Design and Optimization of Thermal Systems Episode 1 Part 4 pps

In the design of thermal systems, common requirements concern ture distributions and variations with time, heat transfer rates, temperature lev-els, and flow rates.. By heating Time Enve

or devices may be employed as part of system design, the focus is on design and not on selection Similarly, analysis is used only as a means for obtaining the inputs needed for design and for evaluating different designs, not for providing detailed information and understanding of thermal processes and systems The synthesis of information from a variety of sources plays an important part in the development of an acceptable design With this background and understanding,

we can now proceed to the basic considerations that arise in the design process

2.1 FORMULATION OF THE DESIGN PROBLEM

A very important aspect in design, as in other engineering activities, is the lation of the problem We must determine what is required of the system, what is given or fixed, and what may be varied to obtain a satisfactory design The final design obtained must meet all the requirements, while satisfying any constraints

formu-or limitations due to safety, environmental, economic, material, and other erations The design process depends on the problem statement, as does the evalu-ation of the design In addition, the formulation of the problem allows us to focus our attention on the quantities and parameters that may be varied in the system This gives the scope of the design problem, ranging from relatively simple cases where only a few quantities can be varied to more complicated cases where most

consid-of the parameters are variable

2.1.1 R EQUIREMENTS AND S PECIFICATIONS

Certainly the most important consideration in any design is the desired function

or task to be performed by the system This may be given in terms of ments to be met by the system A successful, feasible, or acceptable design must satisfy these The requirements form the basis for the design and for the evalu-ation of different designs Therefore, it is necessary to express the requirements

require-quantitatively and to determine the permitted variation, or tolerance level

Sup-pose a water flow system is needed to obtain a specified volume flow rate R o.Since there may be variations in the operating conditions that may result in

changes in the flow rate R, it is essential to determine the possible increase or

decrease in the flow rate that can be tolerated Then the system is designed to

deliver the desired flow rate R owith a possible maximum variation of o ΔR This may be expressed quantitatively as

If a water cooler is being designed, the flow rate R o and the desired temperature

T o at the outflow become the requirements The former is expressed as given in Equation (2.1) and the latter as

where o ΔT is the acceptable variation in the outflow temperature

In the design of thermal systems, common requirements concern ture distributions and variations with time, heat transfer rates, temperature lev-els, and flow rates Total pressure rise, time needed for a given process, total energy transfer, power delivered, rotational speed generated, etc., may also be the desired outputs from a thermal system, depending on the particular applica-tion under consideration Consider the thermal annealing process for materials such as steel and aluminum The material is heated to a given elevated tempera-

tempera-ture, known as the annealing temperature; held at this temperature level for

a specified time, as obtained from metallurgical considerations of the chosen material; and then cooled very gradually, as shown in Figure 2.1 By heating

Time

Envelope of acceptable temperature variation

Desired temperature variation

Cooling Soaking

Heating

Annealing temperature

FIGURE 2.1 Required temperature variation, with an envelope of acceptable variation,

for the thermal process of annealing of a given material.

the material beyond a particular temperature T o , known as its recrystallization

temperature, and maintaining it at this temperature, the internal stresses are relieved and the microstructures become relatively free to align themselves A slow cooling allows the removal of residual and thermal stresses and refinement

of the structure to restore the ductility of the material The desired ture cycle, including the maximum allowable temperature at which the process becomes unsatisfactory and the acceptable variation in the cycle, are shown in the figure The duration Tsoaking, over which the temperature is held constant,

tempera-within the two limits shown, is known as the soaking time and is also

deter-mined by metallurgical considerations of the material These requirements may, thus, be written quantitatively as

where T o, To , and B are specified constants, obtained from the basic

charac-teristics of the given material The acceptable variations in these constants, often given as percentages of the desired values, may also be included in these equations Then, a thermal system is to be designed so that the given mate-rial or body is subjected to the required temperature cycle, with the allowable tolerance

