Design and Optimization of Thermal Systems Episode 3 Part 10 doc

A Acceptable designs, xiv, 42, 71, 81–82 considerations for large practical systems, initial design and, 300–309 with iterative redesign, 103 optimum at boundaries of domain, 501 selecti

A

Acceptable designs, xiv, 42, 71, 81–82

considerations for large practical systems,

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,

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 fit 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 fitting, 146

finding 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, 337influence in thermal systems, 22Ambient temperature variation, 137American Board of Engineering Accreditation (ABET), code of ethics, 623

Ammonia production system, algebraic equation examples, 267–269Analog models, 129–130, 195, 256limitations in engineering design, 130

Analysis, vs design, 5

Analytical solution, 253, 477lumped systems dynamic simulation, 273–275

for sensitivity analysis, 460Annealing furnace, 364system design example, 364–370Annealing temperature, 48Annual compounding, 386, 387, 389Annual costs, 415

Ansys, 247, 281Artificial intelligence, xviii, 600, 621Artificial neural networks (ANNs), 445, 591, 620

Asymptotic convergence factor, 224Automation, 71, 628

in design process, 86–88Automobile engines, 36acceleration as chief design parameter in, 430cost per mile of travel as objective function, 452–453

Average surface temperature rise, 55Axial fans, 352

Axial flow compressors, 353Axial pumps, 352

Axisymmetry, in batch-annealing system design, 366

B

Back-of-the-envelope calculations, 58Back-substitution, 215, 216

Ball valves, 355Banded matrix, 215Batch-annealing furnace, 365acceptable design example, 364–370Index

Bernoulli’s equation, 357

Best fit method, 195

air-cooled copper sphere example, 191–193

circular pipes flow rate example, 193–194

in curve fitting, 183–185

linear regression in, 186–188

multiple independent variables in, 190–191

nonpolynomial forms and linearization,

Blade profiles, in fans, 353

Blending problems, software procedures for,

587

Block representation, of information flow, 260

Blowers, 352, 361

Boilers, 39, 342

use of design libraries for, 304

Boiling, heat transfer coefficients 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

for ordinary differential equations, 233–235

steady-state temperature example, 235–238

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, 398Casting process, 25

in enclosed region, 5Centrifugal compressors, 353Centrifugal fans, 352, 353Centrifugal pumps, 351subcategories of, 352Ceramics, 25, 104typical characteristics, 108Chain rule, 484

Characteristic time of variation, 135Check vales, 354

Chemical composition, specifying operating conditions in terms of, 438

Chemical manufacturing plant, uniform exhaustive search example, 517–518Chemical reactions, in environmental processes, 337

Chemical vapor deposition (CVD) system, 547optimization of, 549

Chlorofluorocarbons (CFCs), 32for cooling of electronic equipment, 331Cholesky’s method, 216

Chvorinov model, 611, 613Circular pipes, flow rate in, 193–194City income tax, 408

Closed-ended problems, 2Coefficient matrix, 215Coefficient of performance (COP), 86Coefficient of volumetric thermal expansion, 109Coils

in batch-annealing system design, 366, 367slow transient response of, 368

Colebrook formula, 356Combined transport modes, of manufacturing processes, 323

Combustors, 33Communicating design, xvii, 71, 90–92, 628Communication modes, 90–91

Complex geometries, of thermal systems, 22Complex systems, modeling approach, 251Component availability, as source of design information, 625

Component designeconomic factors determining decisions, 419

vs system design, 361–362

Component interactions, 47Component modeling, 248isolating system parts for, 248–249mathematical modeling, 249–250numerical modeling, 250

Composite functions, combining objective

function and constraints as, 537

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 finding roots of

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-flow heat exchangers, 8

Concentric pipe parallel-flow heat exchangers, 8

Conceptual design, xiii, 4, 58, 114, 610example, 59–62

existing system design modifications, 64–70innovation in, 58–62

selection from available concepts, 62–64for thermoforming application, 328Condensation soldering facility, 59, 60, 61conceptual design for, 69

control systems for, 88for surface-mounted components, 62Condensation technique

achieving nonzero degree of difficulty with, 578

removal of interior nodes by, 244Condenser, 342

block representation, 260Condensers, 39

Conduction-convection problem, 171, 172Conduction heat transfer, analog model, 129Confidentiality, and professional ethics, 624Conjugate transport, for cooling of electronic equipment, 330

