Design and Optimization of Thermal Systems Episode 2 Part 7 ppsx

Starting with the basic concept for the system, the vari-ous steps involved in design were given as formulation of the problem, initial design, modeling, simulation, evaluation, iterativ

be a natural one such as a lake or a constructed cooling pond, the condensers of the power plant, and the water pumping system consisting of pumps and piping network, as considered in Example 5.8 The requirements for a successful design involve both the recirculation, which raises the temperature at the intake, and the thermal effects on the body of water Thus, the heat transfer and flow in the water body have to be modeled and coupled with the condensers and the pumping system Design variables include the locations and dimensions of the inlet/outlet channels, as well as the dimensions and geometry of the pond itself Operating conditions such as discharge temperature and flow rate must also be considered Various flow configurations may be considered to curb the effects of recirculation (see Figure 5.47) For instance, the outlet may be moved as far away as possible from the inlet, or a wall may be placed as an impediment between the two Com-puter simulations of the cooling pond, including the heat transfer to the surround-ings and the flow due to intake and discharge, and of the pumping system are used

to provide the necessary inputs for design and optimization Since recirculation effects are reduced, but pumping costs increased, as the separation between the intake and discharge is increased, a minimization of the cost for acceptable tem-perature rise at the intake may be chosen as the objective function Clearly, the design of the system is a major undertaking and involves many subsystems that

Outflow (to condensers)

FIGURE 5.47 The flow system for power plant heat rejection to a body of water: (a) Top

view, (b) front view.

make up the overall system Over the years, the power industry has developed strategies to design and optimize such systems.

The design process is fundamentally the same for large and small systems and the basic approach presented in this and earlier chapters can easily be applied

to a wide range of systems using the principles of modeling, simulation, design, and optimization presented in this book However, additional aspects pertaining

to safety, control, input/output, etc., need to be included in industrial systems before the prototype is developed

5.6 SUMMARY

This chapter presents the synthesis of various design steps needed to obtain

an acceptable design for a thermal system Employing the basic considerations involved in design, as outlined in the earlier chapters, an overview of the design procedure is presented Starting with the basic concept for the system, the vari-ous steps involved in design were given as formulation of the problem, initial design, modeling, simulation, evaluation, iterative redesign, and convergence to

an acceptable design Several of these aspects, particularly modeling and tion, were presented in detail earlier and are applied in this chapter Two ingre-dients in the design process that had not been discussed adequately earlier are the development of an initial design and different design strategies These are presented in some detail in this chapter

simula-Initial design is an important element in the design process and is considered

in terms of the different methods that may be adopted to obtain a design that is as close as possible to an acceptable design A range of acceptable designs may be obtained by changing the design variables, starting with the initial design values,

in the domain specified by the constraints The development of an initial design may be based on existing systems, selection of components to satisfy the require-ments and constraints, use of a library of designs from previous efforts, and current engineering practice for the specific application In this way, the effort exerted to obtain an appropriate initial design is considerably reduced by building

on available information and earlier efforts

The main design strategy presented earlier was based on starting with an initial design and proceeding with an iterative redesign process until a converged acceptable design is obtained This systematic approach is used quite extensively

in the design of thermal systems However, several other strategies are possible and are employed In particular, extensive results on the system response to a vari-ation in the design variables (for given operating conditions) as well as to different operating conditions (for selected designs) may form the basis for obtaining an acceptable design Such strategies, though not as systematic as the previous one, are nevertheless popular because extensive results can often be obtained easily from numerical simulation These strategies are also well suited to systems with

a small number of parts and those with only a few design variables The methods

to track the iterative redesign process and to study the convergence characteristics are also discussed

In order to illustrate the coupling of the different aspects and steps involved

in the design process, several important areas of application are considered and a few typical thermal systems that arise in these areas are considered as examples This discussion is important for understanding the design process because the various steps involved in design had been discussed earlier as separate items It

is important to understand how these are brought together for an actual thermal system and how the overall process works

Finally, this chapter presents additional considerations that are often important

in the design and successful implementation of a practical thermal system Included

in this list are safety issues, control of the system, environmental effects, structural integrity of the system, material selection, costs involved, availability of facilities, governmental regulations, and legal issues These considerations are important and must usually be included in the final design However, a detailed discussion

of these aspects is beyond the scope of this book Several of these aspects are included in the design process by a suitable choice of constraints for an acceptable design The application of this process to large practical systems is outlined

REFERENCES

Avallone, E.A and Baumeister, T., Eds (1987) Marks’ Standard Handbook for cal Engineers, 9th ed., McGraw-Hill, New York.

