22 Design and Optimization of Thermal Systems
It is important to recognize that thermal systems arise in many diverse elds of
engineering, such as aerospace engineering, manufacturing, power generation, and
air conditioning. Consequently, a study of thermal systems usually brings in many
additional mechanisms and considerations, making the problem much more com-
plicated than what might be expected from a study of thermal sciences alone.
1.3.2 ANALYSIS
The analysis of thermal systems is often complicated because of the complex
nature of uid ow and of heat and mass transfer mechanisms that govern these
systems. As a result, typical thermal systems have to be approximated, simpli-
ed, and idealized in order to make it possible to analyze them and thus obtain
the inputs needed for design. Following are some of the characteristics that are
commonly encountered in thermal systems and processes:
1. Time-dependent
2. Multidimensional
3. Nonlinear mechanisms
4. Complex geometries
5. Complicated boundary conditions
6. Coupled transport phenomena
7. Turbulent ow
8. Change in phase and material structure
9. Energy losses and irreversibility
10. Variable material properties
11. Inuence of ambient conditions
12. Variety of energy sources
Because of the time-dependent, multidimensional nature of typical systems,
the governing equations are generally a set of partial differential equations, with
nonlinearity arising due to convection of momentum in the ow, variable proper-
ties, and radiative transport. However, approximations and idealizations are used to
simplify these equations, resulting in algebraic and ordinary differential equations
for many practical situations and relatively simpler partial differential equations for
) 0
Introduction 23
f
3
(x
1
, x
2
, x
3
,z, x
n
) 0(1.4)
f
n
(x
1
, x
2
, x
3
,z, x
n
) 0
where the x
i
are the unknowns and the functions f
i
, for i 1, 2, 3,z, n, may be
in the startup and shutdown of the systems, as well as in determining the effects
of changes in operating conditions like ow rate, pressure, and heat input.
If the conditions in the different parts of the system cannot be assumed to
be uniform, the problem is referred to as distributed. A time-dependent, two-
dimensional ow with the assumption of constant uid properties, as in a duct or
over a heated body, is represented by the equations (Burmeister, 1993)
t
t
u
x
t
t
v
y
0(1.6)
t
t
u
T
u
t
t
u
x
v
t
t
u
t
v
T
u
t
t
v
x
v
t
t
v
y
1
R
t
t
p
y
N
t
t
¤
¦
¥
2
2
v
x
y
A
t
t
Ô
Ư
Ơ
2
2
T
x
t
t
à
2
2
T
y
(1.9)
The corresponding three-dimensional equations may similarly be written by
adding the components in the z direction, including the z-momentum equation.
The problem then becomes much more complicated, but many practical circum-
stances, such as environmental processes, cooling of electronic equipment, and
manufacturing systems, require three-dimensional analysis for accurate results
for use in design and optimization.
If there is no ow, for instance, in the circumstance of conduction in a sta-
tionary solid body such as the wall of a building or of a blast furnace, the energy
ity components appear. Equation (1.6) through Equation (1.10) are partial differential
equations and are written for the relatively simpler constant property, two-dimensional
circumstance for the Cartesian coordinate system and a Newtonian uid. Even then,
these are quite complicated. In practical systems, we often encounter many additional
complexities that make the analysis a very difcult and challenging affair.
Inclusion of variable properties and/or radiative transport can give rise to nonlin-
ear mechanisms, the former due to the dependence of the properties on the dependent
variable such as temperature T and the latter due to the variation of radiation heat
transfer as T
4
. For example, if the thermal conductivity k, density R, and specic heat
at constant pressure C
p
vary with temperature T, Equation (1.10) becomes
R
T
() ()TC T
T
x
kT
T
xy
kT
T
y
p
t
t
t
ES()
44
(1.12)
Introduction 25
where E is the surface emissivity and S is the Stefan–Boltzmann constant. This
equation is nonlinear in T due to the presence of temperature as T
4
. Thus, non-
linear equations are frequently obtained, making the solution difcult. Iterative
methods are often needed to obtain the solution. Nonlinearity also makes it dif-
cult to scale up the results from a laboratory model to the full-size system. Many
of these considerations are discussed in detail in Chapter 3.
