Design and Optimization of Thermal Systems Episode 1 Part 6 pdf

The fluid is the most important parameter and may be chosen for high thermal conductivity, which yields a high heat transfer coefficient, low cost, easy availability, nontoxic behavior,

available in the literature (Incropera and Dewitt, 2001) The use of these correlations brings in the dependence of the cooling rate on the physical variables in the prob- lem The fluid is the most important parameter and may be chosen for high thermal conductivity, which yields a high heat transfer coefficient, low cost, easy availability, nontoxic behavior, and high boiling point, if boiling is to be avoided in the liquid If boiling is allowed, the latent heat of vaporization becomes an important variable to obtain a high heat transfer coefficient Oils with high boiling points are generally

used for quenching The temperature T a is another variable that can be effectively used to control the cooling rate A combination of a chiller and a hot fluid bath may be

used to vary T a over a wide range Clearly, many solutions are possible and a unique design is not obtained Different fluids that are easily available may be tried first to

see if the requirement on the cooling rate is satisfied If not, a variation in T a may be considered Optimization of the system may then be based on cost.

2.4 COMPUTER-AIDED DESIGN

An area that has generated a considerable amount of interest over the last two decades as a solution to many problems being faced by industry and as a precur-

sor to the future trends in engineering design is that of computer-aided design

(CAD) With the tremendous growth in the use and availability of digital puters, resulting from advancements in both the hardware and the software, the computer has become an important part of the design practice Much of engineer-ing design today involves the use of computers, as discussed in the preceding

com-sections and as presented in detail in later chapters However, the term aided design, as used in common practice, largely refers to an independent or

computer-stand-alone system, such as a computer workstation, and interactive usage of the computer to consider various design options and obtain an acceptable or optimal design, employing the software for modeling and analysis available on the system Still, the basic ideas involved in a CAD system are general and may be extended

to more involved design processes and to larger computer systems

2.4.1 M AIN F EATURES

As mentioned above, a CAD system involves several items that facilitate the tive design process Some of the important ones are:

itera-1 Interactive application of the computer

2 Graphical display of results

3 Graphic input of geometry and variables

4 Available software for analysis and simulation

5 Available database for considering different options

6 Knowledge base from current engineering practice

7 Storage of information from earlier designs

8 Help in decision making

Thus, the system hardware consists of a central processing unit (CPU) for cal analysis, disk or magnetic tape for storage of data and design information, an interactive graphics terminal, and a plotter for hard copy of the numerical results

numeri-The computer software codes for analysis are often based on finite-element methods (FEM) for differential equations because this provides the flexibility and versatility needed for design (Zienkiewicz, 1977; Reddy, 1993) Different configura-tions and boundary conditions can be easily considered by FEM codes without much change in the numerical procedure Other methods, particularly the finite-volume and the finite-difference method (FDM), are also used extensively for thermal systems (Patankar, 1980) The software may also contain additional codes on curve fitting, interpolation, optimization, and solution of algebraic systems Some of the important numerical schemes are discussed in Chapter 4 Analytical approaches may also be included Commercially available computer software, such as Maple, Mathematica, Mathcad, and Mathlab, may be used to obtain analytical as well as numerical solu-tions to various problems such as integration, differentiation, matrix inversion, root solving, curve fitting, and solving systems of algebraic and differential equations The use of MATLAB for these problems is discussed in detail in Appendix A.The interactive use of the computer is extremely important for design because

it allows the user or designer to try many different design possibilities by ing the inputs numerically or graphically, and to obtain the simulation results

enter-in graphical form that can be easily enter-interpreted Iterative procedures for design and optimization can also be employed effectively with the interactive mode

A graphics terminal is usually employed to obtain three-dimensional, oblique, cross-sectional, or other convenient views of the components

The storage of data needed for design, such as material properties, heat transfer correlations, characteristics of devices, design problem statement, previous design information, accepted engineering practice, regulations, and safety features needed

can also substantially help in the design process In this connection, based design procedures may also be incorporated in the design scheme Besides

knowledge-providing important relevant information for design, the rules of thumb and ristic arguments used for design can be built into the system Such systems are

heu-also often known as expert systems since expert knowledge from earlier design

experience is part of the software, providing help in the decision-making process as well Since knowledge acquired through engineering design practice is usually an important component in the development of a successful design, knowledge-based systems have been found to be useful additions to the CAD process Chapter 11 presents details on knowledge-based systems for design, along with several exam-ples demonstrating concepts that can substantially aid the design process