Conservation lawsconstraints due to, 435, 621and constraints of thermal systems, 486and equality constraints, 537

equality constraints from, 436and finite-element method, 243

in mathematical modeling, 146–148Conservation of mass, 23

Constrained multivariable problems, 553Constrained optimization, 491–493, 514conversion to unconstrained, 489–491, 511geometric programming with, 573–575hot-rolling process geometric example, 576–578

Lagrange multipliers for, 481–484manufacturing cost example, 575–576Constrained steepest descent method, 546–547

Constraints, 14, 41, 53–55, 56 See also Design

constraintsarising from conservation laws, 435choice of components and, 300combining with objective function, 537dependence on mechanical strength and structural integrity, 363

effect of relaxing, 450

in environmental systems design, 337equality and inequality types, 436for extrusion die design, 616

in heat transfer system design, 345

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

Control volume models, 126, 244

inflow and outflow of material and energy

in, 437

Convection coefficients, 101

Convective cooling, lumped mass

approximation of heated body

in environmental systems design, 340

in fluid flow 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 coefficient, 188

Corrosion resistance, 110Cost comparisons, 413annual costs, 415life-cycle savings, 415–417present worth analysis, 413–415

Cost considerations, 362 See also Economic

considerationsbalancing with quality, 383

as constraint on materials selection, 321Cost function, in metal-rolling process example, 563–564

Costs incurred, as objective function, 432Counterflow heat exchanger, 79, 346acceptable design example, 346–350effectiveness of, 344

Coupled equations, 251–252

in numerical modeling, 209Coupled submodels, 78Coupled transport phenomena, of thermal systems, 22

Coupling

in manufacturing processes, 323

of modeled individual parts, 251Crank-Nicolson method, 241, 245for thermoforming application, 326Creative problem solving, 59Critical-path problems, software procedures for, 587

Cross-flow heat exchangers, with unmixed fluids, 8

Crout’s method, 216Crystal growing, 25Cubic spline interpolation, 184Curve fitting, 127, 180–181, 191, 195, 207, 309,

441, 448, 494–495best fit method, 183–191exact fit method, 181–183examples in thermal processes, 128public-domain software for, 212

Custom-made products, vs off-the-shelf, 460

Cylindrical gas furnaces, mathematical modeling example, 153–157Cylindrical storage tank, optimization problem, 490–491

Czochralski crystal-growing process, acceptable design example, 370–373

D

Daily compounding, 386, 387, 389Data comparison, in model validation, 162–163Data reporting, and professional ethics, 624Decision making, in expert systems, 600

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

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

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 specifications, 47–50

Design process, 40acceptable design evaluation, 81–82communicating the design, 90–92defining need or opportunity, 9–10engineering design, 14–15evaluation and market analysis, 10–11fabrication, testing, and production, 18–19feasibility and chances of success, 12–14

as function of number of variables, 52modeling in, 75–76

need for optimization, 16–18optimal design, 83–86patents and copyrights, 92–97physical system, 72–74research and development, 15–16safety features, automation, and control, 86–88

schematic, 6simulation, 76–79steps in, 70–72Design projects, 635–637Design requirements, 47–50, 56choice of components and, 300

in cooling of electronic equipment, 331

in environmental systems design, 337, 339

in heat transfer system design, 345Design rules, 609, 619

for die design, 616Design specifications, 15, 50, 57–60communicating design through, 91Design strategies, 309, 464–465adjusting design variables, 309ingot casting system example, 310–315iterative redesign procedure, 317–322multiple designs, 309–310

and selection of acceptable designs, 315Design values analysis, 2–3

Design variables, 51–52, 56adjusting in initial design, 309choice for optimization, 457–458continuous changes in, 494for cooling of electronic equipment, 331determination for optimization, 438, 439for die design, 615