Mechani-Bejan, A (1993) Heat Transfer, Wiley, New York.

Bloch, H., Cameron, J., Danowski, F., James, R., Swearingen, J., and Weightman, M

(1982) Compressors and Expanders, Marcel Dekker, New York.

Boehm, R.F (1987) Design Analysis of Thermal Systems, Wiley, New York.

Brown, R (1986) Compressors—Selection and Sizing, Gulf Publishing Company,

Houston, TX.

Cengel, Y.A and Boles, M.A (2002) Thermodynamics: An Engineering Approach, 4th

ed., McGraw-Hill, New York.

Fox, R.W and McDonald, A.T (2003) Introduction to Fluid Mechanics, 6th ed., Wiley,

New York.

Gebhart, B (1971) Heat Transfer, 2nd ed., McGraw-Hill, New York.

Ghosh, A and Mallik, A.K (1986) Manufacturing Science, Ellis Horwood, Chichester,

Howell, J.R and Buckius, R.O (1992) Fundamentals of Engineering Thermodynamics,

2nd ed., McGraw-Hill, New York.

Incropera, F.P (1988) Convection heat transfer in electronic equipment cooling, ASME J Heat Transfer, 110:1097–1111.

Incropera, F.P (1999) Liquid Cooling of Electronic Devices by Single-Phase Convection,

Wiley, New York.

Incropera, F.P and Dewitt, D.P (1990) Fundamentals of Heat and Mass Transfer, 3rd ed.,

Wiley, New York.

Incropera, F.P and Dewitt, D.P (2001) Fundamentals of Heat and Mass Transfer, 5th ed.,

Wiley, New York.

Jaluria, Y (1976) A study of transient heat transfer in long insulated wires, J Heat Transfer, 98:127–132, 678–680.

Jaluria, Y (1984) Numerical study of the thermal processes in a furnace, Numerical Heat Transfer, 7:211–224.

Janna, W.S (1993) Design of Fluid Thermal Systems, PWS-Kent Publising Company,

Boston, MA.

Kakac, S., Shah, R.K., and Bergles, A.E., Eds (1983) Low Reynolds Number Flow Heat Exchangers, Taylor & Francis, Washington, DC.

Kalpakjian, S and Schmid, S.R (2005) Manufacturing Engineering and Technology, 5th

ed., Prentice-Hall, Upper Saddle River, NJ.

Kays W.M and London, A.L (1984) Compact Heat Exchangers, 3rd ed., McGraw-Hill,

McGraw-Hill, New York.

Seraphin, D.P., Lasky, R.C., and Li, C.Y (1989) Principles of Electronic Packaging,

McGraw-Hill, New York.

Shames, I.H (1992) Mechanics of Fluids, 3rd ed., McGraw-Hill, New York.

Steinberg, D.S (1980) Cooling Techniques for Electronic Equipment, Wiley-Interscience,

New York.

Stoecker, W.F (1989) Design of Thermal Systems, 3rd ed., McGraw-Hill, New York Thompson, J.E and Trickler, C.J (1983) Fans and fan systems, Chem Eng., March:46–63 Van Wylen, G.J., Sonntag, R.E., and Borgnakke, C (1994) Fundamentals of Classical Thermodynamics, 4th ed., Wiley, New York.

Viswanath, R and Jaluria, Y (1991) Knowledge-based system for the computer aided

design of ingot casting processes, Eng Comput., 7:109–120.

Warring, R (1984) Pumps: Selection, Systems and Applications, 2nd ed., Gulf Publishing

Company, Houston, TX.

PROBLEMS

Note: Appropriate assumptions, approximations, and inputs may be employed to

solve the design problems in the following set A unique solution is not obtained for an acceptable design in many of these problems, and the range in which the solution lies may be given wherever possible

5.1 A refrigeration system is needed to provide 10 kW of cooling at 0nC, with the ambient at 25nC Obtain a workable or acceptable design to achieve these requirements, assuming that a variation of o5nC in both temperature levels is permissible You may choose any appropriate fluid, component efficiencies in the range 75 to 90%, and a suitable thermodynamic cycle for the purpose

5.2 Develop an acceptable design for a cooling system, using vapor pression, to achieve 0.5 ton of cooling at –10nC, with the ambient tem-perature as high as 40nC The use of CFCs is not permitted because

com-of their environmental effect The efficiency com-of the compressor may

be assumed to lie between 75 and 85% Discuss any sensors that you might need for temperature control

