Design and Optimization of Thermal Systems Episode 3 Part 7 doc

622 Design and Optimization of Thermal Systems in the operating conditions, the user, ambient conditions, raw materials, and other unpredictable parameters are used to leave an acceptable margin of safety. For instance, a dimension obtained as 2 cm from the feasible or optimal design may be increased to 3 cm for safety, giving a factor of safety of 1.5, particularly if this dimension refers to the outer wall of a system and may fail. Higher safety factors are used if damage to an operator may result from leakage of radiation, hot uid, high-pressure gases, etc. This is particularly true in the design of nuclear reac- tors, boilers, furnaces, and many other such systems where high temperatures and pressures arise. Therefore, the design obtained on technical grounds is adjusted to account for safety of the user as well as of the materials and the system. Similarly, environmental concerns can affect the design. Constraints are placed on the types of materials that can be used, on temperature and concentration of discharges into the environment, on maximum ow rates that may be used, on types and amount of solid waste, and so on. For instance, chlorouoro- carbons (CFCs) are not allowed because of their effect on the ozone layer. The temperature of the cooling water (from the condensers of a power plant) that is discharged into a lake or a river is constrained to, say, within 10nC of the ambient water temperature by federal regulations. This imposes an important constraint on the design of the system. Similarly, the concentration of pollutants and the ow rate of the uid discharged into air are constrained by regulations to ensure a clean environment. Again, these aspects arise as additional constraints on the design and must be taken into account. The legal issues are often related to federal and state regulations on waste dis- posal, zoning, procurement, transportation, security, permits, etc., and can generally be considered in terms of the cost incurred, since these involve additional expen- ditures by a company. Similarly, social issues can often be translated into costs for the company. For instance, providing housing, health, and other benets to the employees results in expenses for the rm. Therefore, these aspects lead to nancial constraints that may be quantied. However, many aspects are not easy to account for, such as the social effects of layoffs resulting from a particular industrial development. There may be substantial effect on the local level. However, these aspects are largely considered at higher levels of management and affect the design only as far as the viability of the overall project is concerned. National considerations, such as those pertaining to defense, sometimes override the technical and economic aspects. Items and materials that have to be imported may be substituted by those that are available in the domestic market. Thus, constraints may be placed on the choice of materials, components, and subsystems to take these concerns into account. These additional constraints are usually considered after a feasible design has been obtained. At this stage, the constraints due to the costs, safety, environment, and other aspects are considered to ensure that these are not violated by the design. However, some of these constraints may also be more effectively used at earlier stages of the design process. The temperature and pressure limitations arising from safety concerns, for instance, may be built into the design and optimization process. The nal design that is communicated to the management and fabrication facilities must satisfy all such additional constraints. Knowledge-Based Design and Additional Considerations 623 11.3 PROFESSIONAL ETHICS A topic that has come under considerable scrutiny in recent years is that of professional ethics. This is due to the large number of cases that have been uncovered indicating lack of proper behavior, and resulting in damage to life and property. Ethics refers to the principles that govern the conduct of an individual or groups of people involved in a profession. Every profession sets down its own code of ethics to provide rules of behavior that are proper, fair, and morally correct. It is important for individuals involved in a profession that is self-regulated, such as engineering, to know the ethical behavior that is expected of them and to pre- serve their integrity under various circumstances. Though many recent cases have involved the legal and medical professions, mainly because of their direct impact on people, engineers are also concerned with many decisions that involve professional ethics. Certainly, design is an area that has far-reaching implications for the profession and must, therefore, be carried out with strict adherence to ethical standards. Ethics has its roots in moral philosophy, and the basic features are simply the moral values that govern personal behavior. Some of the important aspects of proper conduct can be listed as follows: 1. Be fair to others. 2. Respect the rights of others. 3. Do not do anything illegal. 4. Do not break contracts. 5. Help others and avoid harming anyone. 