Design and Optimization of Thermal Systems Episode 3 Part 11 potx

722 Design and Optimization of Thermal Systems Trademarks, 93 Transience effect on complexity of problem, 176 in mathematical modeling, 135–139 and time-dependent modeling, 138–139 Transient response, of ue gases, 368 Transportation cost minimization with dynamic programming, 589 dynamic programming example, 589–590 software procedures for, 587 Transportation systems, 33 requirements for, 49 thermal systems for, 34 torque delivered as objective function for, 450 weight as objective function in, 433 Tree structures, in knowledge-based systems, 600, 601 Trial points in hemstitching method, 542, 545 moving in steepest ascent methods, 534, 535 in search along constraint methods, 542 Trial runs in dichotomous search method, 519, 520–521 with golden section search method, 524 reduction ratio as function of number of, 525 Trials, 449 Tridiagonal matrix algorithm (TDMA), 215, 236 Turbine ow, integral formulation, 149 Turbulent ow, 25 in environmental processes, 337 in environmental systems design, 349 in heat transfer system design, 348 and Reynolds number, 355 in thermal systems, 22 Two-dimensional model, of ingot casting, 612 Two-dimensional problems, 139–140 in environmental systems design, 341 Two-variable problems, 527, 540 hemstitching method for, 542 U Unconstrained design problems, 439, 511 conversion of constrained to, 489–491 Unconstrained multivariable search methods, 527–529 lattice search, 529–530 steepest ascent/descent method, 532–537 univariate search, 530–532 Unconstrained optimization, 486–487 and converting constrained to unconstrained problems, 489–491 determining minimum/maximum in, 487–489 with geometric programming, 561 Lagrange multiplier method for, 480–481 multivariable problems, 567–570 with single independent variable, 562–567 single-variable problems, 562–567 terms vs. number of variables for, 561 use of gradients, 487 Uniform dichotomous search, 519–520 Uniform exhaustive search, for single-variable problems, 517–519 Uniform ow at inlet, approximation of, 143 Uniform heat ux, approximation, 143 Unimodal objective function distributions, 516 Unique solutions, 42, 86, 629 failure to achieve through overconstraint, 440 lacking in design process, 5 vs. domain of acceptable designs, 40 Unit vectors, 480 Univariate search methods, 442, 513, 514, 529, 548 for unconstrained multivariable problems, 530–532 Unix operating system, numerical modeling with, 211 Unknowns, solving problems with numbers of, 503 Utilization stage, of thermal energy, 39 V Validation, 283 example, 163–165 of mathematical models, 128, 160–163 of numerical models for systems, 252–253 three strategies for, 161–162 Valve types, 354, 355 Vapor absorption, 17, 35 Vapor compression, 17, 33, 35 mathematical modeling example, 150–151 thermodynamic cycle for, 86 Vapor compression cooling system, initial design example, 305–306 Vapor cooling systems, 17 Variable costs, 420 Variable payment frequencies, 403 Variables, deriving dimensionless parameters from combinations of, 167 Index 723 Vector notation, 477, 483, 487 Velocity, variation with time, 232, 233 Velocity components, 24 Viscosity, 109 Visual aids, communicating design through, 91 Volume, as objective function, 432 Volume ow rate constraints, 54 specifying operating conditions in terms of, 438 Volume restrictions, 54 Vortex promoter, 550, 551, 552 W Waste disposal, 31 and design of environmental systems, 36 of materials, 110 Water bodies, heat transfer factors, 337 discharge of thermal energy and chemicals into, 336 in heat rejection system, 371 modeling for environmental systems, 338 Water cooler, requirements and specications, 48 Water distribution system, acceptable design example, 356–359 Water thermal energy storage system, 313 Water treatment plants, 31 Wave motion, in water bodies, 177 Weber number, 170 Weight as objective function, 432 in transportation systems, 433 Weight restrictions, 54 Weighting factors, 514, 573, 574 Welding processes, 25 Workable designs, xiv, 81, 430, 628–629. See also Acceptable designs optimization as extension of, 465 vs. optimal design, 18 Working models, communicating design through, 91 Worth as function of time, 384, 385, 390 future worth, 391–393 ination and, 393–396 present worth, 390–391 Y Years to maturity, 407 . disposal, 31 and design of environmental systems, 36 of materials, 110 Water bodies, heat transfer factors, 33 7 discharge of thermal energy and chemicals into, 33 6 in heat rejection system, 37 1 modeling. 722 Design and Optimization of Thermal Systems Trademarks, 93 Transience effect on complexity of problem, 176 in mathematical modeling, 135 – 139 and time-dependent modeling, 138 – 139 Transient. communicating design through, 91 Worth as function of time, 38 4, 38 5, 39 0 future worth, 39 1 39 3 ination and, 39 3 39 6 present worth, 39 0 39 1 Y Years to maturity, 407