5.3 A heat pump is to be designed to obtain a heat input of 2 kW into a region that is at 25nC, as shown in Figure P5.3 The ambient temperature may be

as low as 0nC Obtain an acceptable design to satisfy these requirements, using efficiencies in the range 80 to 90% for the components The only constraint is that the working fluid should not undergo freezing

5.4 For the casting process considered in Problem 3.7, briefly discuss the simulation of the process and the anticipated results from the simula-tion Develop a workable design for a thermal system to achieve the desired heating

5.5 In an oven, the support for the walls is provided by long horizontal

bars, of length L and square in cross-section, attached to two vertical

walls, as shown in Figure P5.5 A crossflow of ambient air, at

veloc-ity V and temperature T a, cools the bars The walls may be assumed

to be at uniform temperature T w We can vary T a, the material of the

supporting bars, and the width H of the bars The temperature at the midpoint A, T A , must be less than a given value Tmax due to strength considerations

Heat pump Enclosed

space

2 kW 25°C

0°C Ambient

(a) Develop a suitable mathematical model for this system, giving the governing equations and the relevant boundary conditions.

(b) Sketch the expected temperature distribution in the bar

(c) What are the fixed quantities, requirements, and design variables

in the problem?

(d) Discuss the simulation of the system and obtain an acceptable design for this application

5.6 In the energy storage system consisting of concentric cylinders,

consid-ered in Problem 3.1, L and R2 are given as fixed, while R1 can be varied

over a given range, (R1)min R1 (R1)max The approximations are the same as those given before The metal pieces are to be heated without

exceeding a maximum temperature Tmax and interest lies in storing the maximum amount of energy

(a) Formulate the corresponding design problem, focusing on ties that can be varied

quanti-(b) Simulate the system to determine the dependence of energy stored

on the design variables

(c) Obtain an acceptable design

5.7 If in the problem considered in Example 5.3, the hot water ments are changed to 50 to 75nC, determine the effect on the final results Also, vary the ambient temperature to 30nC and determine the range of acceptable designs

require-5.8 A solar energy power system is to be designed to operate between 90nC,

at which hot water is available from the collectors, and 25nC, which is the ambient temperature, in order to deliver 200 kW of power Using any appropriate fluid and thermodynamic cycle, obtain an acceptable design for this process Assume that boilers, compressors, and turbines

of efficiency in the range 70 to 80% are available for the purpose.5.9 A cold storage room of inner dimensions 4 m r 4 m r 3 m and contain-ing air is to be designed The outside temperature varies from 40°C during the day to 20°C at night The outside heat transfer coefficient is

10 W/(m2 · K) and that at the inner surface of the wall is 20 W/(m2 · K)

A constant energy input of 4 kW may be assumed to enter the air through the door, as shown in Figure P5.9 A refrigerator system is used to extract energy from the enclosure floor What are the important design variables in this problem? Develop a simple model for simu-lating the system and obtain the refrigeration capacity needed The energy extracted by the refrigerator need not be constant with time Also, determine the values of the other design variables to maintain

a temperature of 5nC o 2nC in the storage room The wall thickness must not exceed 15 cm, and it is desirable to have the smallest possible refrigeration unit Also, suggest any improvements that may be incor-porated in your mathematical model for greater accuracy

5.10 An electronic equipment is to be designed to obtain satisfactory ing of the components The available air space is 0.45 m r 0.35 m r0.25 m The distance between any two boards must be at least 5 cm The total number of components is 100, with each dissipating 20 W The dimensions of a board must not exceed 0.3 m r 0.2 m The heat transfer coefficient may be taken as 20 W/(m2 · K) if there is only one board With each additional board, it decreases by 1 W/(m2 · K) Develop a suit-able model for design of the system and obtain the minimum number of boards needed to satisfy the temperature constraint of 100nC in an ambi-ent at 20nC How can your model be improved for greater accuracy?5.11 In Example 5.4, the use of hollow mandrels is suggested as an improve-ment in the design Consider this change and determine the effect on the simulation and the design However, the thickness of the wall of the mandrel should not be less than 0.5 mm from strength consider-ations Also, consider the circulation of hot fluid through the mandrel

cool-to impose a higher temperature at the inner boundary of the plastic Determine the effect of this change on the design