2.4.2 C OMPUTER -A IDED D ESIGN OF T HERMAL S YSTEMS

The main elements of a CAD system for the design of thermal processes and equipment are shown in Figure 2.27 The various features that are usually included in such CAD systems are indicated The modeling aspect is often the most involved one when dealing with thermal systems The remaining aspects are common to CAD systems for other engineering fields Much of the effort in CAD has, over recent years, been largely devoted to the design of mechanical systems and components such as gears, springs, beams, vibrating devices, and structural

parts, employing stress analysis, static and dynamic loading, deformation, and solid body modeling Many CAD systems, such as AutoCAD and ProE, have been developed and are in extensive use for design and instruction.

Because of the complexity of thermal systems, it is not easy to develop lar CAD systems for thermal processes However, the availability of numerical codes for many typical thermal components and equipment has made it pos-sible to develop CAD systems for relatively simple applications such as heat exchangers, air conditioners, heating systems, and refrigerators Even for these systems, inputs from other sources, particularly on heat transfer coefficients, are often employed to simplify the simulation For more elaborate thermal systems, interactive design generally is not possible because numerical simulation might involve considerable CPU time and memory requirements Supercomputers are also needed for accurate simulations of many important thermal systems, such

simi-as those in materials processing and aerospace applications However, parallel machines that employ a large number of computational processors to accelerate

numerical analysis are being used in powerful workstations that may be used for CAD of practical thermal processes In addition, detailed simulation results from large machines such as supercomputers may be cast in the form of algebraic equations by the use of curve fitting If a given thermal system can be represented accurately by such algebraic systems, the design process becomes considerably simplified, making it possible to develop a CAD system for the purpose

Engineering practice and regulations

Computational

module and analysis

User inputs Material database

Information on existing systems and designs

Graphics module (outputs)

CAD system

FIGURE 2.27 Various elements or modules that constitute a typical computer-aided

design system.

6 Material to be baked or heated

The basic thermal cycle that the material must undergo is similar to the one shown

in Figure 2.1 Thus, an envelope of acceptable temperature variation, giving the maximum and minimum temperatures within which the material must be held for

a specified time, provides the design requirements The constraints are given by the temperature limitations for the various materials involved and any applicable restrictions on the airflow rate and heater input The materials, dimensions, and geometry are given and are, thus, fixed for the design problem Only the fan and the heater may be varied to obtain an acceptable design.

The first step is to develop a mathematical and numerical model for the cal system shown in Figure 2.28 The basic procedures for modeling are discussed

physi-in the next chapter and a relatively simple model to obtaphysi-in the temperatures physi-in the various parts of the system may be developed here The simplest model for this dynamic problem is one that assumes all components to have uniform temperature

at a given time Thus, the material, air, heater, wall, and insulation are all treated as lumped, with their temperatures as functions of time T only The governing equa- tions for these components may be written as

R T

CV dT

d A q( in q out)

Opening

Material Flow

Fan

Heater

Air

Wall Insulation

FIGURE 2.28 Forced-air oven for thermal processing of materials.

where R is the density, C is the specific heat at constant pressure, V is the volume,

A is the surface area, q in is the input heat flux, and q out is the heat flux lost at the surface All the properties are taken as constant to simplify the analysis Thus, a system of ordinary differential equations is obtained.

For the boundary conditions that link the governing equations for the various system parts, both convection and radiation are considered, assuming gray-diffuse transport with known surface properties The properties for different materials are used when considering each component of the system The conditions under which such a model is valid are discussed in detail in Chapter 3 Even though analytical solutions may be possible in a few special cases, all of these equations are coupled

to each other through the boundary conditions and are best solved numerically to provide the desired flexibility and versatility in the solution procedure.

With the mathematical and numerical model defined, the fixed quantities in the problem may be entered These include the geometry and the dimensions of the system The size and weight of the item undergoing thermal processing are given The relevant material properties must also be given Frequently a material database is built into the system for common materials, such as ceramics, composite materials, and so on, and may be used to obtain these properties The requirements for the design, as well as the constraints (particularly the temperature limitations on the various materials), are also entered All of these inputs are given interactively, so that the design variables and oper- ating conditions can be varied and the resulting effects obtained from the CAD system This allows the user to select the input parameters based on the outputs obtained.

