each steam generator is 3.3 x 106
lbm/hr at an enthalpy of 419 BTU/lbm. The steam existing each steam generator is at 800
psia with 100% steam quality. Ignoring blowdown and pump heat, what is the core thermal
power?
A.
B.
C.
D.
3.6.15
At constant pressure, temperature does not change during phase changes
At constant pressure, temperature changes radically during phase changes
Changes in temperature during phase changes are not easily measured
Temperature CAN be used to measure heat transfer during phase changes
967 MWt
1160 MWt
1257 MWt
1508 MWt
Which of the below statements is NOT true regarding the rate of heat transfer through a
solid material?
A.
B.
C.
D.
Heat transfer rate increases with an increase in DT.
Heat transfer rate decreases with an increase in thickness.
Heat transfer rate decreases with an increase in surface area.
Heat transfer rate increases with an increase in thermal conductivity.
3-51
ESP100.30 Rev. 4
Heat Transfers and Heat Exchangers
Chapter 3
3.6.18
The mass flow rate of circulating water through the tubes of the main condenser 3.0 x 108
lbm/hr with an inlet temperature of 72°F. The heat being discharged is 6.98 x 109 BTU/hr.
What is the outlet temperature? (Assume cp = 1.0)
A.
B.
C.
D.
3.7.1
87.8°F
93.2°F
95.3°F
102.8°F
Tube scaling in a parallel-flow heat exchanger will cause heat transfer to decrease because:
A.
B.
C.
D.
Flow through the heat exchanger increases
Surface area of the tubes decreases
Heat transfer coefficient decreases
Inlet temperature of the cooling fluid increases
3-52