Design and Optimization of Thermal Systems Episode 3 Part 10 doc

697 A Acceptable designs, xiv, 42, 71, 81–82 considerations for large practical systems, 362–373 design strategies, 309–322 domain of, 40 failure to achieve within requirements and constraints, 82 initial design and, 300–309 with iterative redesign, 103 optimum at boundaries of domain, 501 selection of, 315 for solar collector/storage tank system, 316 solar energy collector system example, 315–317 system design applications, 322–323 of thermal systems, 299–300 vs. optimal design, 18, 83, 429 Active variables, vs. slack variables, 585 Actuators, 87 Aerospace systems, 33 weight as important design parameter in, 430 Air conditioning systems, 33–38, 57 component selection for, 301 single-variable problems for, 515 Air-conditioning systems, design problem, 56 Air-cooled copper sphere, best t method of modeling, 191–193 Air-cooled electronic equipment, 4 Air cooling systems, 28 Air-cycle refrigeration system, 301–303 Aircraft propulsion gas turbine engines for, 35 thrusting systems for, 34 Algebraic equations converting minimum/maximum problem into systems of, 476 from curve tting, 146 nding roots of, 221 Algebraic roots, 224 Allocation problems linear programming example, 582–583 software procedures for, 587 using slack variables, 582–583 Alternating direction implicit (ADI) method, 242 Ambient conditions in environmental processes, 337 inuence in thermal systems, 22 Ambient temperature variation, 137 American Board of Engineering Accreditation (ABET), code of ethics, 623 Ammonia production system, algebraic equation examples, 267–269 Analog models, 129–130, 195, 256 limitations in engineering design, 130 Analysis, vs. design, 5 Analytical solution, 253, 477 lumped systems dynamic simulation, 273–275 for sensitivity analysis, 460 Annealing furnace, 364 system design example, 364–370 Annealing temperature, 48 Annual compounding, 386, 387, 389 Annual costs, 415 Ansys, 247, 281 Articial intelligence, xviii, 600, 621 Articial neural networks (ANNs), 445, 591, 620 Asymptotic convergence factor, 224 Automation, 71, 628 in design process, 86–88 Automobile engines, 36 acceleration as chief design parameter in, 430 cost per mile of travel as objective function, 452–453 Average surface temperature rise, 55 Axial fans, 352 Axial ow compressors, 353 Axial pumps, 352 Axisymmetry, in batch-annealing system design, 366 B Back-of-the-envelope calculations, 58 Back-substitution, 215, 216 Ball valves, 355 Banded matrix, 215 Batch-annealing furnace, 365 acceptable design example, 364–370 Index 698 Design and Optimization of Thermal Systems Bernoulli’s equation, 357 Best t method, 195 air-cooled copper sphere example, 191–193 circular pipes ow rate example, 193–194 in curve tting, 183–185 linear regression in, 186–188 multiple independent variables in, 190–191 nonpolynomial forms and linearization, 189–190 polynomial best t, 188–189 vs. exact t, 186 Between-model interactions, 133 Biot number, 170, 279, 324, 367 Blade proles, in fans, 353 Blending problems, software procedures for, 587 Block representation, of information ow, 260 Blowers, 352, 361 Boilers, 39, 342 use of design libraries for, 304 Boiling, heat transfer coefcients for, 331 Bonds, investment through, 406–407 Book value, 412 Boundary conditions, 101, 244 complexities in thermal systems, 127 for conduction-convection problem, 173 in cylindrical gas furnace, 156 in environmental systems design, 339 for forced convective cooling, 334 simplication of, 142–144 slowly changing, 136 of thermal systems, 22 Boundary element methods, 244 Boundary-value problems, 227, 234 for ordinary differential equations, 233–235 steady-state temperature example, 235–238 Bracketing methods, 221 Brayton cycle, 301, 302 Buckingham Pi theorem, 178 Buttery valves, 355 Buying power, 396 and interest/ination rates, 394 C C language, numerical modeling with, 211 C++ language, numerical modeling with, 211 Calculus methods, xiv, 41, 448, 449, 454, 467, 494, 512, 541, 545, 553 equality constraints and, 499 in fan and duct system example, 531 and Lagrange multipliers, 473–475 for problem optimization, 440–441 vs. multivariable geometric programming, 570 vs. single-variable geometric programming, 567 Capital recovery factor, 398 Casting process, 25 in enclosed region, 5 Centrifugal compressors, 