5.12 In the cooling system for electronic equipment considered in Example 5.5, determine the effect on the design of allowing the board height to reach 0.2 m and of increasing the convective heat transfer coefficient

to 40 W/(m2 · K) by improving the cooling process Consider the two changes separately, taking the remaining variables as fixed Discuss the implications of these results with respect to the design of the system.5.13 In a condenser, water enters at 20nC and leaves at temperature To Steam enters as saturated vapor at 90nC and leaves as condensate at the same temperature, as shown in Figure P5.13 The surface area of the heat exchanger is 2 m2 and a total of 250 kW of energy is to be transferred in

the heat exchanger The overall heat transfer coefficient U is given by

m

where m is the water mass flow rate in kg/s and U is in kW/(m2· K) Obtain the algebraic equation that gives the water flow rate m Solve

this equation by the Newton-Raphson method, starting with an initial

guess between 0.5 and 0.9 kg/s Also, calculate the outlet temperature T o

for water Take the specific heat and density of water as 4.2 kJ/(kg · K) and 1000 kg/m3, respectively What are the main assumptions made in this model?

5.14 In a counterflow heat exchanger, the cold fluid enters at 20nC and leaves

at 60nC Its flow rate is 0.75 kg/s and the specific heat is 4.0 kJ/(kg · K) The hot fluid enters at 80nC with a flow rate of 1.0 kg/s Its specific heat

is 3.0 kJ/(kg · K) The overall heat transfer coefficient U is given as 200

W/(m2 · K) Calculate the outlet temperature of the hot fluid, the total

heat transfer Q, and the area A needed What are the possible design

variables in this problem, if the cold fluid conditions are fixed?

5.15 In a counterflow heat exchanger, the cold fluid enters at 15nC Its flow rate is 1.0 kg/s and the specific heat is 3.5 kJ/(kg·K) The hot fluid enters

at 100nC at a flow rate of 1.5 kg/s Its specific heat is 3.0 kJ/(kg · K)

The overall heat transfer coefficient U is given as 200 W/(m2· K) It is desired to heat the cold fluid to 60 o 5nC Outline a simple mathemati-cal model for this system, giving the main assumptions and approxi-mations What are the design variables in the problem? Calculate the

outlet temperature of the hot fluid, the total heat transfer q, and the area

20°C

Water

90°C Condensate

FIGURE P5.13

where A is the surface area in square meters Write down the relevant

mathematical model and, employing the Newton-Raphson method for one equation, determine the value of m that results in a heat transfer

rate of 300 kW Start with an initial guess of m.between 3 and 3.5 kg/s Determine the sensitivity of the mass flow rate to the overall heat trans-fer rate by varying the latter about its given value of 300 kW

5.17 Water at 40nC flows at m kg/s into a condenser that has steam

con-densing at a constant temperature of 110nC The UA value of the heat exchanger is given as 2.5 kW/K and the desired total heat transfer rate

is 120 kW The specific heat at constant pressure C p for water may be taken as 4.2 kJ/(kg · K) Write the equation(s) to calculate m and, using any

simulation approach, determine the appropriate value of m for the given

heat transfer rate If the total heat transfer rate varies as 120 o 20 kW, determine the corresponding variation in m.

5.18 A heat exchanger is to be designed to heat water at 1.0 kg/s from 15nC

to 75nC A parallel-flow heat exchanger is to be used and the hot fluid

is water at 100nC Take the specific heat as 4200 J/(kg · K) for both fluids The mass flow rate of the hot fluid must not exceed 4 kg/s The diameter of the inner pipe must not exceed 0.1 m and the length of the heat exchanger must be less than 100 m Obtain an initial, acceptable design for this process and give the dimensions of the heat exchanger Give a sketch of the temperature variation in the two fluid streams.5.19 A condenser is to be designed to condense steam at 100nC to water at the same temperature, while removing 300 kW of thermal energy A counterflow heat exchanger is to be employed Water at 15nC is avail-able for flow in the inner tube and the overall heat transfer coefficient

U is 2 kW/m2K The temperature rise of the cooling water must not

be greater than 50nC, the inner tube diameter must not exceed 8 cm, and the length of the heat exchanger must not exceed 20 m Obtain an acceptable design and give the corresponding mass flow rates, water temperature at the exit, and heat exchanger dimensions

5.20 Choose a design parameter Y to follow the convergence of iterative

redesign of a refrigeration system Give reasons for your choice and sketch its expected variation as the compressor is varied to change the exit pressure

Cold Water

m

20°C

U

Hot Water

5.21 Decide on a design parameter Y to study the convergence of an iterative

design procedure for a shell and tube heat exchanger If the design ables, such as tube and shell diameters, are varied to reach an accept-

vari-able design, how would you expect the chosen criterion Y to vary?