6. Do not cheat, steal ideas, or lie. On the basis of such a set of moral values, many professional societies such as the Institute of Electrical and Electronics Engineers (IEEE) and American Board of Engineering Accreditation (ABET) have adopted appropriate codes of ethics that are expected to guide the members as well as companies if ethical problems arise. Most routine engineering activities do not involve ethical conicts. Since prot and growth are major driving forces in the engineering profession, most engineers are involved with pursuing these goals for advancement. However, if their actions start infringing on the rights of others and may lead to harm to others, through damage to property or to individuals, it is important to balance self-interest against ethics and to follow the appropriate course of action. In some cases, the choice is clear, but the individual may have to sacrice his or her self- interest in order to do the proper thing. An example of this is an engineer who designs a system, but nds that it has safety problems during testing. It is obvious that the system must be redesigned to avoid these problems. However, there may be deadlines to be met, the job of the engineer may be on the line, others involved in the design may try to downplay the problems and want to go ahead, and so on. Therefore, even a relatively straightforward problem like this one may lead 624 Design and Optimization of Thermal Systems to a dilemma for the individuals concerned. However, the correct procedure is to report the problems and redesign the system. Many such ethical questions are faced by engineers, particularly those involved in the development of new processes, systems, and products. Some of the common ethical situations that arise are 1. Preserving condentiality 2. Giving proper credit to appropriate groups or individuals 3. Reporting data correctly 4. Meeting obligations to the public versus the employer 5. Acting in accord with personal conscience 6. Responding to inappropriate behavior by others in the company Many readers may have already experienced some of the preceding situations. Giving proper credit to different people involved in a project is always a touchy issue, but it is important to be fair to all. Similarly, proprietary information must be maintained as condential because access to such information or data is allowed only to a few individuals under the condition of condentiality. A subcontractor who is designing a component for a system manufactured by a different organization is often provided with essential details on the system. These details are for use in the design process and are not to be revealed to other parties who are not involved. Correct reporting of data has been in the news a lot in the last few years, as some researchers have been found to falsify experimental results to downplay the side effects of the product and to claim important advances. Several drugs and their manufacturers have been in the news lately due to allegations of such wrongdoing. When uncovered, these actions have led to large nancial settlements and public ridicule. The issue of inappropriate behavior by others is a very difcult one and requires considerable care. Suppose an engineer nds out that his company is violating federal regulations on dumping of chemical hazardous wastes. Does he or she simply ignore the problem? According to the code of ethics, this matter has to be reported to the proper authorities. This is known as whistle blowing and it cannot be taken lightly. It is necessary to be sure that the activity is illegal and is adversely affecting public safety or welfare. Proper documentation is needed to support the accusation, and it must also be conrmed that management is aware of the activities. If the problem lies within the company and is a consequence of oversight, a simpler solution may be possible. Otherwise, appropriate regulatory bodies may be contacted. Whistle blowing obviously requires great moral cour- age, and the present position as well as the future advancement of anyone who undertakes this effort are at stake. Such instances are rare, but they have been increasing and they test the professional code of ethics. In most cases where ethical conicts need to be resolved, internal appeal processes are adequate. These start with the immediate supervisor, or with some- one outside the region of conict, and follow the internal chain of command. Satis- factory documentation is crucial in such appeals. Conicts arise, for instance, due Knowledge-Based Design and Additional Considerations 625 to unfair treatment, improper credit being given, falsication of data, improper use of funds, etc. Only if the internal appeal process is unsuccessful does one need to resort to external options. These include contacting professional societies, the media, regulatory agencies, personal legal counsel, and other external sources for settling the conict. Many case studies are given by Ertas and Jones (1997) and the IEEE code of ethics is given by Dieter (2000) to indicate the basic issues involved and the types of ethical conicts encountered in practice. 11.4 SOURCES OF INFORMATION An important ingredient in design is availability of relevant information on a variety of topics that are needed for developing a successful design. Informa- tion is needed to provide accurate data for the modeling and simulation of the system and to use past experience and results for help with the design process. Without adequate information on previous design efforts and existing systems, we could repeat past mistakes, spend time on obtaining information that is read- ily available, or generate designs that do not meet appropriate regulations and standards. Therefore, it is crucial that we spend extensive effort on gathering the most accurate and up-to-date information available on all facets of the given design problem. The types of information needed for design are obviously functions of the system under consideration. However, the information sought for the design of thermal systems is generally in the following main areas: 1. Material property data, including cost and availability 2. Design and operation of existing or similar systems and processes 3. Availability and cost of different types of components 4. Available computer software 5. Available empirical results, including heat transfer correlations, relevant technical data, and characteristics of equipment 6. Federal, state, and local regulations on safety and environment 7. Standards and specications set by appropriate professional bodies 8. Current nancial parameters, including rates of interest and ination, different costs, and market trends We have seen in earlier