353 Centrifugal fans, 352, 353 Centrifugal pumps, 351 subcategories of, 352 Ceramics, 25, 104 typical characteristics, 108 Chain rule, 484 Characteristic time of variation, 135 Check vales, 354 Chemical composition, specifying operating conditions in terms of, 438 Chemical manufacturing plant, uniform exhaustive search example, 517–518 Chemical reactions, in environmental processes, 337 Chemical vapor deposition (CVD) system, 547 optimization of, 549 Chlorouorocarbons (CFCs), 32 for cooling of electronic equipment, 331 Cholesky’s method, 216 Chvorinov model, 611, 613 Circular pipes, ow rate in, 193–194 City income tax, 408 Closed-ended problems, 2 Coefcient matrix, 215 Coefcient of performance (COP), 86 Coefcient of volumetric thermal expansion, 109 Coils in batch-annealing system design, 366, 367 slow transient response of, 368 Colebrook formula, 356 Combined transport modes, of manufacturing processes, 323 Combustors, 33 Communicating design, xvii, 71, 90–92, 628 Communication modes, 90–91 Complex geometries, of thermal systems, 22 Complex systems, modeling approach, 251 Component availability, as source of design information, 625 Component design economic factors determining decisions, 419 vs. system design, 361–362 Component interactions, 47 Component modeling, 248 isolating system parts for, 248–249 mathematical modeling, 249–250 numerical modeling, 250 Index 699 Component selection, 15, 301 in initial design, 301–303 rate of return calculations for, 418–419 Components, 19, 21 block representations, 260 dened, 361 modeling effects on system performance, 256 Composite functions, combining objective function and constraints as, 537 Composite materials, 104, 106–107 typical characteristics, 108 Compound amount factor, 392 Compound interest, 385–387 rate tables, 679–685 Compounding frequency effect on investment, 389 variations in, 403 Compressors, 353, 361 block representation, 260 Computational code, developing with numerical modeling, 208 Computational modules, 602 in knowledge-based systems, 603–604 Computer-aided design (CAD), 97, 114, 618 elements or modules in, 99 main features, 97–98 of thermal systems, 98–103 Computer software, 639 communicating design through, 91 direct solution of linear equations, 644–645 dissection method for nding roots of equation, 642–643 expert systems, 600 FORTRAN, 639 Gauss-Seidel method, 650–652 Gaussian elimination for tridiagonal system, 648–650 interpolation, 645–647 for linear programming, 579 MATLAB, 639 for matrices, 640–641 Newton-Raphson method, 653–654 for numerical modeling, 211–212 ordinary differential equations, 647–648 patenting of, 95 polynomials, 641–642 procedures for linear programming problems, 587 root solving with Secant method, 652–653 as source of design information, 625 successive over relaxation, 654–657 Concentric pipe counter-ow heat exchangers, 8 Concentric pipe parallel-ow heat exchangers, 8 Conceptual design, xiii, 4, 58, 114, 610 example, 59–62 existing system design modications, 64–70 innovation in, 58–62 selection from available concepts, 62–64 for thermoforming application, 328 Condensation soldering facility, 59, 60, 61 conceptual design for, 69 control systems for, 88 for surface-mounted components, 62 Condensation technique achieving nonzero degree of difculty with, 578 removal of interior nodes by, 244 Condenser, 342 block representation, 260 Condensers, 39 Conduction-convection problem, 171, 172 Conduction heat transfer, analog model, 129 Condentiality, and professional ethics, 624 Conjugate transport, for cooling of electronic equipment, 330 Conservation laws constraints due to, 435, 621 and constraints of thermal systems, 486 and equality constraints, 537 equality constraints from, 436 and nite-element method, 243 in mathematical modeling, 146–148 Conservation of mass, 23 Constrained multivariable problems, 553 Constrained optimization, 491–493, 514 conversion to unconstrained, 489–491, 511 geometric programming with, 573–575 hot-rolling process geometric example, 576–578 Lagrange multipliers for, 481–484 manufacturing cost example, 575–576 Constrained steepest descent method, 546–547 Constraints, 14, 41, 53–55, 56. See also Design constraints arising from conservation laws, 435 choice of components and, 300 combining with objective function, 537 dependence on mechanical strength and