Similarly, the requirements for other thermal systems outlined in Chapter 1may be considered For instance, the mass flow rate, as well as the tempera-ture and pressure at the inlet to the die in the plastic extrusion process, shown

in Figure 1.10(b), are the requirements for a screw extruder The rate of heat removal and the lowest temperature that can be obtained in the freezer could

be taken as the requirements for a refrigeration system The maximum power delivered and speed attained could be the requirements for a transportation sys-tem The energy removal rate and the maximum allowable temperature of the electronic devices may be the requirements for a cooling system for electronic equipment

It is critical to determine the main requirements of the system and to focus our efforts on satisfying these Since it is often difficult to meet all the desired features of the system, requirements that are not particularly important for the chosen application may have to be ignored It is best to first satisfy the most essen-tial requirements and then attempt to satisfy other less important ones by varying the design within the specified constraints and limitations For instance, after a refrigeration system has been designed to provide the specified temperature and heat removal rate, effort may be exerted to find a substitute for the refrigerants R-11 and R-12, both of which are chlorofluorocarbons, or CFCs; to replace the compressor with one that is more efficient; to vary the dimensions of the freezer;

or to improve the temperature control arrangement Thus, it is important to ognize the main requirements of the system and to design the system to achieve these, rather than consider every desired feature of the system

The system designed on the basis of the given requirements can be described

in terms of its main characteristics These form the product design tions, which list the requirements met by the system and the outputs from the

specifica-design process that characterize the system The final specifications of the system may include the performance characteristics; expected life of the system; recom-mended maintenance, weight, size, safety features; and environmental require-ments For instance, the specifications of a heat exchanger could be the overall heat transfer rate for given fluids and its dimensions For a water chilling system, these could be the lowest attainable temperature and the corresponding flow rate and power consumption The specifications of the system are, thus, the means of communication between the consumer and the designer/manufacturer

2.1.2 G IVEN Q UANTITIES

The next step in the formulation of the design problem is the determination of the quantities that are given and are, thus, fixed These items cannot be changed and, as such, are not varied in the design process Materials, dimensions, geom-etry, and the basic concept or method, particularly the type of energy source, are some of the features commonly given in the design of a thermal system Thus, some of the materials and dimensions may be given, while others are

to be determined as part of designing the system For a particular system, if most of the parameters are fixed, the design problem becomes relatively simple because only a small number of variables are to be determined If the basic concept is not fixed, different concepts may be considered, resulting in consid-erable flexibility in the design

Let us consider the injection molding process for plastics, as shown cally for two different machines in Figure 2.2 It is similar to the metal casting process described earlier and is thus a system dominated by heat transfer and fluid flow considerations (Tadmor and Gogos, 1979) It is an extensively used manufacturing process for a variety of parts ranging from plastic cups and toys

schemati-to bathtubs, car bumpers, and molded parts made of composite materials As shown here, the polymer is melted and injected into a mold cavity by applying force on the melt by means of a plunger or a rotating screw As the polymer starts

to solidify, additional amounts of melt may be injected to fill the gaps left due

to shrinkage during solidification The mold is held together by a clamping unit, which opens and closes the mold and also ejects the final solidified product.For system design, the mold and the injected material may be kept fixed, while the melting and injection processes are varied Similarly, the mold, as well as the material, may be varied while keeping the rest fixed The system is a complicated one, but it can be considerably simplified by keeping several components and fea-tures fixed while a few components, such as the injection mechanism, are varied during design In addition, the basic concept may be kept unchanged, using, for instance, either of the two schemes shown in the figure Other approaches to melt

and inject the mold, as well as to clamp and open the mold, are also possible All these considerations substantially influence the design process.