economic factors determining decisions, 419

in environmental systems design, 337, 339, 372

example, 53hardware, 52

in heat transfer system design, 345

as inputs for fixed operating conditions, 310interdependence of, 321

operating conditions, 52–53

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

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

Direct labor costs, 420

Direct methods, for approximating linear

algebraic equations, 213–216

Dirichlet conditions, 242

Discounted cash flow, 417

Discrete models, 133, 258–259

Discretization, of mathematical equations, 132

Distance, variation with time, 233

Domain of acceptable designs, 40, 83, 430

See also Acceptable designs

Fibonacci search methods for narrowing,

penalty function method for, 540for thermal systems, 299–300Dot product, 479

Drag force, 167

in optimization example, 452–453Draw speed, 547

Draw tower, 74Dry air, properties at atmospheric pressure, 659–662

Drying processes, 25Durability, as objective function, 433Dynamic modeling, 133, 257–258, 277for choice of optimum path, 443Dynamic programming, xiv, 41, 467, 588–590, 592

in optimization, 442–444problems, 594–598requirements for, 559for thermal systems, 449Dynamic similarity, in physical models, 178

E

Eckert number, 170Economic considerations, xiv, 383–384annual costs, 415

application to thermal systems, 419–420bond investments, 406–407

calculation of interest, 385–390changes in payment schedules, 403–405changing amount in series of payments, 400–402

compound interest, 385–387constraints based on, 621–622continuous compounding, 387continuous compounding in series of amounts, 399–400

cost comparisons, 413–417depreciation, 410–413effective interest rate, 388–390future worth, 391–393future worth of uniform series of amounts, 396–397

inclusion of taxes in ROI calculations, 409–410

income taxes, 409inflation, 393–396life-cycle savings, 415–417present worth, 390–391

present worth analysis, 413–415

present worth of uniform series of amounts,

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

Efficiency

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

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,

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, 332–336Electronic materials, 108

Electronic systemswith fan air cooling, 31heat removal rate per unit cost as objective function for, 458

material selection for, 112rate of energy removed as objective function for, 450

Elimination methods, 513, 517, 529comparison for single-variable problems, 524–527

converting constrained to unconstrained problems using, 511

Elliptic problems, 242Empirical models, 130

as source of design information, 625Enclosure configuration models, 126

Encyclopedia of Science and Technology,

627Energy, as maximum useful work, 456Energy analysis, 456

Energy balance constraints, minimizing heat loss with, 495

Energy balance equations, 55, 357, 435

at furnace wall, 146Energy consumption rate

as objective function, 432, 447per unit of output, 433, 447Energy conversion systems, 28Energy exchange, by convection, 274Energy input, minimizing as objective function, 448

Energy losses, 566

in heat transfer system design, 342minimizing as objective function, 448optimizing according to, 431Energy rating, 433

Energy storage, 28Energy supply rate, 565maximizing with multivariable geometric programming, 568–570

Energy systems, 28power per unit cost as objective function for, 449–450

Energy transfer, in environmental systems design, 337

Engine efficiency, in automobiles, 452–453Engineering design, 2, 14–15

defining need or opportunity for, 9–10design values analysis, 2–3

examples, 4–6

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 fitting for, 180

in fluid flow systems, 351

Ethics, 623–625 See Also Professional ethics

Euler number, 170

Euler’s method, graphical interpretation, 230

Evaluation, for economic visibility, 10–11

Exhaustive search method, 442, 513, 551

relative inefficiency of, 519

for single-variable problems, 517–519

vs selective search, 616

Existing systems, 301

design modifications to, 64–70

economic factors determining decisions, 419

information on, 619

modification for initial design, 303

simulation for design modifications, 256

Experimental results, falsification of, 624

Expert knowledge, 301

in ingot casting design, 612–613

for initial design, 304

Extrusion facility, minimum cost example, 488–489

F

Fabriciation, in design process, 18–19Facilities taxes, 409

Facilities upgrades, 413Fan air cooling, 31Fan and duct system, unconstrained multivariable search example, 531–532Fans, 352, 361

blade profiles in, 353cost and interest calculations, 393Fatigue characteristics, 110Feasibility analysis, 12–14Fiber quality, as objective function, 548Fibonacci search methods, 442, 513, 525, 531,

552, 553efficiency of, 526and golden section search, 523reducing interval of uncertainty with, 523for single-variable problems, 521–523Fidap, 212, 247