We are now ready for simulation and design of the given thermal system The heater design involves its location, dimensions, and heat input If the location is fixed at the top surface, as shown in Figure 2.28, and if the effect of dimensions is

assumed to be small, which is reasonable, the heat input Q is the design variable

that represents the heater Similarly, the fan affects the flow rate mand, thus, the

heat transfer coefficients at the material surface, h m , at the heater h h, and at the oven

walls, h w We could solve for the flow and thermal field in the air and obtain these heat transfer coefficients from the numerical results However, this is a more com- plicated problem than the one outlined above Thus, the heat transfer coefficients may be taken from correlations available in the literature.

Simulation results are obtained by varying the heat input Q and the convective heat transfer coefficients, h m , h h , and h w, all these being dependent on the flow rate, geom- etry, and dimensions Figure 2.29 and Figure 2.30 show typical numerical results obtained during the heating phase, indicating the temperatures in the heater, material, gas, and wall for different parametric values The validity of the numerical model is confirmed by ensuring that the results are independent of numerical parameters such

as the grid and time step used, studying the physical behavior of the results obtained, and comparisons with analytical and experimental results for individual parts of the system and for the entire system, if available In most cases, results for the system are not available until a prototype is developed and tested before going into production

However, a higher Q results in higher temperatures, with the heater responding the fastest and the walls the slowest An increase in h increases the energy removed by air

and lowers the temperature levels This is the expected physical behavior.

The next step is to consider various combinations of Q and the flow rate m, which yields the convection coefficients, and to determine if the desired requirements are sat- isfied without violating the given constraints The duration during which the heater or the fan is kept on can be varied In addition, different variations of these with time can

be considered to obtain the desired variation in the material temperature Obviously,

many different designs and operating conditions are possible Again, interactive usage

of the CAD system is extremely valuable in this search for an acceptable design An acceptable design is obtained when all of the requirements and constraints are met, such as that indicated by Figure 2.31 A large number of cases are simulated even for

a relatively simple problem like this one The graphical displays help in determining

if the design process is converging The software can be used to monitor the tures and indicate if a violation of the constraints has occurred in any system part In addition, the temperature of the piece being heated is checked against the envelope of acceptable variation to see if an acceptable design is obtained.

tempera-This example briefly outlines some of the main considerations in developing a CAD system for thermal processes The model is at the very heart of a successful design process, and, therefore, it is important to develop a model that has the needed accuracy and is appropriate for the given application A knowledge-based design pro- cedure could also be included during iterative design to accelerate convergence and

to ensure that only realistic and practical systems emerge from the design (Jaluria and Lombardi, 1991) As mentioned previously, the fluid flow problem needs to be solved for an accurate modeling of the convective heat transfer and for a proper representa- tion of the fan as a design variable However, the problem would then become much too complicated for an interactive CAD system and would probably involve detailed simulation on larger machines to obtain the inputs needed for design.

0.00

400.00

400.00 500.00

500.00 600.00

600.00 700.00

Gas

40000.0

0.00 20000.0

Time (s) 40000.0

0.00 20000.0

Time (s)

Wall

40000.0 50

100 200

50 100 200

Heater

Q = 400 kW

50 100 200

Q = 400 kW

Q = 400 kW

300.00 400.00 500.00 600.00

0.00 20000.0

Time (s) 40000.0 50 100 200

Q = 400 kW

FIGURE 2.29 Variation of the heater, material, gas, and inner wall temperatures with

time for different values of the energy input Q to the heater at a fixed air flow rate  m.