Similarly, in the design of an electronic system, consisting of electronic ponents located on circuit boards, the electronic component size, the geometry and dimensions of the board, the number of electronic components on each board, and the distance between two boards may be given The design then focuses on the cooling system, such as a fan and duct arrangement A two-stroke engine may

com-be chosen for the design of a transportation system, thus fixing the basic concept

In a solar energy system, sensible heat storage in water may be chosen as the concept, with the dimensions, geometry, and material of the tank being varied for the design In the design of a cooling pond for a power plant, the location of the pond, which determines the local ambient conditions, is fixed In all of these cases, some of which are considered in later chapters, the given quantities are kept unchanged during the design process

2.1.3 D ESIGN V ARIABLES

The design variables are the quantities that may be varied in the system in order

to satisfy the given requirements Therefore, during the design process, tion is focused on these parameters, which are varied to determine the behavior

atten-Reciprocating screw (a)

(b)

Barrel

Hopper

Ram Mold

Torpedo

FIGURE 2.2 (a) Ram-fed injection molding machine; (b) screw-fed injection molding

machine (Adapted from Tadmor and Gogos, 1979.)

of the thermal system and are then chosen so that the system meets the given requirements As mentioned earlier, it is important to focus on the main design variables in the problem because the complexity of the design procedure is a strong function of the number of variables.

Let us consider again the plastic injection molding system discussed in the preceding section and shown in Figure 2.2 If only the cooling of the mold is left

to be designed, while the other components in the system are fixed, the problem

is considerably simplified However, even this is an involved design problem and has generated much interest and effort over the last two decades Cooling may be achieved by the flow of a cooling fluid through channels in the mold Different types, configurations, and dimensions of cooling channels may be considered, obtaining the thermal characteristics of the system for each case The solidifi-cation rate and temperature gradients in the material are usually given as the requirements that must be satisfied by using a variety of cooling channels This leads to a domain of acceptable designs An appropriate design may be chosen based on additional considerations such as cost, power requirements, size, etc

If the other components of the system, such as geometry and dimensions of the melting and injection section, are to be varied as well, the design becomes much more involved and the domain of acceptable designs is much larger

The design variables are usually taken to represent the hardware of the system such as the plunger, heating arrangement, mold, clamping unit, cooling channels, and so on, in the above example However, the system performance

is also affected by the operating conditions, which can be adjusted over ranges determined by the hardware Therefore, the variables in the design problem may be classified as:

Hardware

This includes the components of the system, dimensions, materials, geometrical configuration, and other quantities that constitute the hardware of the system Varying these parameters generally entails changes in the fabrication and assem-bly of the system As such, changes in the hardware are not easy to implement

if existing systems are to be modified for a new design, for a new product, or for optimization

Operating Conditions

These refer to quantities that can often be varied relatively easily, over specified ranges, without changing the hardware of the given system, such as the settings for temperature, flow rate, pressure, speed, power input, etc The design process would generally yield the ranges for such parameters, with optimization indicat-ing the values at which the performance is optimal

The design of a thermal system must include both types of variables and the final design obtained must indicate the materials, dimensions, and configurations

of the various components, as well as the ranges over which the operating tions such as pressure, temperature, and flow rate may be varied These ranges

condi-are fixed by the hardwcondi-are design; for instance, the temperature range may be determined by the heaters employed or flow rates by the pumps chosen However, because the product obtained is a function of the operating conditions, these are often given as part of the specifications of the system.

bar-1 Geometry, material, and dimensions of the hopper

2 Geometry, material, and dimensions of the barrel

3 Dimensions, energy requirements, and configuration of heating/cooling arrangement

4 Diameter and material of the screw

5 Shape, height, thickness, and pitch of screw flights

6 Geometry, material, and dimensions of the die

7 Physical characteristics of the drive, motor, and gear system

Clearly, the above list includes a large number of variables A design problem in which all of these can be varied is extremely complicated Therefore, several of these are generally kept fixed and the ranges over which the others can be varied are determined from physical constraints, availability of parts, and information available from similar systems.