chapters that all this information is needed at various stages of the design process to obtain the desired inputs as well as to evaluate the design. Property data are particularly important because the accuracy of the simulation results, which are crucial to the design process, is determined by the data provided to the model. Economic data are needed to evaluate costs, make economic decisions during design, and determine if a project is nancially viable. The design must meet the standards and regulations specied for the given process or application and, therefore, it is necessary to obtain accurate information on these. Finally, information on existing systems, software, and technical results helps in minimizing the effort and avoiding duplication of work. 626 Design and Optimization of Thermal Systems Throughout this book, references have been made to books, papers, and other publications that deal in depth with a particular topic or area. Certainly, textbooks in the areas of heat transfer, thermodynamics, and uid mechanics are a good starting point for the design of thermal systems. Similarly, text and reference books on numerical methods, engineering economics, optimization, and design are important sources of relevant information. These can be used to provide the basic technical background needed for the various aspects that are involved in design. Different methods for analyzing various processes and systems, including mathematical, numerical, and experimental techniques, are given in detail in such books, along with characteristic results. Some information is also available on common materials; components of interest in thermal systems such as pumps, compressors, and heat exchangers; and general features of standard systems, like air conditioners and diesel engines. The references quoted in these books and papers may be further used to expand the source base. However, for detailed information on material properties, applicable regulations, current economic parameters, existing systems, characteristics of available equipment, and current trends in industry, other sources of information are needed. There are two main types of sources of information for design. These are 1. Public sources: Libraries, universities, research organizations, departments and agencies of the federal, state, and local government 2. Private sources: Manufacturing and supplying companies, banks, professional societies, consultants, individuals, computer software companies, and membership and trade associations Public sources are extensively used because the information obtained is free or relatively inexpensive. Government reports and publications from departments such as commerce, defense, energy, and labor are very valuable because these provide detailed information on results obtained, requirements and regulations, methods used, material property data, and various other guidelines. Patents issued also provide an excellent source of information on existing systems. These are available from public sources, through libraries and the Internet. Private sources are usually expensive, but a lot of information can be obtained through company brochures for advertising their products. The specications, cost, maintenance, servicing, and performance of available equipment can be obtained from the supplier. In many cases, additional details on the materials used, tests performed, basic design of the component, and even samples can be obtained if one is interested in a particular item. Though complete information on the component is generally condential, enough information can be obtained to decide if a given item is appropriate for the system being designed. Similar considerations apply to commercially available software. Extensive catalogs of manufacturers and suppliers are available from listings such as Thomas Register of American Manufacturers. The Internet is another important and expanding source of such information. Most engineering companies maintain their own libraries that contain books, technical magazines, journals, reports, information on their own products and systems, listing of suppliers, and so on. In the present information age, they also Knowledge-Based Design and Additional Considerations 627 have access to information available in the public domain, through the Internet, library exchanges, and agreements with other research or professional establish- ments. Such a collection may be large or small, depending on the size of the company itself, but the available methods of literature search and procurement make it a very important source of information. In addition, results from earlier efforts, information on existing systems, properties of materials used in the past, information on relevant regulatory and legal aspects, and so on, as applicable to the given industry, are probably best stored here. Therefore, there are many important sources of information on materials, detailed technical data, existing processes and systems, items available in the market, economic data, and on other inputs needed for design. These may be listed as follows: 1. Handbooks 2. Encyclopedias 3. Monographs and books 4. Journals: technical and professional 5. Catalogs 6. Indexes and abstracts 7. Technical reports 8. Internet Handbooks and encyclopedias are very useful in obtaining relevant and detailed technical information for a given process or system. Encyclopedias are available on physics, materials science, chemistry, uid mechanics, and so on. McGraw-Hill’s Encyclopedia of Science and Technology is an example of such reference books. Similarly, handbooks are available on pumps, air conditioning, heat exchangers, material properties, industrial engineering, manufacturing, etc. Marks’ Standard Handbook for Mechanical Engineering, also published by McGraw-Hill, is an example. A substantial amount of relevant and focused information is generally available in such sources. Listings of indexes and abstracts