structural integrity, 363 effect of relaxing, 450 in environmental systems design, 337 equality and inequality types, 436 for extrusion die design, 616 in heat transfer system design, 345 700 Design and Optimization of Thermal Systems nontechnical, 621–622, 631–632 in problem formulation for optimization, 434–437 reducing number of, 490 relationship to slack variables, 582 sensitivity of optimum design to, 461 Construction materials, 108 Consumer price index (CPI), 394 Continuous casting, 26, 454 Continuous compounding, 387, 389 in series of amounts, 399–400 Continuous models, 133, 258–259 Continuous processes, difculty of dividing into steps, 589 Contour plots, 528 in Lagrange expressions, 479 Control mass models, 126 Control strategies, 87 Control systems, xvii, 71, 362, 363 in design process, 86–88 Control thermocouple, 368, 370 Control volume models, 126, 244 inow and outow of material and energy in, 437 Convection coefcients, 101 Convective cooling, lumped mass approximation of heated body undergoing, 141 Convective heating, temperature variation for, 327 Convector plates, in batch-annealing system design, 366 Convergence, 223 for linear systems, 216, 217 in numerical modeling, 211 with steepest ascent methods, 536 Convergence criterion, 217 in environmental systems design, 340 in uid ow system design, 358 for iterative redesign, 317–320 Cooling systems, 33 economic factors determining decisions, 419 for electronic equipment, 28–31, 329–336 heat removed per unit cost as objective function for, 450 maximizing heat transfer rate in, 463 objective function for, 454–455 requirements for, 49 tree structure for, 601 Copper, vs. gold and silver in electrical connections, 383 Copyrights, 92–97, 93 Correlation coefcient, 188 Corrosion resistance, 110 Cost comparisons, 413 annual costs, 415 life-cycle savings, 415–417 present worth analysis, 413–415 Cost considerations, 362. See also Economic considerations balancing with quality, 383 as constraint on materials selection, 321 Cost function, in metal-rolling process example, 563–564 Costs incurred, as objective function, 432 Counterow heat exchanger, 79, 346 acceptable design example, 346–350 effectiveness of, 344 Coupled equations, 251–252 in numerical modeling, 209 Coupled submodels, 78 Coupled transport phenomena, of thermal systems, 22 Coupling in manufacturing processes, 323 of modeled individual parts, 251 Crank-Nicolson method, 241, 245 for thermoforming application, 326 Creative problem solving, 59 Critical-path problems, software procedures for, 587 Cross-ow heat exchangers, with unmixed uids, 8 Crout’s method, 216 Crystal growing, 25 Cubic spline interpolation, 184 Curve tting, 127, 180–181, 191, 195, 207, 309, 441, 448, 494–495 best t method, 183–191 exact t method, 181–183 examples in thermal processes, 128 public-domain software for, 212 Custom-made products, vs. off-the-shelf, 460 Cylindrical gas furnaces, mathematical modeling example, 153–157 Cylindrical storage tank, optimization problem, 490–491 Czochralski crystal-growing process, acceptable design example, 370–373 D Daily compounding, 386, 387, 389 Data comparison, in model validation, 162–163 Data reporting, and professional ethics, 624 Decision making, in expert systems, 600 Index 701 Declining balance, 410, 411 Decoupling, for thermal transport models, 249 Degree of difculty in geometric programming, 561 in geometric programming example, 575–576 in industrial hot water example, 565 nonzero, 578–579 DENDRAL, 600 Density, 109 Dependability, as objective function, 433 Depreciation, 410 –413 Descriptive models, 125–126 Design, 609 economic factor in, 413–419 as part of engineering enterprise, 20 role in engineering enterprise, 1, 9–19, 43 role of economic factors in, 413–419 vs. analysis, 5 vs. selection, 7–8, 610 Design concepts, selection from available, 62–64 Design considerations, 47 computer-aided design, 97–103 conceptual design, 58–70 design problem formulation, 47–57 design process steps, 70–97 material selection, 104–113 problems, 116–123 Design constraints, 41. See also Constraints for cooling of electronic equipment, 331 Design evaluation, 71, 611, 628 by system simulation, 254 Design libraries, 301, 616 as resource for initial design, 304304 Design methodology, in knowledge-based systems, 609–610 Design modications example, 67–70 in