The various other complexities mentioned earlier also complicate the analysis
and design of thermal systems. Complex geometry and boundary conditions arise
in most practical systems, making it necessary to use simplications and versatile
numerical techniques such as nite element and boundary element methods. Tur-
bulent ow is encountered in many important processes, particularly in energy
systems and environmental transport. Special numerical models and experimental
procedures have been developed to take turbulent transport into account. Phase
change, coupling with material characteristics, time-varying ambient conditions,
irreversibility, and different energy sources, such as lasers, gas, oil, electricity,
and viscous heating, further complicate the analysis of thermal systems and pro-
cesses. Several of these aspects will be seen to arise in examples given in later
chapters. However, our focus is not on analysis but on design, even though analy-
sis provides many of the inputs needed for design. Therefore, only a brief outline
of the basic characteristics of thermal systems is given here. Specialized books,
such as Ozisik (1985) and Incropera and Dewitt (2001) in heat transfer, Fox and
McDonald (2003) and Shames (1992) in uid mechanics, Howell and Buckius
(1992), Cengel and Boles (2002) and Moran and Shapiro (2000) in thermodynam-
ics, among others, may be consulted for details on different analytical and experi-
skin thickness)
Water sprays
Supporting and
withdrawing rolls
Withdrawal of casting
at velocity U
+
y
++
+
Heated and cooled surface
(b)
Feed hopper
Extrudate
Die
FIGURE 1.10 A few manufacturing systems. (a) Continuous casting, (b) plastic screw
extrusion, (c) optical ber drawing, (d) hot rolling. (Figure 1.10(a) adapted from Ghosh
and Mallik, 1986; Figure 1.10(b) from Tadmor and Gogos, 1979.)
Introduction 27
(c)
(d)
Distance
Temperature
Station 2Station 1
Rollers
U
Hot
material
Feed mechanism
Glass rod
glass rod, typically 5–10 cm in diameter and known as a preform, is heated in a
furnace and pulled to sharply reduce the diameter to 100–125 Mm, yielding an opti-
cal ber in glass ber drawing. In hot rolling, the material is heated and reduced
in thickness by pushing it through two rollers that are at a given distance apart.
Several sets of rollers may be used to obtain the desired decrease in thickness or
diameter. Similarly, new thermal processes have been developed for the fabrica-
tion of nanomaterials through chemical vapor deposition and other approaches.
Heat transfer is very important in these processes because the temperature
determines the forces needed, the withdrawal speed, and the quality of the nal
product. Further details on these and other processes may be found in specialized
books on manufacturing, such as Ghosh and Mallik (1986), Doyle et al. (1985),
and Kalpakjian (1989). Some of these processes will be considered again later in
the book as examples. With the development of new and improved materials, the
design of thermal systems for materials processing has become crucial for manu-
facturing new products and for meeting international competition.
Energy Systems
Examples of energy systems include power plants, solar energy utilization, geo-
thermal energy systems, energy storage, solar ponds, and conventional and non-
conventional energy conversion systems.
This is one of the most frequently mentioned areas for thermal energy con-
siderations. Different types of thermal systems arise depending on the nature of
the energy source, such as nuclear, oil, gas, solar, or wind energy. Most of these
systems are covered in thermodynamics courses and are often treated as steady,
lumped systems. Figure 1.11 shows sketches of typical solar and nuclear energy
systems. In both cases, the energy collected or generated is used to run the tur-
bines, which are then used to generate electricity. A considerable literature exists
on thermal systems of interest in this eld because of the tremendous importance
of power generation in our society; see, for instance, Howell et al. (1982), Hsieh
(1986), Van Wylen et al. (1994), and Dufe and Beckman (1991).
Cooling Systems for Electronic Equipment
flux
Turbine
Storage
Pump
Solar energy
collection system
(a)
Condenser
FIGURE 1.11 Power systems based on (a) solar energy and (b) nuclear energy. (Adapted
from Howell and Buckius, 1992.)
30 Design and Optimization of Thermal Systems
most of which are not directly connected with uid ow and heat transfer. But the
cooling of the electronic system in order to ensure that the temperature T
c
of the
various components, particularly of the chips or semiconductor devices, does not
exceed the allowable temperature level T
max
, that is, T
c
a T
max
, is often the most
crucial factor in the design and operation of the system. Further size reduction
of the system is frequently constrained by the heat transfer considerations. Figure 1.12
shows typical air cooling and liquid immersion systems for electronic equipment.
The energy dissipated by the electronic components is removed by the uid ow,
thus allowing the temperatures to remain below the specied limit. Figure 1.2
showed a sketch of a heat pipe for enhanced cooling of an electronic chip. Many
books, such as those by Steinberg (1980) and Kraus and Bar-Cohen (1983), have
disposal, including global warming and depletion of the ozone layer, has made
it essential to minimize the effect on our environment by developing new and
FIGURE 1.13 Typical electronic systems with air cooling by means of a fan. (From Stein-
berg, 1980.)
