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أخواني في الله أحضرت لكم كتاب Multiphysics Modeling Using COMsOL 5 and Matlab Second edition Roger W. Pryor, Ph.D. COMSOL Certified Consultant
![كتاب Multiphysics Modeling Using COMsOL 5 and Matlab M_m_p_13](https://i.servimg.com/u/f61/15/36/74/14/m_m_p_13.jpg) و المحتوى كما يلي :
Contents Preface xi Introduction xiii Chapter 1: Modeling Methodology Using COMSOL Multiphysics 5.x 1 Guidelines for New COMSOL Multiphysics 5.x Modelers 1 Hardware Considerations 2 Simple Model Setup Overview 4 Basic Problem Formulation and Implicit Assumptions 12 1D Window Heat Flow Models 13 1D 1 Pane Window Heat Flow Model 13 1D 2 Pane Window Heat Flow Model 35 1D 3 Pane Window Heat Flow Model 49 First Principles as Applied to Model Definition 60 Some Common Sources of Modeling Errors 62 References 63 Suggested Modeling Exercises 63 Chapter 2: Materials Properties Using COMSOL Multiphysics 5.x 65 Materials Properties Guidelines and Considerations 65 COMSOL Materials Properties Sources 66 Other Materials Properties Sources 68vi • Contents Material Property Entry Techniques 69 Multipane Window Model 69 Set Boundary Conditions 86 References 88 Chapter 3: 0D Electrical Circuit Interface Modeling Using COMSOL Multiphysics 5.x 89 Guidelines for Electrical Circuit Interface Modeling in 5.x 90 Electrical / Electronic Circuit Considerations 90 Simple Electrical Circuit Interface Model Setup Overview 99 Basic Problem Formulation and Implicit Assumptions 104 0D Basic Circuit Models 105 0D Resistor-Capacitor Series Circuit Model 105 0D Inductor-Resistor Series Circuit Model 112 0D Series-Resistor Parallel-Inductor-Capacitor Circuit Model 118 0D Basic Circuit Models Analysis and Conclusions 125 First Principles as Applied to 0D Model Definition 126 References 127 Suggested Modeling Exercises 128 Chapter 4: 1D Modeling Using COMSOL Multiphysics 5.x 129 Guidelines for 1D Modeling in 5.x 129 1D Modeling Considerations 130 1D Basic Models 131 1D KdV Equation Model 131 1D Telegraph Equation Model 148 1D Spherically Symmetric Transport Model 167 1D Spherically Symmetric Transport Model Animation 184 1D Advanced Model 186 1D Silicon Inversion Layer Model: A Comparison of the Results obtained from using the Density-Gradient (DG) Theory and the Schrodinger-Poisson (SP) Theory Methodologies 186Contents • vii First Principles as Applied to 1D Model Definition 223 References 224 Suggested Modeling Exercises 226 Chapter 5: 2D Modeling Using COMSOL Multiphysics 5.x 227 Guidelines for 2D Modeling in 5.x 227 2D Modeling Considerations 228 2D Basic Models 233 2D Electrochemical Polishing Model 233 2D Hall Effect Model 256 First Principles as Applied to 2D Model Definition 270 References 271 Suggested Modeling Exercises 272 Chapter 6: 2D Axisymmetric Modeling Using COMSOL Multiphysics 5.x 273 Guidelines for 2D Axisymmetric Modeling in 5.x 273 2D Axisymmetric Modeling Considerations 274 2D Axisymmetric Heat Conduction in a Cylinder Model 278 2D Axisymmetric Basic Models 278 2D Axisymmetric Cylinder Conduction Model 278 2D Axisymmetric Transient Heat Transfer Model 290 First Principles as Applied to 2D Axisymmetric Model Definition 303 References 304 Suggested Modeling Exercises 304 Chapter 7: 2D Simple and Advanced Mixed Mode Modeling Using COMSOL Multiphysics 5.x 307 Guidelines for 2D Simple Mixed Mode Modeling in 5.x 307 2D Simple Mixed Mode Modeling Considerations 308 2D Simple Mixed Mode Models 313 2D Electric Impedance Sensor Model 313 2D Metal Layer on a Dielectric Block Model 332 Heat Transfer 2 (ht2) Interface 346 Heat Transfer in Solids (ht) Interface 358viii • Contents First Principles as Applied to 2D Simple Mixed Mode Model Definition 363 References 364 Suggested Modeling Exercises 365 Chapter 8: 2D Complex Mixed Mode Modeling Using COMSOL Multiphysics 5.x 367 Guidelines for 2D Complex Mixed Mode Modeling in 5.x 367 2D Complex Mixed Mode Modeling Considerations 368 2D Complex Mixed Mode Models Using the RF Module 370 Finding the Impedance of a Two (2) Wire, Parallel-Wire, Air-Dielectric, Transmission Line 370 2D Finding the Impedance of a Two (2) Wire, Parallel-Wire, Air-Dielectric, Transmission Line Model Summary and Conclusions 389 2D Finding the Impedance of a Concentric, Two (2) Wire, Transmission Line (Coaxial Cable) 389 2D Finding the Impedance