existing systems, 64–67 Design parameters, 320. See also Convergence criterion effects on system performance and cost, 429 relative importance of various, 459 Design problem formulation, 47, 113 additional considerations, 55–57 constraints and limitations, 53–55 design variables, 51–53 given quantities, 50–51 for heat transfer equipment, 345–346 requirements and specications, 47–50 Design process, 40 acceptable design evaluation, 81–82 communicating the design, 90–92 dening need or opportunity, 9–10 engineering design, 14–15 evaluation and market analysis, 10–11 fabrication, testing, and production, 18–19 feasibility and chances of success, 12–14 as function of number of variables, 52 modeling in, 75–76 need for optimization, 16–18 optimal design, 83–86 patents and copyrights, 92–97 physical system, 72–74 research and development, 15–16 safety features, automation, and control, 86–88 schematic, 6 simulation, 76–79 steps in, 70–72 Design projects, 635–637 Design requirements, 47–50, 56 choice of components and, 300 in cooling of electronic equipment, 331 in environmental systems design, 337, 339 in heat transfer system design, 345 Design rules, 609, 619 for die design, 616 Design specications, 15, 50, 57–60 communicating design through, 91 Design strategies, 309, 464–465 adjusting design variables, 309 ingot casting system example, 310–315 iterative redesign procedure, 317–322 multiple designs, 309–310 and selection of acceptable designs, 315 Design values analysis, 2–3 Design variables, 51–52, 56 adjusting in initial design, 309 choice for optimization, 457–458 continuous changes in, 494 for cooling of electronic equipment, 331 determination for optimization, 438, 439 for die design, 615 economic factors determining decisions, 419 in environmental systems design, 337, 339, 372 example, 53 hardware, 52 in heat transfer system design, 345 as inputs for xed operating conditions, 310 interdependence of, 321 operating conditions, 52–53 702 Design and Optimization of Thermal Systems optimization of, 433 priority for changing, 322 sensitivity of, 431 varying continuously over allowable ranges, 441 varying for system redesign, 321 Deterministic models, 133, 259 Dichotomous search methods, 442, 513, 552 for single-variable problems, 519–521 uniform dichotomous search, 519–520 Die design initial design module, 617 with knowledge-based systems, 615–618 redesign model, 617 Diesel engines, 33 Difference vs. ow rate graphs, 270 Differential equations, 74, 149 in conservation formulation, 146 stone motion example, 231 for transient problems, 141 Dimensional analysis, 165–166, 165–180, 166–167 scale-up in, 166 Dimensionless equations, 139, 173, 246 for conduction-convection problem, 173 and dynamic similarity, 178 Dimensionless groups, 169, 170 in uid mechanics and heat and mass transfer, 170 Dimensionless temperature, partial differential equation example, 244–247 Dimensionless variables, 139 Direct labor costs, 420 Direct methods, for approximating linear algebraic equations, 213–216 Dirichlet conditions, 242 Discounted cash ow, 417 Discrete models, 133, 258–259 Discretization, of mathematical equations, 132 Distance, variation with time, 233 Distributed models, 133 partial differential equations for, 147 Distributed systems linearization for, 281–282 numerical simulation methods for, 278–281 Ditrus-Boelter equation, 344 Dividends, 408 Domain of acceptable designs, 40, 83, 430. See also Acceptable designs Fibonacci search methods for narrowing, 521–523 for heat treatment, metal extrusion electronic equipment, 435 minimizing number of, 511 narrowing to optimized system, 86 optimization following achievement of, 399 optimum design within, 430 penalty function method for, 540 for thermal systems, 299–300 Dot product, 479 Drag force, 167 in optimization example, 452–453 Draw speed, 547 Draw tower, 74 Dry air, properties at atmospheric pressure, 659–662 Drying processes, 25 Durability, as objective function, 433 Dynamic modeling, 133, 257–258, 277 for choice of optimum path, 443 Dynamic programming, xiv, 41, 467, 588–590, 592 in optimization, 442–444 problems, 594–598 requirements for, 559 for thermal systems, 449 Dynamic similarity, in physical models, 178 E Eckert number, 170 Economic considerations, xiv, 383–384 annual costs, 415 application to thermal systems, 419–420 bond