allow one to search for the appropriate source rapidly, particularly if the information exists in journals, translations, and published reports. Technical and professional journals are also good sources, though these are often either too detailed or too sketchy. Nevertheless, these can be used effectively to narrow the search to specic and relevant sources of information. The Internet is certainly one of the most important sources of information today. Thus, information that is a crucial factor in design may be obtained from a wide variety of sources. Many of these are free or quite inexpensive, while others may be expensive. However, the current techniques available for literature searches range from CD-ROM databases to the Internet, making it much less time consuming than before to cover much of the available eld and determine what information is available and at what cost. It is desirable to obtain as much relevant information as possible on the given application or system so that the design process is carried out efciently and without repeating existing data or past mistakes. 628 Design and Optimization of Thermal Systems 11.5 AN OVERVIEW OF DESIGN OF THERMAL SYSTEMS Basic aspects. In this book, we have considered the design and optimization of systems in which thermal transport involving heat and mass transfer, uid ow, and thermodynamics play a dominant role. Many different types of thermal systems, ranging from refrigeration, heating, and power systems to manufacturing and electronic equipment cooling systems, are employed as examples. The complicated nature of these systems, particularly their typically nonlinear, transient, three-dimensional, geometrically complex, and combined-mode characteristics, leads to coupled systems of governing partial differential equations. These are simplied through modeling to obtain algebraic equations and ordinary differential equations in many cases. Such models are combined with experimental results, material property data, and other available information, often using curve tting, to obtain a complete model for the system. This model is then used to simulate the system and obtain detailed results, which can be used for the design and optimization of the system. Thus, modeling and simulation form the core of the design effort for thermal systems, and a successful completion of the project is closely linked with the accuracy and validity of the model. This aspect of design is stressed throughout the book. The design of a thermal system starts with a close look at the problem. This involves determining what is given or xed in the problem, what can be varied to obtain an acceptable design, what the main requirements are, and what constraints or limitations must be satised by the design. This consideration leads to the problem formulation in terms of given quantities, design variables, requirements, and constraints. It also denes the feasible domain for the design. The next step is to obtain a conceptual design to achieve the desired goals. Different ideas for the system are considered based on what is presently in use, and innovative concepts are employed as well. A particular conceptual design is chosen by employing simple estimates and contrasting different ideas. With the design problem formulated and a conceptual design chosen, we can now proceed to a detailed design process, the main steps of which are 1. Characterization of the physical system 2. Modeling 3. Simulation 4. Evaluation of different designs 5. Iteration to obtain an acceptable design 6. Optimization 7. Automation and control 8. Communication of the nal design Workable design. Though all the preceding steps are involved in the development of a successful design, modeling and simulation are particularly crucial because most of the relevant inputs for design and optimization are obtained from a simulation of the system using analytical, numerical, and experimental Knowledge-Based Design and Additional Considerations 629 approaches to study the model developed for the system. Different types of models and simulation strategies are available to generate the inputs needed for design. Even though the basic approach to modeling can be established and applied to common thermal processes and systems, modeling remains a very elusive and difcult element in the design process. It involves simplication, approximation, and idealization to obtain a model that may be used to study the behavior of the actual physical system. Creativity and experience are important ingredients in the development of a model. A good understanding of the physical characteristics of the system and the basic processes that govern its behavior is essential in decid- ing what to neglect or how to approximate. The governing equations are obtained based on the conservation principles for mass, momentum, and energy, taking these simplications into account. A very important question that must be answered for a model is if it accu- rately and correctly predicts the characteristics of the actual system. This requires a detailed validation of the model and estimation of the accuracy of the results obtained. In many cases, simple models are rst obtained by neglecting many effects that complicate the analysis. These models are then improved by including additional effects and features to bring them closer to the real system. This ne-tuning of the model is generally based on the simulation, experimental, and prototype testing results. The model is used to study the system response and behavior under a wide variety of conditions, including those that go beyond the expected region of operation to establish safety limits and ensure satisfactory operation in real life. Simulation results are also used to determine if a particular design, specied in terms of the design variables, satises the requirements and the constraints. All these ideas concerning problem formulation, conceptual design, modeling, simulation, and