32 Design and Optimization of Thermal Systems
improved methods for disposal. Many thermal systems have been developed in
response to this need. These include systems based on uids that would sub-
stitute refrigerants like CFCs (chlorouorocarbons) that adversely affect the
ozone layer, improved incineration techniques for solid waste disposal, catalytic
converters in automobiles to reduce harmful emissions, and scrubbers in power
plants to reduce pollutants. Figure 1.14 shows sketches of typical heat rejection
systems from power plants, employing a lake as a cooling pond in the rst case
and a natural draft cooling tower in the second. The effect on the local environ-
ment, in terms of temperature rise, increased ow, and disturbance to natural
yearly cycle, is of particular concern in these cases. Safety is also a very impor-
tant consideration. Figure 1.15 shows a sketch of a room re, indicating a hot
upper layer containing the toxic and hot combustion products and a relatively
(a) (b)
Temperature
profile
Lake
Intake
Pump
Average flow
u
Outfall
Power plant heat
rejection system
T
b
everything in the room catches re and the room is engulfed in ames. Thus, the
design of the system, which may be a building, ship, submarine, or airplane, for
re safety is clearly an important element in the overall construction and opera-
tion of the system.
Aerospace Systems
Many thermal systems in aerospace applications are of interest here. Some of the
common ones are gas turbines, rockets, combustors, and cooling systems.
This has been a particularly important area over the last three decades
because of the space program. Considerable progress has been made on the vari-
ous thermal systems and subsystems that are needed. Because of the large thrust
needed at rocket launch and high cooling rates during reentry, much of the effort
in designing efcient systems has been directed at these two stages. However,
cooling, air conditioning, and electronic and energy systems during orbit, as well
as for a space station, have their own requirements and challenges.
Transportation Systems
Most of the relevant systems in this area are thermal in nature. These include
internal combustion engines such as spark ignition and diesel engines; steam
engines; fuel cells; and modern automobile, airplane, and train engines.
This is an extensive eld, closely associated with different kinds of thermal sys-
tems. Though a traditional mechanical engineering eld, this area has seen many
signicant changes in recent years, most of these being related to the optimization of
existing systems. New systems have also evolved in response to the need for higher
efciency, size that is more compact, greater safety, and lower costs. Supersonic air
transport has led to several interesting innovations in this eld. Figure 1.16 shows
a few typical systems that arise in transportation. Figure 1.16(a) shows two designs
for a jet engine, with hot gases being ejected from the nozzle to provide the thrust.
Figure 1.16(b) shows a spark ignition engine where the combustion process in the
cylinder drives the piston, which moves the crankshaft and thus the wheels.
Figure 1.17 shows photographic views of gas turbine systems, indicating the intake,
exhaust, and combustion chamber. Similarly, Figure 1.18 shows sketches of engines
&
#
FIGURE 1.16 Thermal systems for transportation. (a) Thrusting systems for aircraft
propulsion: Turbojet engine with and without afterburner (b) reciprocating internal com-
bustion engine. (Figure 1.16a adapted from Reynolds and Perkins, 1977, and Figure 1.16b
from Moran and Shapiro, 1996).
Introduction 35
and vapor absorption cooling systems, heat pumps, ice and food freezing plants,
gas, oil, and water heating systems, and refrigerators.
Even though this eld has been around for a long time, the need for more ef-
cient, dependable, and safe systems, at lower cost, has led to many improvements.
In particular, better design of the main components such as the compressor and
the condenser, better control of the system, and better design of the overall system
to minimize losses have resulted in reduced energy consumption and lower costs.
Figure 1.8 presented sketches of the vapor compression and vapor absorption sys-
tems for refrigeration. In both cases, energy is removed from a given space or
material due to the evaporation of the working uid in the evaporator and heat is
rejected to the ambient in the condenser. The driving mechanism is the compres-
sor in one case and the absorption process in the other. In a heat pump, which
operates on the same thermodynamic cycle as a refrigeration system, energy is
FIGURE 1.17 Typical gas turbine engines for aircrafts. (From AlliedSignal, Inc.)