5.22 Take the refrigeration system considered in Example 5.1 If the age facility is to be maintained in the temperature range of 0 to 5nC, while the outside temperature range and the total thermal load remain unchanged, redesign the system to achieve these requirements

stor-5.23 Develop the initial, acceptable design for the problem considered in Example 5.2 if the maximum temperature obtainable from the heat source is only 290nC

5.24 Redesign the solar energy storage system considered in Example 5.3 if the total amount of energy to be stored is halved, while the remaining

requirements remain the same Also, choose a design parameter Y that

may be used to examine the convergence of the redesign process, ing reasons for your choice

giv-5.25 Redesign the heat exchanger considered in Example 5.7 for the ments that the outer tube diameter be less than 6.0 cm and the inner tube diameter be greater than 2.0 cm, keeping the remaining condi-tions unchanged

require-5.26 Redesign the heat exchanger in Example 5.7 to obtain a total length of less than 75.0 m, while keeping the outer tube diameter greater than 3.0

cm No constraints are specified on the inner tube

5.27 For a fluid flow system similar to the one considered in Example 5.8,

take the design values of P1, P2, H, A, B, and C as 470, 700, 135, 10,

20, and 5, respectively, in the units given earlier Simulate this system, employing the Newton-Raphson method Study the effect on the total flow rate of varying the zero-flow pressure values (470 and 700 in the preceding equations) and the height (135) by o20% Find the maximum and minimum flow rates

5.28 Determine the effect of varying the heat transfer coefficient to

100 W/(m2· K) and the equilibrium temperature T e to 15nC in Example 5.6 Compare the results obtained with those presented earlier and dis-cuss the implications for the design of a heat rejection system What do such changes mean in actual practice?

5.29 A plastic (PVC) plate of thickness 2 cm is to be formed in the shape of

an “N” For this purpose, it must be raised to a uniform temperature of 200nC and held at this temperature for 15 sec to complete the process The temperature must not exceed the melting temperature, which is 300nC for this material Develop a conceptual design and a mathemati-cal model for this process Obtain an acceptable design to achieve the desired temperature variation

5.30 The surface of a thick steel plate is to be heat treated to a depth of 2.5 mm A constant heat flux input of 106 W/m2 is applied at the sur-face The required temperature for heat treatment is 560nC, and the

maximum allowable temperature in the material is 900nC Can this arrangement be used to achieve an acceptable design? If so, determine the time at which the heat input must be turned off Can you suggest a different or better design?

5.31 For the preceding problem, suggest a few conceptual designs and choose one as the most appropriate Justify your choice

be taken into account to make the effort economically viable It is necessary

to find a balance between the product quality and the cost, since the product would not sell at an excessive price even if the quality were exceptional For a given item, there is obviously a limit on the price that the market will bear As discussed in Chapter 1, the sales volume decreases with an increase in the price Therefore, it is important to restrain the costs even if this means some sacrifice

in the product quality However, in some applications, the quality is extremely important and much higher costs are acceptable, as is the case, for instance, in racing cars, rocket engines, satellites, and defense equipment Similarly, a poor-quality product at a low price is not acceptable The key aspect here is finding a proper balance between the quality and cost for a given application

Even if it can be demonstrated that a project is technically sound and would achieve the desired engineering goals, it may not be undertaken if the anticipated profit is not satisfactory Since most industrial efforts are directed at financial profit,

it is necessary to concentrate on projects that promise satisfactory return; otherwise, investment in a given company would not be attractive Similarly, a very large ini-tial investment may make it difficult to raise the funds needed, and the project may have to be abandoned Decisions at various stages of the design are also affected by economic considerations The choice of materials and components, for instance, is often guided by the costs involved The use of copper, instead of gold and silver, in electrical connections, despite the advantages of the latter in terms of corrosion resis-tance, is an example of such a consideration The characteristics and production rate

of the manufactured item are also affected by the market demand and the associated financial return Thus, economic aspects are closely coupled with the technical con-siderations in the development of a thermal system to achieve the desired objectives.Economic factors, though crucial in design and optimization, are not the only nonengineering ingredients in decision making As seen earlier, several additional nontechnical aspects such as environmental, safety, legal, and political issues arise and may influence the decisions made by industrial organizations However, several

of these can be frequently considered as additional expenses and may again be cast

in economic terms For instance, pollution control may involve additional facilities