Time (s)

Time (s)

Wall

20000.0 0.00

300.00 400.00 500.00 600.00 700.00 800.00 900.00

300.00 350.00 400.00

20000.0

100

100 100

50

50 50

20

20

Material Heater

2.0 1.0

FIGURE 2.31 Results from iterative redesign to obtain an acceptable design,

indi-cated by the solid line, which satisfies the given requirements and does not violate any constraints.

of material was frequently restricted to available metals, alloys, and common nonmetals Thus, it used to be a fairly routine procedure to select a material that would satisfy the requirements of a given application However, material selec-tion today is a fairly sophisticated and involved process The properties of the material, as well as its processing into a finished component, must be considered

in the selection The substitution of the current material by a new or different material is also commonly employed to reduce costs and improve performance However, material substitution should be carried out in conjunction with design

in order to derive the full benefits of the new material

Metals and alloys have been employed extensively in engineering systems

because of their strength, toughness, and high electrical and thermal conductivity Availability, cost, and ease in processing to obtain a desired finished product, through processes such as forming, casting, heat treat-ment, welding, and machining, have contributed to the traditional popu-larity of metals A variety of metals have been employed in different applications to satisfy their special requirements Thus, copper has been used for tubes because of its malleability, which allows easy bending, and for electrical connections because of its high electrical conductivity Similarly, aluminum has been used for its low weight in airplanes and in other transportation systems Gold has been used in electronic circuitry because of its resistance to corrosion Alloys substantially expand the

range of applicability of metals due to significant changes achieved in the properties Steel, in its different compositions, is probably the most versatile and widely used material in practical systems, from automo-biles and trains to turbines and furnaces Solder, which is an alloy of tin and lead, is widely employed in electronic circuitry to make electrical connections Changes in its composition can be used to obtain different strengths and melting points For instance, a eutectic mixture of 63% tin and 37% lead has a melting point of 183nC and a mixture of 10% tin and 90% lead has a melting range of 275 to 302nC Additions of silver

/&)'# ./##'

/&)'# ./##' %-*(#./##' - *)./##' *)./)/)

also affect the melting point and other properties, as discussed by Dally (1990) Similarly, other alloys such as brass, inconel, nichrome, and tita-nium alloys are used in different applications.

Ceramics, which are generally formed by fusing powders, such as those

of aluminum oxide (Al2O3), beryllium oxide (BeO), and silicon carbide (SiC), under high pressure and temperature, have many characteristics that have led to their increased usage in recent years These include high temperature resistance, low electrical conductivity, low weight, hardness, corrosion resistance, and strength, though they are generally brittle They have a relatively low thermal resistance, as compared to other electrical insulators Consequently, ceramics are extensively employed in elec-tronic circuitry, particularly in circuit boards They are also used in high temperature and corrosive environments, as tool and die materials, and

in engine components Ceramics also include glasses as a subdivision and these have their own range of applications due to transparency The optical fiber is a recent addition to this group of materials, with applica-tions in telecommunications, sensors, measurements, and controls Vari-ous other optical materials used in TV screens, optical networks, lasers, and biosensors are also of considerable interest to industry

Polymers, which include plastics, rubbers or elastomers, fibers, and coatings,

have the advantages of easy fabrication, low weight, electrical insulation, resistance to corrosion, durability, low cost, and a wide range of properties with different polymers Consequently, plastics have replaced metals and alloys in a wide range of applications Because these materials are electri-cally insulating, they find use in plastic-coated cables, plastic casings for electronic equipment, and electrical components and circuitry Similarly, the ease of forming or molding polymeric materials has led to their use in many diverse areas ranging from containers, trays, and bottles to panels, calculators, and insulation Clearly, polymers are among the most versa-tile materials today, despite the temperatures that can be withstood by them without damage being limited to 200 to 300nC in most cases

Composite materials, which are engineered materials formed as

combina-tions of two or more constituent materials usually consisting of a forcing agent and a binder, have grown in importance in the last two decades The component materials generally have significantly different mechanical properties and remain separate and distinct within the final structure Many naturally occurring materials such as wood, bone, and muscle are composite materials Therefore, many biological implants are made of appropriate composite materials The demand for materi-als with high strength-to-weight ratio has led to tremendous advance-ments in this field The reinforcing elements are largely fibers of glass, carbon, ceramic, metal, boron, or organic materials The base or matrix material is usually a polymer, metal, or ceramic Chemical bonding is generally used to bind the different elements to obtain a region that may

rein-be regarded as a continuum Different techniques are available for the

fabrication of composite materials, as discussed by Hull (1981) and Luce (1988) The main advantage of composite materials is that they can often

be custom-made for a particular design need In addition, they have low weight and high stiffness, strength, and fatigue resistance They are used for helicopter rotor blades, car body moldings, pressure vessels, glass-reinforced plastics, concrete, asphalt, printed circuit boards, bone replacements, and many other applications