investments, 406–407 calculation of interest, 385–390 changes in payment schedules, 403–405 changing amount in series of payments, 400–402 compound interest, 385–387 constraints based on, 621–622 continuous compounding, 387 continuous compounding in series of amounts, 399–400 cost comparisons, 413–417 depreciation, 410–413 effective interest rate, 388–390 future worth, 391–393 future worth of uniform series of amounts, 396–397 inclusion of taxes in ROI calculations, 409–410 income taxes, 409 ination, 393–396 life-cycle savings, 415–417 present worth, 390–391 Index 703 present worth analysis, 413–415 present worth of uniform series of amounts, 397–399 problems, 422–427 property and local taxes, 409–410 raising capital, 405–408 rate of return, 417–419 role in design, 413–419 series of payments, 396–405 shift in time effects on payments, 402 simple interest, 385 stock investments, 408 taxes, 408–413 variable payment frequencies, 403 worth of money as function of time, 390–396 Economic data, as source of design information, 625 Effective interest rate, 388–390 Effectiveness, in heat transfer system design, 344 Efciency of Fibonacci search methods, 527 of lattice search method, 529 maximizing in optimization process, 447 as objective function, 432 Electric circuit board model, 333 Electric heat treatment furnace, 161 information-ow diagram, 262, 263 validation model example, 163–165 Electrical conductivity, 113 cost considerations for copper, gold, silver, 383 Electrical insulation, 113 Electronic components cooling by forced convection and heat pipe, 4 forced air cooling acceptable design example, 332–336 forced convective cooling of, 63 heat treatment system for silicon wafers, 303 minimizing heat loss as constrained/ unconstrained problem, 496–498 optimization without vortex promoter, 552 physical arrangement of cooling system, 332 search methods for cooling problem, 549–551 single-variable problems for, 515 Electronic equipment boundaries of acceptable design domain for, 435 cooling system design for, 619–620 cooling system requirements for, 49, 62 cooling systems for, 28–31, 30 multiple objective functions for cooling, 84–85 Electronic equipment cooling, acceptable design examples, 329–332, 332–336 Electronic materials, 108 Electronic systems with fan air cooling, 31 heat removal rate per unit cost as objective function for, 458 material selection for, 112 rate of energy removed as objective function for, 450 Elimination methods, 513, 517, 529 comparison for single-variable problems, 524–527 converting constrained to unconstrained problems using, 511 Elliptic problems, 242 Empirical models, 130 as source of design information, 625 Enclosure conguration models, 126 Encyclopedia of Science and Technology, 627 Energy, as maximum useful work, 456 Energy analysis, 456 Energy balance constraints, minimizing heat loss with, 495 Energy balance equations, 55, 357, 435 at furnace wall, 146 Energy consumption rate as objective function, 432, 447 per unit of output, 433, 447 Energy conversion systems, 28 Energy exchange, by convection, 274 Energy input, minimizing as objective function, 448 Energy losses, 566 in heat transfer system design, 342 minimizing as objective function, 448 optimizing according to, 431 Energy rating, 433 Energy storage, 28 Energy supply rate, 565 maximizing with multivariable geometric programming, 568–570 Energy systems, 28 power per unit cost as objective function for, 449–450 Energy transfer, in environmental systems design, 337 Engine efciency, in automobiles, 452–453 Engineering design, 2, 14–15 dening need or opportunity for, 9–10 design values analysis, 2–3 examples, 4–6 704 Design and Optimization of Thermal Systems selection vs. design, 7–8 synthesis for, 6 Engineering drawings, communicating design through, 91 Engineering systems, software simulation of, 95 Entropy, 455–456 Environmental impact, 362, 363 constraints based on, 621, 622 as objective function, 432 Environmental requirements, 12 of materials, 110 Environmental systems, 31–33 acceptable design of, 336–338 heat rejection system design example, 338–342 intake-outfall location decisions, 342 Equality constraints, 436, 483 with calculus methods, 499 determination for optimization, 439 linear programming with, 573 vs. number of independent variables, 491, 537 Equipment costs, 564 Equipment