design evaluation may then be put together for obtaining acceptable designs. Different areas such as manufacturing, energy, transportation, and air conditioning, where thermal systems are of interest, are considered to apply the various steps in the design process. It can again be seen that modeling and simulation are at the very core of the design effort since the results obtained are used to choose the appropriate design variables, evaluate different designs, and obtain a domain of acceptable designs. Many additional aspects, such as safety and environmental issues, may also be considered at this stage. A unique solution is generally not obtained and several acceptable designs are often generated. Thus, the systematic progression from problem formulation and conceptual design to an acceptable design is highlighted in the rst ve chapters. Though relatively simple thermal systems are considered in many cases to present the methodology, much more complicated problems that typically arise in actual practice can be treated in a similar way. Some actual industrial systems are considered to demonstrate the use of this methodology. Optimization. Economic considerations and optimization need to be considered to complete the design and optimization process. Economic aspects are obviously very important in most problems of practical interest and are of particular signicance in optimization since minimization of costs and maximization of 630 Design and Optimization of Thermal Systems prot are important criteria for an optimal design. Economic considerations, such as cost, return, payment, investment, depreciation, ination, and time value of money, in the design process are discussed. Examples are given to show how economic considerations can affect decisions on design in areas such as material selection, choice of components, energy source, and so on. The importance of nancial aspects in design cannot be exaggerated since the viability and success of the project itself is usually determined by the prot, return, stock price, etc. Again, several relatively simple situations are discussed to illustrate the approach for considering economic factors. However, these ideas can easily be extended to more complicated circumstances where several different considerations may arise and interact with each other. Optimization is discussed in detail to stress the crucial need to optimize thermal systems in today’s competitive international market. The design process generally leads to a domain of acceptable designs with no unique solution. Optimi- zation with respect to a chosen criterion or objective function narrows this domain substantially, as desired for a given application, so that the nal design is chosen from a small range of design variables, making it close to a unique solution. Many different strategies are available for optimization. Search methods are particularly useful for thermal systems since discrete values of the variables are often encountered and simulation is complicated and time consuming, making it necessary to limit the number of runs. Methods such as Fibonacci and univariate searches are efcient and easy to use. Hill climbing techniques can also be used with numeri- cally determined derivatives. Calculus methods and geometric programming are useful if the simulation results are curve tted to obtain continuous expressions to represent system characteristics. Other methods such as linear and dynamic programming have limited use for thermal systems. Efcient computer programs are available for most of the techniques presented here and may be used when dealing with the large and complicated systems encountered in actual practice. The choice of the optimization method is guided by the form in which the simulation results are available and how involved each simulation run is. Several simple examples are employed here to illustrate the basic ideas and the techniques. These may be extended easily to many of the more complicated problems discussed in earlier chapters and examples of practical thermal systems given in the book. Typical large systems are considered rst in terms of the components and subsystems, with the overall model and simulation scheme obtained by cou- pling the simpler submodels. The complete model is simulated to obtain the characteristics and behavior of the system. These results are then used for developing acceptable designs, followed by an optimal design. There are obviously cases where an acceptable design is not obtained, with the given requirements and constraints, or where acceptable designs lie within a narrow range of variables, making it unnecessary to optimize the system. Concluding remarks. The design and optimization of thermal systems is an important, though complicated, eld. Many different situations can arise in actual practice and may require specialized treatment. However, the basic approach given in this book provides the general framework under which the design and Knowledge-Based Design and Additional Considerations 631 optimization of a thermal system may be undertaken. Some modications may be necessary in a few cases and additional information pertaining to materials, economic parameters, regulations, available components, and so on, may have to be obtained for specic applications. Creativity and originality are also important ingredients in design, particularly in the development of the concept and the model. In engineering practice, commercially available software packages are often used for system simulation and optimization. However, some of the software may be developed or programs in the public domain may be employed to provide the exibility and versatility needed in many cases. Additional aspects, such as safety and environmental issues, are of concern in most problems and are built into the decision-making. The nal design is communicated to the appropriate groups such as the management and fabrication facilities. Depending on management decisions, this could lead to prototype development, testing, marketing, and sales. All these aspects are expected to be considered in the design projects included at the end of this chapter. 