The operating conditions refer to the quantities that may be varied without changing the hardware These may be listed as

1 Plastic flow rate or throughput

2 Speed (revolutions/minute)

3 Temperature distribution at the barrel

4 Material used

All of these operating conditions can be varied over ranges that are determined

by the hardware design of the system In addition, in actual practice these may not

be varied completely independent of each other For instance, the screw geometry and dimensions, along with the speed, will determine the maximum flow rate in the extruder The heating/cooling arrangement determines the range of temperature variation The plastic or polymer used may limit the speed or the temperature level, and so on.

2.1.4 C ONSTRAINTS OR L IMITATIONS

The design must also satisfy various constraints or limitations in order to be acceptable These constraints generally arise due to material, weight, cost, avail-ability, and space limitations The maximum pressure and temperature to which

a given component may be subjected are limited by the properties of its material For instance, a plastic or metal component may be damaged if the temperature exceeds the melting point The performance of semiconductor devices is very sensitive to the temperature and, therefore, the temperatures in electronic equip-ment are constrained to values less than 100nC The pressure rise in a thermal system is constrained by the strength of the materials at the operating temperature

levels Such constraints may be written for temperature T, pressure P, and volume flow rate R as

T a T max, P a P max, R a R max (2.4)

Generally, the maximum values, indicated here by the subscript max, would be

considerably less than levels at which permanent damage to the component or

sys-tem might occur Therefore, T max may be taken as, say, 50nC lower than the melting point of the material of which a given component is made, depending on the desired safety, accuracy of the model on which the design is based, and the material.The choice of the material itself may be limited by cost, availability, waste disposal, and environmental impact even if a particular material has the best characteristics for a given problem In fact, material selection is a very important element in design, as discussed later in this chapter Volume and weight restric-tions also frequently limit the domain of acceptable design Again, these may be given as

W a W max, L a L max, V a V max (2.5)

where W, L, and V are the weight, length, and volume, respectively Such

con-straints arise from the expected application of the system For instance, weight restrictions are very important in the design of portable computers, airplanes, rocket systems, and automobiles Similarly, volume constraints are important

in room air conditioners, household refrigerators, and industrial furnaces All such constraints and limitations determine the range of the design variables and, thus, indicate the boundaries of the domain over which an acceptable design is sought

Constraints also arise due to conservation principles For instance, mass conservation dictates the speed of withdrawal in a hot rolling process For a

two-dimensional flat plate being reduced in thickness from D1 to D2 across a set

of rollers, as shown in Figure 1.10(d), mass conservation leads to the equation

U1D1 U2D2, where U1 is the speed before the rollers and U2 after, if the density

of the material remains unchanged Then this equation serves as a constraint on the speed after the rollers if the remaining quantities are specified

Similarly, the energy rejected Qrejected from a power plant to a cooling pond is

rise in order to lose the energy to the ambient medium An energy balance equation may thus be written to determine the average surface temperature rise as

Qrejected m C p ΔT  hAsurface(Tnew old) (2.6)

where h is the overall heat transfer coefficient, Asurface is the surface area, and

(Tnew – Told) is the rise in the average surface temperature A limitation of around 5nC on this temperature rise is specified by federal, state, county, or city regula-tions directed at minimizing the environmental effect Therefore, the maximum amount of energy that may be rejected to the pond may be calculated Similar considerations could lead to restrictions on temperature rise in the condensers, as well as on the total flow rate (Moore and Jaluria, 1972)

2.1.5 A DDITIONAL C ONSIDERATIONS

Several additional considerations have to be taken into account for obtaining an acceptable or workable design These considerations may arise from safety and environmental concerns, procurement of supplies needed, availability of raw materials, national interests, import and export concerns, waste disposal problems, financial aspects, existing technology, and so on Many of these aspects affect the overall engineering enterprise, as discussed earlier in Chapter 1 However, the design itself may be strongly influenced by these considerations, particularly those pertaining to the environmental and safety issues For instance, even though nuclear energy is one of the cheapest and cleanest methods of generating electric-ity, concerns on radioactive releases have strongly curbed the growth of nuclear power systems Systems are designed in the steel industry to use the hot combus-tion products from the blast furnace in order to reduce the discharge of pollutants and thermal energy into the environment, while also decreasing the overall energy input Thermal pollution concerns could make it undesirable to depend only on a lake or river for discharge of thermal energy from a power plant, making it neces-sary to design additional systems such as cooling towers for heat disposal