selection curve tting for, 180 in uid ow systems, 351 Ethics, 623–625. See Also Professional ethics Euler number, 170 Euler’s method, graphical interpretation, 230 Evaluation, for economic visibility, 10–11 Evaporators, 342 Exact t method, 195 in curve tting, 181–183 vs. best t method, 186 Exergetic efciency, 456 Exhausters, 352 Exhaustive search method, 442, 513, 551 relative inefciency of, 519 for single-variable problems, 517–519 vs. selective search, 616 Existing systems, 301 design modications to, 64–70 economic factors determining decisions, 419 information on, 619 modication for initial design, 303 simulation for design modications, 256 Experimental results, falsication of, 624 Expert knowledge, 301 in ingot casting design, 612–613 for initial design, 304 in knowledge-based systems, 607–609 Expert systems, 98, 600, 631 features of, 609 Exponential variations, 189 Extrema, 473, 481 Extrusion die design, with knowledge-based systems, 615–618 Extrusion facility, minimum cost example, 488–489 F Fabriciation, in design process, 18–19 Facilities taxes, 409 Facilities upgrades, 413 Fan air cooling, 31 Fan and duct system, unconstrained multivariable search example, 531–532 Fans, 352, 361 blade proles in, 353 cost and interest calculations, 393 Fatigue characteristics, 110 Feasibility analysis, 12–14 Fiber quality, as objective function, 548 Fibonacci search methods, 442, 513, 525, 531, 552, 553 efciency of, 526 and golden section search, 523 reducing interval of uncertainty with, 523 for single-variable problems, 521–523 Fidap, 212, 247 Fin-tube compact heat exchanger cores, 8 Final optimized design, 431–432, 611 Financial aspects, xvii importance in design, 630 Finite-difference grid, 240 Finite-difference method (FDM), 98, 132, 235, 242, 243, 276, 619 in knowledge-based systems, 603 of partial differential equations, 240–242 Finite-element methods (FEM), 98, 132, 235, 243 in knowledge-based systems, 603 of partial differential equations, 242–244 Finite-volume method, 98 Fire extinguishing systems, 31 First law of thermodynamics, 455 Fixed costs, 420 Fixed roof storage vessels, 354 Flat curve, 473 Flow in enclosed region, 149 scale models for, 166 Flow rate best t modeling for circular pipes, 193–194 as design parameter in pumping systems, 430 minimizing as objective function, 447 Index 705 Flue gases in batch-annealing furnace design, 364 in batch-annealing system design, 366 fast transient response of, 368 Fluent, 212, 247, 281 Fluid distribution systems, 38 Fluid ow, 362, 447 analytical results, 3 complex nature of, 22 for cooling of electronic equipment, 331 physical modeling over a car, 131 velocity prole for, 2 Fluid ow rate, minimizing as objective function, 448 Fluid ow systems and equipment, 1, 38, 357 acceptable design of, 350–351 objective function for, 450 pipes and pumps in, 350 piping systems, 355–356 selection of, 351–355 water distribution system design example, 356–359 Fluid leakage, minimizing as objective function, 448 Fluid mechanics, 38 dimensionless groups in, 170 use of analog models in, 129 Fluorocarbon coolants, for cooling of electronic equipment, 331 Food processing system material selection for, 112 present worth of investments calculations, 399 Forced-air baking oven CAD development of, 99–103 knowledge-based design of, 618–619 for thermal materials processing, 100 Forced air cooling, 30 acceptable design example, 332–336 in electronic systems, 171 governing equations and boundary conditions, 169–176 heat transfer coefcients in, 331 variation of board width for components, 334, 335, 336 Forced convection heat transfer correlations for external ow, 690–691 for ow in circular tube, 694–695 FORTRAN, xvii, 607, 611, 639 Forward time control space (FTCS) method, 241 Fouling factor, in heat transfer system design, 345 Four-stroke Otto cycle, 73 Fourier number, 170 Fracture characteristics, 110 Freezing plants, 35 Frictional losses, neglecting, 144 Front end, 602 in knowledge-based systems, 603 Froude number, 170, 177, 180 Fuel cells, 33 Fuel consumption rate, per unit output, 448 Fully implicit method, 241 Furnace temperature, in optical ber drawing, 547 Furnace walls, in batch-annealing system design, 366 Furnaces, 39 Future factor worth, 392 Future worth, 391–392 of bond investments, 406 of lumped sum at present, 402 packaging facility