Fin-tube compact heat exchanger cores, 8Final optimized design, 431–432, 611Financial aspects, xvii

importance in design, 630Finite-difference grid, 240Finite-difference method (FDM), 98, 132, 235,

242, 243, 276, 619

in knowledge-based systems, 603

of partial differential equations, 240–242Finite-element methods (FEM), 98, 132, 235, 243

Fixed roof storage vessels, 354Flat curve, 473

Flow

in enclosed region, 149scale models for, 166Flow rate

best fit modeling for circular pipes, 193–194

as design parameter in pumping systems, 430minimizing as objective function, 447

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 flow, 362, 447

analytical results, 3

complex nature of, 22

for cooling of electronic equipment, 331

physical modeling over a car, 131

velocity profile for, 2

Fluid flow rate, minimizing as objective

function, 448

Fluid flow systems and equipment, 1, 38, 357

acceptable design of, 350–351

objective function for, 450

pipes and pumps in, 350

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 coefficients in, 331

variation of board width for components,

334, 335, 336

Forced convection heat transfer correlations

for external flow, 690–691

for flow in circular tube, 694–695

in knowledge-based systems, 603Froude number, 170, 177, 180Fuel cells, 33

Fuel consumption rate, per unit output, 448Fully implicit method, 241

Furnace temperature, in optical fiber drawing, 547

Furnace walls, in batch-annealing system design, 366

Furnaces, 39Future factor worth, 392Future worth, 391–392

of bond investments, 406

of lumped sum at present, 402packaging facility example, 404, 405

of series of increasing amounts, 402

of series of uniform amounts, 402with shift in time, 402

of uniform series of amounts, 396–397Fuzzy logic, 445, 591, 620

G

Galerkin’s method, 244Gas holders, 354Gas turbines, 33Gas water heaters, 10Gases, properties at atmospheric pressure, 662–665

Gate valves, 355Gauss-Jordan elimination, 214, 218, 219, 586

in knowledge-based systems, 603simplex algorithm basis in, 583Gauss-Seidel method, 217, 227, 237, 266, 270, 650–652

Gaussian elimination, 214, 216, 234, 236for tridiagonal system, 648–650General form of polynomial method, 181Generalized reduced gradient method,

542, 547Generation stage, of thermal energy, 39Genetic algorithms (GAs), 445, 591, 620Geometric programming, xiv, 41, 467, 559–560

applicability, 560–561constrained optimization with, 573–578degree of difficulty in, 561

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 difficulty,

578–579

problems, 594–598

rate of energy supply example, 588–589

with single independent variable, 562–567

unconstrained optimization with, 561–570

in environmental systems design, 337, 339

in heat transfer system design, 345

Glass fiber drawing system, 73

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,

Graphical representation models, 126

for linear programming, 580–581

Grashof number, 170, 173, 179, 180Guessed values, 503

H

Hardware

as design variable, 52optimization of, 431

vs operating conditions in problem

formulation, 437–438Head losses, 359

in fluid flow systems, 351

in piping systems, 356Heat conduction, analytical results, 3Heat exchange rate, maximizing in optimization process, 447Heat exchangers, 39, 85, 342, 361block representation, 260convergence criterion selection for, 318domain of acceptable designs, 83fouling of, 345

given requirements, 318idealization of perfectly insulated outer surface, 145

mathematical modeling example, 151outer diameter constraints on, 346

selection vs design for, 7

types of, 8use of design libraries for, 304variation of cost with heat transfer rate in, 443

Heat flux, step change in, 145Heat input rate

optimizing according to, 431specifying operating conditions in terms

of, 438Heat losses

in environmental systems design, 337, 338minimizing in electronic circuitry, 496–498

minimizing while meeting energy balance constraints, 495

neglecting, 14Heat pipes, 28Heat pumps, 35, 36, 37use of design libraries for, 304Heat rejection, 32, 371, 451–452acceptable system design example, 338–342