Disposal of solid waste, particularly hazardous waste from chemical plants and radioactive waste from nuclear facilities, is another very important consideration that could substantially affect the design of the system The energy source is chosen in order to meet the federal or state guidelines for solid waste disposal Adequate arrange-ments have to be included in the design to satisfy waste disposal requirements.Safety concerns, particularly with nuclear facilities, demand that adequate safety features be built into the system For instance, if the temperature or heat flux levels exceed safe values, the system must shut down If the fluid level were too low in a boiler, a safety feature would not allow it to be turned on, thus avoiding damage to the heaters and keeping the operation safe Similarly, the energy source may be changed from gas to electricity because of safety concerns

in an industrial system An oil furnace may be developed instead of a gas furnace for the same reason

The formulation of the design problem is based on all of the above aspects Therefore, before proceeding to the design of the thermal system, the problem statement is given in terms of the following:

1 Requirements

2 Given quantities

3 Design variables

4 Limitations or constraints

5 Safety, environmental, and other considerations

Since the design strategy, evaluation of the designs developed, and final design are all dependent on the problem statement, it is important to ensure that all of these aspects are considered in adequate detail and quantitative expressions are obtained to characterize these It is worthwhile to investigate all important con-siderations that may affect the design and to formulate the design problem in exact terms, as far as possible, along with allowable variations or trade-offs in the various quantities and parameters of interest Once the design problem is formulated, we can proceed to the development of the design, starting with the basic concept

Example 2.2

An air-conditioning system is to be designed for a residential building The rior of the building is to be maintained at a temperature of 22 o 5nC The ambient temperature can go as high as 38nC and the rate of heat dissipated in the house is given as 2.0 kW The location, geometry, and dimensions of the building are given Formulate the design problem and give the problem statement.

inte-Solution

The given quantities are the maximum ambient temperature, which is 38nC, and the rate of energy input due to activities in the house, specified as 2.0 kW The location, geometry, and dimensions of the house are all fixed quantities The requirements for the system to be designed are given in terms of the temperature range, 17–27nC (22 – 5nC to 22 5nC), which is to be maintained in the house No constraints are given in the problem However, typical constraints will involve limitations on the size and volume of the system, on the flow rate of air circulating in the building, and on the total cost Use of chlorofluorocarbons (CFCs) as refrigerants may be unacceptable due to environmental considerations.

The thermal load due to heat transfer to the house from the ambient must be determined This load will involve absorbed solar flux, back radiation to the envi- ronment, convective transport from ambient air, evaporation or condensation of moisture, and conductive energy loss to the ground The ambient thermal load is

a function of ambient conditions, geometry of the building, its geographical

loca-tion, and dimensions It can often be modeled as hAΔT, where h is the overall heat transfer coefficient, A is the total surface area, and ΔT is the temperature difference between the ambient and the house The total thermal load Q is then the ambient load plus the rate of energy dissipated in the building The rate of heat removal Q r

by the thermal system shown in Figure 2.3 must be greater than this total load.

The transient cooling of the building is also an important consideration If the

total thermal capacity of the building (mass X specific heat) is estimated as S, then its average temperature T is governed by the energy balance equation

S dT dT Q – Q r

From this equation, the time Tr needed to cool the building to 1/e of its initial

tem-perature difference from the ambient, i.e., the characteristic response time, may be calculated, as discussed in Chapter 3 If this time is posed as a requirement, the heat

removal rate Q r or the capacity of the system may be appropriately determined;

other-wise Q r must simply be greater than Q.