example, 404, 405 of series of increasing amounts, 402 of series of uniform amounts, 402 with shift in time, 402 of uniform series of amounts, 396–397 Fuzzy logic, 445, 591, 620 G Galerkin’s method, 244 Gas holders, 354 Gas turbines, 33 Gas water heaters, 10 Gases, properties at atmospheric pressure, 662–665 Gate valves, 355 Gauss-Jordan elimination, 214, 218, 219, 586 in knowledge-based systems, 603 simplex algorithm basis in, 583 Gauss-Seidel method, 217, 227, 237, 266, 270, 650–652 Gaussian elimination, 214, 216, 234, 236 for tridiagonal system, 648–650 General form of polynomial method, 181 Generalized reduced gradient method, 542, 547 Generation stage, of thermal energy, 39 Genetic algorithms (GAs), 445, 591, 620 Geometric programming, xiv, 41, 467, 559–560 applicability, 560–561 constrained optimization with, 573–578 degree of difculty in, 561 706 Design and Optimization of Thermal Systems expanding application of, 579 industrial hot water example, 564–567 manufacturing cost example, 569–570 mathematical proof, 570–573 for metal extrusion example, 454 metal-rolling process example, 563–564 with multiple independent variables, 567–570 with nonzero degree of difculty, 578–579 problems, 594–598 rate of energy supply example, 588–589 with single independent variable, 562–567 unconstrained optimization with, 561–570 Geometric similarity, 176–177 scale models for ow and heat transfer with, 166 Geometry, for cooling of electronic equipment, 329 Geothermal energy systems, 28 Given quantities, 50–51, 56, 73 in cooling of electronic equipment, 330–331 in environmental systems design, 337, 339 in heat transfer system design, 345 Glass ber drawing system, 73 Glass processing, 25 Global competition, and need for optimization, 16 Global equations, 244 Global extrema, 474 in allowable design domain, 500 Global maximum, 500, 516 Global minimum, 500 Global optimal point, 430 Global warming, 31 Globe valves, 355 Golden section search method, 513, 531 for single-variable problems, 523–524 solar energy system example, 526–527 Governing equations, 207 for distributed systems, 280 simplifying in mathematical modeling, 148–149 Gradient projection method, 542, 547 Gradient vectors, 477, 481, 492 in Lagrange multipliers, 478–480 in steepest/ascent methods, 533 use in optimization, 487 Graphical input/output, 602 in knowledge-based systems, 604–605 Graphical representation models, 126 for linear programming, 580–581 Grashof number, 170, 173, 179, 180 Guessed values, 503 H Hardware as design variable, 52 optimization of, 431 vs. operating conditions in problem formulation, 437–438 Head losses, 359 in uid ow systems, 351 in piping systems, 356 Heat conduction, analytical results, 3 Heat exchange rate, maximizing in optimization process, 447 Heat exchangers, 39, 85, 342, 361 block representation, 260 convergence criterion selection for, 318 domain of acceptable designs, 83 fouling of, 345 given requirements, 318 idealization of perfectly insulated outer surface, 145 mathematical modeling example, 151 outer diameter constraints on, 346 selection vs. design for, 7 types of, 8 use of design libraries for, 304 variation of cost with heat transfer rate in, 443 Heat ux, step change in, 145 Heat input rate optimizing according to, 431 specifying operating conditions in terms of, 438 Heat losses in environmental systems design, 337, 338 minimizing in electronic circuitry, 496–498 minimizing while meeting energy balance constraints, 495 neglecting, 14 Heat pipes, 28 Heat pumps, 35, 36, 37 use of design libraries for, 304 Heat rejection, 32, 371, 451–452 acceptable system design example, 338–342 to ambient air and water, 31, 338–342 cost per unit of generated power in, 451 in environmental systems, 336–342, 338–342 three-dimensional problem, 339 two-dimensional surface ow due to, 341 [...]