36 Design and Optimization of Thermal Systems
extracted from a colder environment and supplied to a warmer region, such as a
house. Photographs of practical heat pumps are shown in Figure 1.19. Though
these are often treated as components, they are actually thermal systems with
many interacting parts. Specialized books such as those by Stoecker and Jones
CAM FOLLOWERS
weight reduction: 14%
CYLINDER BLOCK AND GIRDLE
CYLINDER HEAD
PISTON RINGS
• Magnesium with thermal spray
synthectic Iron bore surface
(.004'' thickness)
weight reduction: 33%
• Magnesium weight
reduction: 35%
• 1.0mm top compression
• 1.2mm 2nd compression
• 2.0mm oil ring weight
reduction: 35%
• Titanium-aluminide exhaust
weight reduction: 57%
(a)
FIGURE 1.18 (a) A lightweight engine for an automobile. (From Ford Motor Co.) (b) A
turbocharged diesel engine. (From Cummins Engine Co.)
Power turbine
(b)
exhaust system
Turbocharger
Turbocompound
diesel engine
Vibration isolation
(fluid coupling)
Power transfer
to crankshaft
High speed
Introduction 39
Heat Transfer Equipment
Such equipment includes heat exchangers, condensers, boilers, furnaces, ovens,
hot water baths, and heaters.
Heat transfer equipment often forms part of the various other applications men-
tioned here. Thus, condensers and boilers may be part of a power system. Simi-
larly, furnaces may be regarded as constituents in a heat treatment system. However,
such equipment frequently can be designed without considering the application. As
mentioned earlier, in the design of a thermal system some of these items may be
procured through selection rather than through design. In this case, companies spe-
cializing in, say, heat exchangers, would design and manufacture these. Different
types of heat exchangers, such as those seen in Figure 1.5, would then be produced
for selected ranges of design specications and made available for marketing (Kays
and London, 1984). Similar considerations apply for drying ovens, furnaces, heated
oil baths, etc., which may be designed for a specic application or for general use.
Other Systems
There are several other thermal systems that may not be as easily classied as was
done here for some of the more common and practical systems. Thus, chemical
reactors and systems for experimentation, space systems, construction systems,
etc. also often involve thermal considerations in their design and may be treated
by the techniques discussed in this book.
Other methods of classifying thermal systems can also be used. The follow-
ing approach divides these systems into three types, representing the three main
stages undergone by thermal energy:
1. Generation: Solar, geothermal, nuclear and oil-red power systems,
combustors, engines, energy conversion systems, turbines, boilers, and
chemical reactors
2. Utilization: Manufacturing, car engines, airplanes, and rockets
3. Rejection: Heat removal, pollution, waste disposal, electronic systems,
air conditioning, heat pumps, cooling towers, and radiators
considerations are generally common to other types of systems as well. Starting
with the problem statement in terms of the requirements, constraints, and other
specications, a conceptual design, which is based on creativity and existing sys-
tems, is obtained. The design variables that arise in the problem are determined
and varied to obtain a variety of designs, which are evaluated through analysis
to determine if an acceptable design can be chosen. Because the solution is not
unique, a range or domain of acceptable designs is generally obtained. The evalu-
ation of the designs requires detailed information on the performance of the sys-
tem. Because of the complexity of most practical thermal systems, it is necessary
to develop a mathematical model of the system by simplifying and idealizing the
processes involved. Several types of models are discussed in Chapter 3, particu-
larly mathematical and experimental models. Modeling of the system is one of
the most important and creative elements in the design process because it allows
relevant inputs to be generated.
Numerical modeling and simulation are generally needed for most practi-
cal systems, as considered in detail in Chapter 4. Numerical simulation approxi-
mates the actual system and yields quantitative information on the behavior of
the system under a wide range of design and operating conditions. Therefore, the
characteristics of the system can be investigated for different designs, making it
possible to evaluate the design. The various methods and techniques for modeling
and simulation are discussed. The presentation of these results in a form suitable
for design is also discussed. Several examples of thermal systems are then taken
from different application areas in Chapter 5 to discuss the synthesis of all these
aspects to obtain a design that meets the given requirements and constraints. The
modeling, simulation, and design of large, practical systems are also considered.
Trade-offs have to be made to meet constraints due to regulations, economics,
Introduction 41
safety, and other such considerations. In most cases, a domain of acceptable
designs is obtained, with the best or optimal design to be chosen from these. If
an acceptable design is not obtained, the requirements may be relaxed, new con-
such as professional ethics, sources of information, and additional constraints on
the design are also discussed.
