Design and Optimization of Thermal Systems Episode 1 Part 3 pptx

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. Inuence 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

others. These considerations are discussed in Chapter 3 as part of modeling of the
system. However, the equations for a few simple cases are given here to illustrate the
nature of the governing equations and the effect of some of these complexities.
The simplest problems are those that assume steady-state conditions, with or
without ow, while also assuming uniform conditions in each part of the system.
These problems lead to algebraic equations, which are often nonlinear for ther-
mal systems. This situation is commonly encountered in thermodynamic systems
such as refrigeration, air conditioning, and energy conversion systems. Then, the
governing set of algebraic equations may be written as
f
1
(x
1
, x
2
, x
3
,z, x
n
)  0
f
2
(x
1
, x
2
, x
3
,z, x
n

)  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

linear or nonlinear. Such problems are generally referred to as steady, lumped
circumstances and have been most extensively treated in papers and books deal-
ing with system design, such as Hodge (1985), Stoecker (1989), and Janna (1993).
However, these approximations are applicable for only a few idealized thermal
systems. Additional complexities, mentioned earlier, generally demand analysis
that is more accurate and the solution of ordinary and partial differential equa-
tions. Nevertheless, because of the ease in analysis, steady lumped systems are
effective in illustrating the basic ideas of system simulation and design. There-
fore, these are used as examples throughout the book while bearing in mind that,
in actual practice, more elaborate analysis would generally be needed.
If the time-dependent behavior of the system is sought, for a study of the
dynamic characteristics of the system, the resulting governing equations are ordi-
nary differential equations in time, if the assumption of uniform conditions within
each part is still employed. Then the governing equations may be written as
dx
d
Fx x x x fori n
i
in
T
(, , , , ) ,,, ,
123
123 (1.5)
where, again, the functions F
i
may be linear or nonlinear. The systems for which
these approximations can be made are known as dynamic, lumped systems. Such
a treatment is valuable in many cases because of the resulting simplicity. In many
thermodynamic systems, such as heat engines and cooling systems, the individual
components are approximated as lumped and the dynamic analysis is of interest

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

y

1
R
t
t
p
x
N
t
t
¤
¦
¥
2
2
u
x

t
t
³
µ
´
2
2
u
y
(1.7)
t

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


t
t
³
µ
´
2
2
v
y
(1.8)
where the rst equation gives the conservation of mass and the other two give the
momentum force balance in the x and y directions, respectively. Here, u, v are the
24 Design and Optimization of Thermal Systems
velocity components in the x, y coordinate directions, p is pressure, R is the density,
T is time, and N is the kinematic viscosity of the uid. The corresponding energy
equation for the temperature T in the uid, with A as its thermal diffusivity, is
t
t
T
T
u
t
t
T
x
v
t
t
T

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

equation, Equation (1.9), reduces to
t
t
T
T
A
t
t
Ô
Ư
Ơ
2
2
T
x

t
t

à

2
2
T
y
(1.10)
Here, the energy equations, (1.9) and (1.10), are linear because T appears in its rst
power. The ow is obtained from Equation (1.6) through Equation (1.8), which are cou-
pled with u, v, and p as the unknowns. The momentum equations are nonlinear because
of the inertia terms u u/x, v u/y, etc., in which higher powers of the unknown veloc-

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

t
t
t
Đ
â
ă
ả
á
ã

t
t
t
t
() ()
ĐĐ
â
ă
ả
á
ã
(1.11)
Similarly, Equation (1.9) may be modied for variable properties. Thus, nonlin-
earity arises due to nonlinear powers of T resulting from property variation with T.
If radiative heat loss occurs at a surface, the corresponding energy exchange rate q,
per unit area, with a black environment at temperature T
e
may be written as
qTT
e