11.6 SUMMARY This chapter concludes the presentation on the design and optimization of thermal systems by considering some recent trends, particularly knowledge-based design aids, and some additional considerations. Knowledge-based, or expert, systems, which use the expertise of people who are procient in given areas, have been used effectively in several elds, such as medicine, chemical analysis, and mining. In traditional design, such expertise is traditionally brought in by the designer, who uses his or her knowledge of the process, materials, and system to make decisions throughout the design process in order to obtain a realistic and practical design. Expert systems use computer software based on articial intel- ligence (AI) techniques to bring such considerations into the design process. The basic components — expert knowledge and databases — in knowledge-based design methodology are discussed. The advantages of this approach over traditional design methods are indicated. Several examples of thermal systems are taken to illustrate the use of this methodology. These efforts are still recent and have not been employed to their full potential. However, there is growing interest in these methods and many relevant techniques have been developed in recent years to help convergence to a realistic acceptable or optimal design. This chapter also discusses the important topics of professional ethics, sources of information, and additional constraints. These aspects arise in most engineering endeavors, but these are particularly signicant for design because of the innovative and creative ideas that are often involved. Different sources of information are discussed, indicating methods to locate these and extract the relevant information from them. Professional ethics can play a very signicant role in the development of the design, in the use of available information, in the implementation of the design, and in the progress of the entire project. A brief discus- sion of the important issues is given. Additional constraints that could affect the feasibility of a design are presented and discussed in the context of the material [...]... exact fit % c1=[x(1)^5 x(1)^4 x(1) ^3 x(1)^2 c2=[x(2)^5 x(2)^4 x(2) ^3 x(2)^2 c3=[x (3) ^5 x (3) ^4 x (3) ^3 x (3) ^2 c4=[x(4)^5 x(4)^4 x(4) ^3 x(4)^2 c5=[x(5)^5 x(5)^4 x(5) ^3 x(5)^2 c6=[x(6)^5 x(6)^4 x(6) ^3 x(6)^2 c=[c1;c2;c3;c4;c5;c6]; 7. 67] ’; x(1)^1 x(2)^1 x (3) ^1 x(4)^1 x(5)^1 x(6)^1 1]; 1]; 1]; 1]; 1]; 1]; 646 Design and Optimization of Thermal Systems % % Find coefficients of polynomial % a=c\y plot(x,y,‘-b’,x,y,‘*’)... and requirements 4 Computer simulation of the system: Off -design conditions, effect of various parameters 5 Economic analysis and optimization of the system: Discuss the initial cost and the operating costs Also, outline the control and safety of your design 6 Final report: Description of design and operation of the system, numerical results, drawings, references, specifications of components The design. .. languages and computer systems A few MATLAB commands were discussed in Chapter 3 and Chapter 4, and several references for numerical 639 640 Design and Optimization of Thermal Systems analysis and computer solutions were given Additional MATLAB commands and programs are given here The results obtained from some of the programs given in this appendix are discussed in the text The main purpose of presenting... 632 Design and Optimization of Thermal Systems covered in the book These could be of crucial importance in many cases and could determine whether it is worthwhile to proceed with the implementation of a given design Finally, the chapter integrates all the ideas presented in this book as an overview of the design of thermal systems and includes a few design projects as problems... % Calculate New Values % x(1)=( 17- x(2)-2*x (3) )/5; x(2)=(8-x(1)-x (3) ) /3; x (3) =( 23- 2*x(1)-x(2))/6; % % Check for Convergence % if abs(x-xold)> d = a + b d = 2 6 12 20 % addition >> d = b - a d = 0 2 6 12 % subtraction >> [q,r] =deconv(c,b) q = 1 2 3 4 r = 0 0 0 0 % division % quotient polynomial % remainder polynomial >> g = [1 6 20 48 69 72 44]; >> h = polyder(g) h = 6 30 80 144 138 72 >> x = [0 1 2 3 4 5 6 7 8 9 1.0]; >> y = [-.45 1.98 3. 28 6.16 7. 08 7 .34 7. 66 9.56 9.48 9 .30 11.2];... in the testing division of a large company The division is involved in testing and evaluating equipment from various subcontractors and recommending the best ones to the 634 Design and Optimization of Thermal Systems production department You are asked to test two different heaters, A and B, for durability and performance You find that heater B is superior and inform your boss of your recommendation... available on similar systems? Knowledge-Based Design and Additional Considerations 635 DESIGN PROJECTS Give the following information on the various design projects: 1 Problem statement: Fixed quantities, design variables, requirements, and constraints 2 Conceptual design: Sketch various possible systems, evaluate each, and select one for design 3 Mathematical modeling of the chosen design: Obtain governing . in most problems of practical interest and are of particular signicance in optimization since minimization of costs and maximization of 630 Design and Optimization of Thermal Systems prot are. that the design process is carried out efciently and without repeating existing data or past mistakes. 628 Design and Optimization of Thermal Systems 11.5 AN OVERVIEW OF DESIGN OF THERMAL SYSTEMS Basic. affect the feasibility of a design are presented and discussed in the context of the material 632 Design and Optimization of Thermal Systems covered in the book. These could be of crucial importance

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