Liquids and gases are of particular interest in thermal processes because

fluid flow is commonly encountered in many thermal systems Gases such as inert gases, oxygen, air, carbon dioxide, and water vapor are fre-quently part of the system and affect the transport processes Similarly, liquids such as water, oils, hydrocarbons, and mercury (which is also

a metal) are employed in thermal systems for heat transfer, material flow, pressure transmission, and lubrication In addition, in many cases, materials that are solid at normal temperatures are employed in their molten or liquid state, for instance, plastics in extrusion and injection molding, metals in casting, and liquid metals in nuclear reactors The flow characteristics of the fluid, as indicated by its viscosity; thermal properties, particularly the thermal conductivity; availability and cost; corrosive behavior; and phase change characteristics vary substantially from one fluid to another and usually form the basis for selecting an appropriate material

Semiconductor and other materials These include elements like silicon

and germanium, compounds like gallium arsenide and gallium phide, and several other similar materials that are often termed semicon-ductor materials because they are neither good electrical conductors nor good electrical insulators They are used extensively in electronic sys-tems because they have the appropriate properties to develop electronic devices like transistors and integrated circuits, which are obviously of tremendous importance and value today Diamond, which is pure car-bon, may also be included here Several other materials of engineering interest are not covered by the groups given earlier These include mate-rials like different types of wood, stone, rock, and other naturally occur-ring materials that are of interest in various applications

phos-Therefore, the six main categories of materials are metals and alloys, ceramics, polymers, composite materials, fluids, and semiconductor materials Each group has its own characteristics Some were just mentioned; see also Table 2.1 The range of application of each type of material is determined by the physical charac-teristics and the cost New materials in each category are continually being devel-oped to meet the demand for specific properties and characteristics and to improve existing materials in a variety of applications Substantial research and develop-ment effort is directed at obtaining new and improved materials for enhancing the performance of present systems, reducing costs, and helping future technological advancements Materials may also be categorized in terms of their applications,

for instance, electronic, insulation, construction, optical, and magnetic materials However, it is more common and useful to discuss materials in terms of their basic characteristics and to use the six classes of materials outlined above.

2.5.2 M ATERIAL P ROPERTIES AND C HARACTERISTICS FOR T HERMAL S YSTEMS

We have discussed different types of materials, their general properties, and cal areas of application Though most of the properties mentioned earlier are

typi-of interest in engineering systems, let us now focus on thermal processes and systems Obviously, many material properties are of particular interest in thermal systems; for instance, a low thermal conductivity is desirable for insulation and

a high thermal conductivity is desirable for heat removal A large thermal ity, which is the product of density and specific heat, is needed if a slow transient response is desired and a small thermal capacity is necessary for a fast response The material properties that are of particular importance in thermal systems, along with their usual symbolic representation employed in this book, are:

capac-TABLE 2.1

Typical Characteristics of Common Materials

High electrical conductivity Electrically insulating Electrically insulating

High thermal conductivity Low thermal conductivity Low thermal conductivity

Easy processing Difficult processing Easy fabrication

Susceptible to corrosion Corrosion resistance Corrosion resistance

Easily available Light weight Low cost

Temperature resistance Temperature sensitive

Composites Liquids and Gases Semiconductor Materials

Strong Material flows Specialized characteristics

Fatigue resistant Inert or corrosive Not good electrical conductor Stiff Wide range of properties Not good electrical insulator Range of electrical

conductivity

Low electrical conductivity Electrical insulator at low

temperatures Range of thermal

conductivity

Low thermal conductivity Electronic properties altered by

doping Versatile Versatile Wide range of other properties Low weight Generally low weight

Low cost Generally low cost

fabrication of composite materials, as discussed by Hull (19 81) and Luce (19 88) The main advantage of composite materials... processes and systems Obviously, many material properties are of particular interest in thermal systems; for instance, a low thermal conductivity is desirable for insulation and

a high thermal. .. types of materials, their general properties, and cal areas of application Though most of the properties mentioned earlier are

typi -of interest in engineering systems, let us now focus on thermal