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 difcult. 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 simplications 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-

mental techniques as well as for results obtained on a variety of fundamental and
applied problems.
1.3.3 TYPES AND EXAMPLES
As mentioned earlier, thermal systems are important in a wide variety of engi-
neering elds and disciplines. Let us consider some important examples, types,
and applications of these systems. Several different ways of classifying thermal
systems may be employed because of their diversity. A common method is in
terms of the function or application of the system. Using this approach, several
important types of thermal systems, along with commonly encountered applica-
tions and examples, follow.
Manufacturing and Materials Processing Systems
Examples include processes such as casting, crystal growing, heat treatment,
metal forming, drying, soldering and welding, laser and gas cutting, plastic extru-
sion and injection molding, powder metallurgy, optical ber drawing, ceramics,
and glass processing. Also included are food processing systems as well as com-
mon household appliances such as ovens and cooking ranges. This is an important
area and many diverse thermal systems are employed for the different manufac-
turing processes used in practice. We have already discussed ingot casting, as
26 Design and Optimization of Thermal Systems
sketched in Figure 1.3. Figure 1.10 shows the schematics for continuous casting,
plastic extrusion, glass ber drawing, and hot rolling processes.
In continuous casting, molten material is allowed to solidify across an inter-
face as the bulk material is withdrawn at a given speed through a mold, which is
U
(a)
Tundish
Liquid metal feed
Water cooled
mold
δ(Solidified

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

(preform)
Furnace
Furnace
Fiber cooling
distance
Fiber diameter
monitor
Accelerated
cooling
Coating
applicator
Coating concentricity
monitor
Coating diameter monitor
Coated fiber
Winding drum
Drawing pulley
Curing furnace
or lamps
Fiber
Neck-
down
region
FIGURE 1.10 (Continued).
28 Design and Optimization of Thermal Systems
usually water cooled. In plastic screw extrusion, the solid plastic is fed through a
hopper, melted by energy input, and conveyed by the rotation of the screw, with
an associated pressure and temperature rise, nally pushing the molten material
through a die to obtain a desired shape. The material may also be injected into a
mold and solidied for a process known as injection molding. Similarly, a special

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 Dufe and Beckman (1991).
Cooling Systems for Electronic Equipment

Systems that are of interest in this area include air cooling, liquid immersion, heat
pipes, heat sinks, heat removal by boiling, and microscale systems.
This is one of those areas where thermal considerations are extremely impor-
tant for the satisfactory performance of the system even though the main applica-
tion is in a different area. Thus, electronic systems, such as computers, televisions,
digital multimeters, and signal conditioners, are used for a variety of applications,
Introduction 29
Containment vessel
Steam generator
Power
output
Condenser
Secondary
loop pump
Primary
loop pump
Low-
pressure
turbine
High-
pressure
turbine
Nuclear
reactor
(b)
Power
output
Bypass line
Solar boiler
Solar

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 specied 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

been written in response to the growing importance of this area. Photographs
Air
flow
Wall
(a)
Electric
circuit
boards
Relief valve
Coolant inCoolant out
Electronic
components
Expansion chamber
Condenser plate
Electrically
nonconducting
liquid
(b)
FIGURE 1.12 Cooling systems for electronic equipment. (a) Forced air cooling, (b) liquid
immersion cooling.
Introduction 31
of typical electronic equipment with air cooling by means of a fan or a blower
are shown in Figure 1.13, indicating the complexity of such systems in actual
practice.
Environmental and Safety Systems
Examples of these systems include arrangements for heat rejection to ambient
air and water, control of thermal and air pollution, cooling towers, incinerators,
waste disposal, water treatment plants, smoke and temperature control systems,
and re extinguishing systems.
The growing concern with the environmental impact of waste and energy

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 (chlorouorocarbons) 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

T
s
T
x
Cooled
water
Intake water
Hot water
Air flow
Cooling
tower
FIGURE 1.14 Systems for heat rejection from a power plant. (a) Natural lake as a cooling
pond, (b) natural draft cooling tower.
Temperature
distribution
Fire
Plume
Opening
Inflow
Outflo
w
Wake
Ceiling
Stably stratified
region
Walls
T
FIGURE 1.15 Flow and temperature due to re in a room with an opening.
Introduction 33
cooler and less toxic lower layer that is often safe until ashover occurs when

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 efcient 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
signicant 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
efciency, 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

for transportation, indicating a lightweight engine and a diesel engine that is turbo-
charged for boosting power. Clearly, the practical systems are extremely complicated
and involve intricate ow paths, combustion processes, and control mechanisms. For
details on these and other systems, books on thermodynamics, such as those by Van
Wylen et al. (1994) and by Howell and Buckius (1992), and more specialized books
on various relevant topics, such as Heywood (1988), may be consulted.
Air Conditioning, Refrigeration, and Heating Systems
Several different thermal systems are associated with this application, which is
of considerable interest to us in our daily lives. These include vapor compression
34 Design and Optimization of Thermal Systems








#
"
$

$
&!%
#
 !!