It must be noted that the book presents all the major elements needed for the
design and optimization of thermal systems. However, some of these may have
been covered in earlier courses at a particular college or university. The instructor
could then decide to avoid covering these in a given design course. Examples of
such topics are various aspects in economic considerations given in Chapter 6,
physical modeling and dimensional analysis in Section 3.4 and solution pro-
cedures in Section 4.2. Though obviously needed for design and optimization,
coverage of such topics may be curtailed or eliminated depending on the back-
ground and preparation of the class. Similarly, examples of thermal systems range
from simple pipe and channel ows through thermodynamic systems to more
42 Design and Optimization of Thermal Systems
involved heat transfer processes. Again, the instructor may choose to emphasize
simpler thermodynamic and ow systems, rather than the more complicated sys-
tems that involve multidimensional heat transfer mechanisms, depending on the
background of the students. In many curricula, heat transfer is taught much later
than thermodynamics and uid mechanics, making it easier to consider lumped,
steady, or transient, thermodynamics and uid ow systems for design, rather than
distributed ones. However, wide ranges of examples, problems, and exercises are
presented in this book, along with all the ingredients needed for design and opti-
mization, to make such a choice possible on the basis of the needs and preparation
of the class.
A Note on Problems and Examples
Several examples and problems, or exercises, are given on each topic in order to
strengthen the discussion and clarify the important issues involved. In many cases,
the problems are reasonably straightforward and build on the material presented
in the book. This is particularly true for examples and exercises in optimization
and on other topics where a particular aspect of analysis or simulation is being
demonstrated. However, design involves open-ended problems and synthesis of
mental impact.
1.5 SUMMARY
This chapter presents the introductory material for a study of the design and opti-
mization of thermal systems. It introduces three main topics: engineering design,
thermal systems and processes, and optimization. In addition to providing de-
nitions for the relevant terms, the discussion considers the basic characteristics
and relevance of thermal systems and design to engineering enterprises. Design,
which is a creative process undertaken to solve new or existing problems, is an
extremely important engineering task because it leads to new and improved pro-
cesses and systems. Design, which involves an open-ended solution with mul-
tiple possibilities, is contrasted against analysis, which gives rise to unique,
well-dened, closed-ended results. Thus, design generally involves considering
many different solutions and nding an acceptable result that satises the given
problem. Synthesis brings several different analyses and types of information
together, thus forming an important facet in system design. In many applications,
components or equipment are to be chosen from available items. This is the pro-
cess of selection, rather than of design, which starts from the basic concept and
develops a system for a given application. The focus in this book is on the design
of systems and not on selection, although in several instances a particular compo-
nent may be selected from those available in the market.
Design is also considered as part of an overall engineering enterprise. The
project starts with the denition of a need or opportunity and is followed by mar-
ket and feasibility analyses. Once these are established, engineering design is ini-
tiated with inputs from research and development. The design process leads to a
domain of acceptable designs from which the best or optimal design is obtained.
Finally, the results are communicated to other divisions of the company for fab-
rication, testing, and implementation. Thus, design occupies a prominent position
in typical engineering enterprises. In most cases, optimization of the design is
essential in order to obtain the best output/input ratio.
Processes, systems, components, and subsystems are discussed in terms of
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Hodge, B.K. (1985) Analysis and Design of Energy Systems, Prentice-Hall, Englewood
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Howell, J.R. and Buckius, R.O. (1992) Fundamentals of Engineering Thermodynamics,
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Howell, J.R., Vliet, G.C., and Bannerot, R.B. (1982) Solar Thermal Energy Systems:
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Incropera, F.P. and Dewitt, D.P. (1990) Fundamentals of Heat and Mass Transfer, 3rd ed.,
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Incropera, F.P. and Dewitt, D.P. (2001) Fundamentals of Heat and Mass Transfer, 5th ed.,
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Janna, W.S. (1993) Design of Fluid Thermal Systems, PWS-Kent Pub. Co., Boston.
John, J.E.A. and Haberman, W.L. (1988) Introduction to Fluid Mechanics, 3rd ed.,
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Kalpakjian, S. and Schmid, S.R. (2005) Manufacturing Engineering and Technology, 5th
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Kays, W.M. and London, A.L. (1984) Compact Heat Exchangers, McGraw-Hill, New York.
Kraus, A.D. and Bar-Cohen, A. (1983) Thermal Analysis and Control of Electronic Equip-
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Kreider, J.F. and Rabl, A. (1994) Heating and Cooling of Buildings: Design for Efciency,
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Introduction 45
Moran, M.J. and Shapiro, H.N. (2000) Fundamentals of Engineering Thermodynamics,
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