to ambient air and water, 31, 338–342cost per unit of generated power in, 451

in environmental systems, 336–342, 338–342three-dimensional problem, 339

two-dimensional surface flow due to, 341

Heat removal

by boiling, 28

rate per unit mass flow rate of refrigerant,

306

Heat removal rate

in electronic component cooling, 85

maximizing in optimization process, 447

Heat removal subsystems, dynamic simulation

from cooling ponds, 337

dimensionless groups used in, 170

length constraints in system design, 349

physical modeling of, 131

scale models for flow and, 166

use of analog models in, 129

Heat transfer coefficient, 80, 103, 496

for cooling of electronic equipment, 331

effect on solidification rate, 313

in environmental systems design, 338

for forced convective cooling, 333

in heat transfer system design, 344

relationship to Reynolds number, 346

Heat transfer correlations, 687, 692–694

forced convection correlations for flow in

circular tube, 694–695

forced convection heat transfer correlations

for external flow, 691–692

natural convection correlations for external

flows over isothermal surfaces, 687–688

for natural convection in 2D rectangular

enclosures, 689–690

Heat transfer equipment, 28, 39

acceptable design strategies, 342

counterflow heat exchanger design example,

346–350

design problem, 345–350

modeling and simulation of, 342–345

Heat transfer rate, 79

in electronic cooling problem, 549

maximizing for heat exchangers and cooling

systems, 463

variation of cost with, 443

Heat transfer systems, objective function for, 450

in, 522heat per unit cost as objective function for, 450

single-variable problems for, 515Height, as objective function, 435Hemstitching method, 542, 543cost function example, 544–547Heuristics, 620

in knowledge-based systems, 603Hill-climbing techniques, 513–514, 529, 553steepest ascent methods as, 532Hot rolling, 26, 28, 454

calculus-based optimization example, 474–475

constrained optimization geometric programming example, 576–578Hot water baths, 39

Hot water storage systems, 313, 354calculated temperature profiles for inflow/outflow configurations, 316computer flowchart for, 132mathematical modeling example, 152–153, 157–160

I

Ideal turbine behavior, 145Idealizations, in mathematical modeling, 144–145

Immersion cooling, heat transfer coefficients for, 331

Imprecise characteristics, in knowledge-based design, 620

Incinerators, 31Increment present worth factor, 401Independent variables, 467, 475data points for exact fit with second-order polynomials, 185

dimensional analysis to reduce, 166and gradient vector direction in steepest ascent method, 533

multiple, 190–191

vs number of equality constraints for

optimization, 491, 537Indian Institute of Technology, xvIndustrial bonds, example calculations, 407Industrial hot water, geometric programming single-variable example, 564–567

Inequality constraints, 436, 499, 539, 542

converting to equality constraints, 439, 475

determination for optimization, 439

penalty function method for domain with, 540

solid-liquid interface movement, 614

Ingot casting system, design strategy example,

component selection in, 301–303

expert knowledge for, 304

library of previous designs for, 304

modification of existing systems in, 303

power plant example, 307–309

refrigeration system example, 305–306

Institute of Electrical and Electronics

Engineers (IEEE), codes of ethics, 623

Insulated wire manufacturing, dynamic

4% compound interest rate, 679–68010% compound interest rate, 680–68316% compound interest rate, 683–685Interior nodes, removal by condensation, 244Internal appeal processes, 624

Internal combustion engines, 33mathematical modeling example, 150–151Internal rate of return, 417

Internet, as source of design information, 627Interpolation, 645–647

with single polynomials, 184Interval of uncertainty, 513, 518reducing with Fibonacci method, 523reduction in uniform exhaustive search, 518

in sequential dichotomous search method, 521

in uniform dichotomous search method, 520

Inventionsdescription in patents, 94proof of authenticity, 92Investment yields, example, 395–396Isotherms, 174

Iterations, 449, 628

in hill-climbing techniques, 513–514with slack variables, 586

Iterative methods, 234, 300–301convergence criterion, 317

in numerical modeling, 211for solving linear algebraic systems, 216–218Iterative redesign, 103, 112, 317, 373

convergence criterion for, 317–320

of existing systems, 303initial design effects on convergence

of, 300similarities to nonlinear algebraic equations, 319

system redesign and, 320–322

J

Jacobian method, 266Jaluria, Yogesh, xixJet compressors, 353Judgment, role in design, 3