!!



&
#


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

LIGHTWEIGHT CONCEPT ENGINE
VALVES, INTAKE & EXHAUST
VALVE SPRING RETAINERS
VALVE SPRINGS
PISTON
PISTON PIN
CONNECTING ROD
CRANKSHAFT
• Stamped steel w/ ceramic roller
weight reduction: 24%
• Ceramic Intake
weight reduction: 61%
• Polymer composite
weight reduction: 84%
• Titanium
weight reduction: 57%
• Magnesium forging
weight reduction: 33%
• Ceramic
weight reduction: 61%
• Forged aluminium metal matrix
composite
weight reduction: 33%
• Total engine weight production engine (356 lbs.)
• Total engine weight as shown (306 lbs.)
• Total engine weight including the additional weight reduction opportunities (292 lbs.)
Additional weight reduction opportunities include magnesium or polymer composite substitutions for valve covers,
front cover, oil pan, water pump housing, thermostat housing, oil pump housing, intake manifold and throttle body
• Counterweights reduced due to lighter
weight piston, pin and connecting rod

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

reduction gearing
Introduction 37
FIGURE 1.19 Photographs of practical heat pumps. (From KIST, Korea.)
38 Design and Optimization of Thermal Systems
(1982), Cooper (1987), and Kreider and Rabl (1994) may be consulted for details
on these systems.
Fluid Flow Systems and Equipment
These include components and uid ow circuits such as pipe ows, hydraulics,
hydrodynamics, uidics, turbines, pumps, compressors, fans, and blowers.
Many of these are auxiliary subsystems to the main thermal systems and may
be used for control; power transmission; cooling; and transport of mass, energy,
and momentum. Fluid mechanics itself is closely linked with thermal energy
transport in most practical processes and uid ow systems refer to only a subset
dealing with ow circuits. Figure 1.20 shows the sketches of a few typical ow
distribution systems. Fluid ow equipment such as pumps, fans, and blowers are
extensively used in thermal systems. Books on uid mechanics, such as those by
Fox and McDonald (2003), White (1994) and John and Haberman (1988), contain
information on the analysis of such uid ow systems and equipment.
Water treatment
facility
Piping network
3
2
1
h
Tank
Pump
Pump
Lake/river
FIGURE 1.20 Examples of uid distribution systems.

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 specications 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 specic application or for general use.
Other Systems
There are several other thermal systems that may not be as easily classied 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

Even though such a classication would cover most practical systems, several
systems are left out and may, again, be categorized under other systems. In addi-
tion, systems such as automobiles involve all three aspects of generation, utiliza-
tion, and rejection. Thermal systems may also be classied by their size, by the
nature and number of the constituents, by their interaction with other systems,
and so on. However, classication by the application of the system is probably the
most useful and also the most frequently employed.
The preceding discussion has presented many different types of thermal sys-
tems that are of interest in a wide range of applications. Clearly, different systems
have different concerns, and the design specications and requirements are also
different. However, they are all governed by basic considerations in heat and mass
transfer, uid ow, and thermodynamics. Consequently, the basic techniques for
40 Design and Optimization of Thermal Systems
design and optimization are similar, making it possible to discuss the fundamen-
tal issues and procedures involved in their design.
1.4 OUTLINE AND SCOPE OF THE BOOK
This book focuses on the design and optimization of thermal systems, several
examples of which have been given in the preceding section. The importance of
thermal systems in a wide range of applications makes its essential to optimize
existing systems in order to achieve the best performance or output per unit
input. In addition, the development of new techniques and materials demands
new and improved systems to take advantage of such innovations. However,
the design of thermal systems is usually complicated by the complexity of the
underlying mechanisms and the resulting lack of adequate information on the
system for obtaining a satisfactory design. Therefore, the design process often
involves obtaining the relevant inputs from analysis and incorporating them
into existing information on similar systems and processes to generate an
acceptable design.
We shall rst consider the basic features of the design process, highlight-
ing the various steps that are involved in the design of a thermal system. These