The system is designed for the highest load, which arises at an ambient ture of 38nC and inside temperature of 17nC Simulation is used to determine the effect of ambient conditions as well as the transient response of the building From these considerations, an acceptable design is obtained for the given design problem The problem statement for the given system design may, thus, be summarized as

tempera-Given: Building geometry, location, and dimensions Maximum ambient

tem-perature as 38nC Rate of heat dissipated inside the house as 2.0 kW.

Requirements: Temperature inside the building must be maintained within 17 and 27nC

In typical cases, the rate of cooling or response time Tr is also a requirement.

Constraints: Limitations on size, volume, weight, and cost of air conditioner

Also on maximum air flow rate circulating in the house.

Design variables: Systems parts, such as condenser, evaporator, compressor, and

throttling valve Also, the refrigerant may be taken as a design variable Because of these requirements and constraints, the evaporator must operate at temperatures lower than 17nC to extract heat at the lowest temperature in the build- ing The condenser must operate at temperatures higher than 38nC in order to reject heat at the highest ambient temperature Similarly, the total load will determine the

capacity of the system This specification is usually given in tons, where 1 ton is

3.52 kW and refers to the energy removal rate required to convert one ton (2000 lb)

of water to ice in one day A thermostat control with an on/off mechanism is often used with the designed thermal system to maintain the desired temperature levels.



FIGURE 2.3 A thermal system for air conditioning a house.

2.2 CONCEPTUAL DESIGN

At the very core of any design activity lies the basic concept for the process or the system The design effort starts with the selection of a conceptual design, which is initially expressed in vague terms as a method that might satisfy the given require-ments and constraints As the design proceeds, the concept becomes better defined Conceptual design is a creative process, though it may range from something inno-vative, representing an invention or a new approach not employed before, to modi-fications in existing systems Inventions may lead to patents, as discussed later Creativity, originality, experience, knowledge of existing systems, and information

on current technology play a large part in coming up with the conceptual design For instance, microprocessors, laser-Doppler velocimeters, ultrasonic probes, composite materials, iPod, digital cameras, and liquid crystals represent some of the innovative ideas introduced in recent years Solutions based on existing and developing technology can also lead to valuable conceptual designs such as those

of interest in computer workstations, automobile fuel injection systems, hybrid cars, and solar power stations Changes can be made in existing systems to meet the given need or opportunity In fact, much of the present design and development effort is based on improvements in current processes and systems

For a given problem statement, several concepts or ideas may be considered and evaluated to estimate the chances of success The ideas at this stage are nec-essarily fuzzy and rough estimates are carried out to determine if the concepts are feasible or if there are problems that may be difficult to overcome Sometimes,

these are simply back-of-the-envelope calculations that yield the overall inputs,

outputs, expected ranges, etc Such estimates allow the design group to narrow down the selection of the conceptual design to a few possible approaches The selected conceptual designs are then subjected to the detailed design process, which would yield an acceptable design, if possible

In order to illustrate the availability of different concepts and the choice of the most suitable one, let us consider the task of transporting coal from the loading dock to the blast furnace in a steel plant Obviously, this can be achieved in many ways Trucks, trains, conveyor belts, pipes, and carts are some of the methods that may be used Each of these represents a different concept for the transportation system The final choice is guided by the distance over which the material is to be transported, size and form in which coal is available, and rate at which the mate-rial is to be fed For small plants, individual carts and trucks driven by workers may be adequate, whereas trains may be the most appropriate method for large distances and large plants Clearly, there is no unique answer In addition, within each concept, different techniques may be used to achieve the desired goals

2.2.1 I NNOVATIVE C ONCEPTUAL D ESIGN

Innovative and original ideas can lead to major advancements in technology and must, therefore, be encouraged Not all original concepts are earth shaking and not all of these are practical However, an environment conducive to the generation of