... knowledge-based systems, 605 Synthesis, for engineering design, 6 System design, vs component design, 36 1 36 2 720 Design and Optimization of Thermal Systems System design applications, 32 2 32 3 component design vs system design, 36 1 36 2 electronic equipment cooling, 32 9 33 5 environmental systems, 33 6 34 2 fluid flow systems, 35 0 35 9 heat transfer equipment, 34 2 35 0 manufacturing processes, 32 3 32 9 miscellaneous... source of design information, 625 thermal properties of metals and alloys, 669–674 variability in thermal systems, 22 Material requirements, determination of, 110 111 Material selection, 104 , 110 1 13, 111, 114–115, 36 2, 36 3, 36 4, 611 categories of materials, 104 108 cost constraints on, 32 1 example, 112–1 13 material properties and characteristics for thermal systems, 108 – 110 role in design process, 6 and. .. modeling, 211 for solving linear algebraic systems, 216–218 Iterative redesign, 1 03, 112, 31 7, 37 3 convergence criterion for, 31 7 32 0 of existing systems, 30 3 initial design effects on convergence of, 30 0 similarities to nonlinear algebraic equations, 31 9 system redesign and, 32 0 32 2 J Jacobian method, 266 Jaluria, Yogesh, xix Jet compressors, 35 3 Judgment, role in design, 3 Index K Karmarkar scheme, 587 Kinematic... cooling, 33 3 of plastic cord in thermoforming application, 32 9 Thermal diffusivity, 34 0 in environmental systems design, 33 9, 34 9 Thermal efficiency as objective function, 432 optimizing according to, 431 Thermal processes CAD systems for, 102 tree structures for, 601 Thermal properties, in material databases, 604 Thermal sciences, 21 Thermal similarity, in physical models, 178–179 Thermal systems, ... cooling systems for electronic equipment, 28 31 dependence of cost and output on system design, 83 design of, 15 dimensions of parts, 32 1 discrete stages in, 588 energy systems, 28 environmental and safety systems, 31 33 fluid flow systems and equipment, 38 geometric programming applicability to, 560–561 geometrical configuration, 32 0 heat transfer equipment, 39 importance in industry, 43 inputs and components... models of, 132 knowledge-based design of, 610 621 limitations of linear programming in, 579 manufacturing and materials processing systems for, 25–28 material properties and characteristics for, 108 – 110, 32 0 methods of classifying, 39 miscellaneous systems, 39 –40 modeling of, 125 optimization of, 18, 41, 447–456 search method examples, 547–551 steps in design, 95 transportation systems, 33 types and examples,... classifications, 133 – 134 numerical models, 131 – 133 physical models, 130 – 131 Modeling, xiv, 70, 610, 628 analog models, 129– 130 basic features of, 125–128 conservation laws in, 146–148 curve fitting in, 180–194 712 Design and Optimization of Thermal Systems in design process, 75–76 dimensional analysis, 165–180 of heat transfer equipment, 34 2 34 5 idealizations in, 144–145 interaction between models in, 133 lumped... acceptable design of, 299 30 0 aerospace systems, 33 air conditioning, refrigeration, and heating systems, 33 38 Index analysis, 22–25 application of economic factors to, 419–420 application of Lagrange multipliers to, 494–5 03 application of search methods to, 514–515 basic characteristics, 19–22 characteristics of, 22 complexity of typical, 194 component characteristics, 32 1 computer-aided design of, 98–1 03. .. methods, 441–442 sensitivity analysis, 459–461 thermal systems optimization, 447–456 trade-offs in, 461–462 Problems and examples, xiv, 42– 43 acceptable designs, 37 5 38 7 design considerations, 116–1 23 economic considerations, 422–427 geometric, linear, dynamic programming, 594–598 716 Design and Optimization of Thermal Systems knowledge-based design, 633 – 634 Lagrange multipliers, 505–509 modeling, 197–206... for thermal systems design, 625–627 Ingot casting, 25 geometrical configuration, 607 knowledge-based systems design example, 611–615 solid-liquid interface movement, 614 Ingot casting system, design strategy example, 31 0 31 5 Inheritance, in object-oriented programming, 608 Initial cost, 562 Initial design, 30 0 30 1, 37 3 component selection in, 30 1 30 3 expert knowledge for, 30 4 library of previous designs . strategies, 30 9, 464–465 adjusting design variables, 30 9 ingot casting system example, 31 0 31 5 iterative redesign procedure, 31 7 32 2 multiple designs, 30 9 31 0 and selection of acceptable designs, 31 5 Design. conditions, 31 0 interdependence of, 32 1 operating conditions, 52– 53 702 Design and Optimization of Thermal Systems optimization of, 433 priority for changing, 32 2 sensitivity of, 431 varying continuously. 28 Heat pumps, 35 , 36 , 37 use of design libraries for, 30 4 Heat rejection, 32 , 37 1, 451–452 acceptable system design example, 33 8 34 2 to ambient air and water, 31 , 33 8 34 2 cost per unit of generated