considerations are generally common to other types of systems as well. Starting
with the problem statement in terms of the requirements, constraints, and other
specications, 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-

cepts considered, or the effort terminated. The common problems that arise in the
design process and possible approaches to avoid these are also outlined.
This brings us to the problem of optimization. Because of growing competi-
tion in the world today, it is essential to optimize a chosen objective function such
as the output per unit cost or quality per unit energy consumption. The range of
design variables over which acceptable designs are obtained may be quite large,
making it necessary to narrow the domain to choose the best design that opti-
mizes the cost or some other chosen variable. Because economic considerations
play an important role in the successful completion of the project and in the opti-
mization effort, basic considerations in engineering economics are presented in
Chapter 6. This chapter brings out the economic evaluation of an enterprise in
terms of the return on investment, costs, nancing, present and future worth, and
depreciation.
The formulation of the basic problem for optimization is discussed in
Chapter 7, indicating the need for optimization and the different approaches
available for thermal systems. Optimization with respect to the hardware of the
system, as well to the operating conditions, is discussed. The next three chapters
present different methods used for the optimization of thermal systems, employ-
ing examples from a variety of practical areas to illustrate the basic approaches
and their limitations and advantages. Among the methods considered are calculus
methods, particularly the method of Lagrange multipliers, search methods, geo-
metric programming, and linear and dynamic programming. Different systems
that are particularly suited to each of these methods are considered and the result-
ing optimal conditions derived. Several examples such as those mentioned in the
present chapter are employed to illustrate the strategies involved.
Several additional considerations are covered in the last chapter. This chapter
discusses knowledge-based design, which has become an important and valuable
element in design methodology today. The use of existing knowledge, databases,
heuristic arguments, and expert systems is outlined. The improvements over clas-
sical approaches for certain types of systems are presented. Other considerations

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

information from different sources. Many problems are given to bring out these
features of the design process. A unique solution is typically not obtained in these
cases and the reader may have to make certain decisions, providing appropriate
information or personal choice, to solve the problem. The lack of particular infor-
mation in a problem does not mean that it cannot be solved; instead, it implies
that there are choices and inputs that must be provided by the reader to obtain
different acceptable designs for the given requirements and constraints. Thus,
many different answers may be acceptable for a given problem. Several exercises,
particularly the design projects, are given with this exibility and personal selec-
tion and input in mind.
Effort is also made to link the different topics and considerations that arise
in the design process. Thus, an acceptable design of a given thermal system in an
earlier chapter may be optimized in later chapters and different techniques may be
employed for the same problem to demonstrate the difference. Relatively simple
examples and problems are given in certain cases to illustrate the methodology.
However, the overall focus of the book is on the design of thermal systems, which
may range from very simple systems consisting of a small number of parts to
complex systems that have a large number of components and subsystems and
involve many additional considerations. The basic approach is similar in these
two extreme circumstances, and, therefore, the discussion, treatment, and prob-
lems can be varied easily to consider different types of systems.
Effort was made to choose examples and problems from both traditional
thermal systems as well as from new and emerging areas such as fabrication
of advanced materials, cooling of electronic equipment, and new approaches
in energy and environmental systems. This allows the reader to see the eld as
vibrant and growing, with an excitement about new technologies and important
Introduction 43
practical applications. These examples also demonstrate the critical importance
of optimizing many of these systems due to the growing need to reduce cost and
energy consumption while enhancing product quality and reducing the environ-

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-dened, closed-ended results. Thus, design generally involves considering
many different solutions and nding an acceptable result that satises 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 denition 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

their basic features. A system consists of individual constituents that interact
with each other and must be considered as coupled for a study of the overall
behavior. Thermal systems, which are governed by the principles of heat transfer,
thermodynamics, uid mechanics, and mass transfer, arise in a wide range of
engineering applications. The basic characteristics of these systems are outlined,
along with a few typical mathematical equations that describe them. Different
types of thermal systems are considered and examples are presented from many
diverse areas such as manufacturing, energy, environment, electronic, aerospace,
air conditioning, and transportation systems. These examples serve to indicate
the considerable importance of thermal systems in industry and in many practical
44 Design and Optimization of Thermal Systems
applications. The diversity of thermal systems and the range of concerns in these
systems are also examined. The need for design and optimization of these sys-
tems is clearly indicated.
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Introduction 45
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