of a Concentric, Two (2) Wire 405 2D Axisymmetric Transient Modeling of a Coaxial Cable 405 First Principles as Applied to 2D Complex Mixed Mode Model Definition 431 References 431 Suggested Modeling Exercises 432 Chapter 9: 3D Modeling Using COMSOL Multiphysics 5.x 433 Guidelines for 3D Modeling in 5.x 433 3D Modeling Considerations 434 3D Models 438 3D Spiral Coil Microinductor Model 438 3D Linear Microresistor Beam Model 455 Multiphysics Thermal Linear Elastic 1 (te1) 476 Heat Transfer in Solids (ht) 477 First Principles as Applied to 3D Model Definition 489 References 489 Suggested Modeling Exercises 490Contents • ix Chapter 10: Perfectly Matched Layer Models Using COMSOL Multiphysics 5.x 493 Guidelines for Perfectly Matched Layer (PML) Modeling in 5.x 493 Perfectly Matched Layer (PML) Modeling Guidelines and Coordinate Considerations 494 Perfectly Matched Layer Models 497 Building the 2D Concave Metallic Mirror PML Model 497 Building the 2D Energy Concentrator PML Model 517 First Principles as Applied to PML Model Definition 539 References 540 Suggested Modeling Exercises 540 Chapter 11: Bioheat Models Using COMSOL Multiphysics 5.x 543 Guidelines for Bioheat Modeling in 5.x 543 Bioheat Modeling Considerations 544 Bioheat Transfer Models 547 2D Axisymmetric Microwave Cancer Therapy Model 574 First Principles as Applied to Bioheat Model Definition 601 References 602 Suggested Modeling Exercises 602 Appendix: A Brief Introduction to LiveLinkTM for MATLAB![:registered: ®](https://cdn.jsdelivr.net/emojione/assets/png/00ae.png?v=2.2.7) Using COMSOL Multiphysics 5.x 605 Guidelines for LiveLink Exploration through Modeling in 5.x 605 Getting Started using LiveLink for MATLAB with COMSOL Multiphysics 5.x on a Windows 10 platform 606 First Principles as Applied to Scripting and GUI Model Definition 614 References 615 Suggested Modeling Exercises 615 Index 617 Index A Axisymmetric modeling, 2D coordinate system, 275 First Principles Analysis, 303 heat conduction theory, 276–277 heat transfer theory, 275–276 numerical solution model, 277 Axisymmetric transient heat transfer model, 2D axisymmetric sphere, 292–295 building, 290–292 computed results, 300–301 3D results, 301–302 Fick’s First Law, 288–289 Fick’s Second Law, 289–290 heat transfer in solids, 295–297 mesh type, 298 study settings, 299–300 Axisymmetric transient modeling of a coaxial cable, 405–430 B Bioheat Models bioheat equation theory, 544–546 First Principles Analysis, 601–602 tumor laser irradiation theory, 546 C Concave metallic mirror, 497 Concept of impedance, 311 D Distributed memory parallelism, 2 E Electrochemical polishing model, 229–232 animation, 250–251 building, 233 computed results, 249–250 deformed geometry (dg) interface, 241–243 electric currents (ec) interface, 243–246 mesh type, 247 parameters, 234 time dependent study type, 248 variables, 235–241 Electromagnetic induction discovery, 436 mutual inductance, 437 self-inductance, 436 F Fick’s First Law, 288–289 Fick’s Second Law, 289–290 First Principles Analysis bioheat models, 601–602 1D modeling, 223–224 2D axisymmetric modeling, 303 2D complex mixed mode modeling, 431 2D Hall Effect model, 270–271618 • Index 2D simple mixed mode modeling, 363–364 3D modeling, 489 LiveLink for MATLAB , 614 modeling methodology, 60–61 perfectly matched layer (pml) models, 539 0D electrical circuit interface modeling, 126–127 Fourier’s Law, 277 H Hall Effect model animation, 269–270 building, 256–257 computed results, 268–269 current conservation edit windows, 262–263 discovery, 254 electric currents (ec) interface, 259 First Principles Analysis, 270–271 Lorentz Force, 254 mesh type, 266 model geometry electric insulation 2 boundaries, 263 electric potential 1, 264 floating potential 1 setting, 265 floating potential 2 setting, 265 ground 1 boundary, 263 Ohm’s Law, 252 parameters edit window, 257–258 rectangle entry windows, 259 resistance, 253 sensors, 253 settings electric currents, 260–261 silicon conductivity parameters, 261–262 study settings, 267–268 Heat conduction theory, 276–277 Heat transfer theory, 275–276 Hyperthermic oncology, 574 K Kirchhoff’s law Current Law, 94–95 Voltage Law, 95–96 L LiveLink for MATLAB![:registered: ®](https://cdn.jsdelivr.net/emojione/assets/png/00ae.png?v=2.2.7) First Principles Analysis, 614 on Windows 10 platform COMSOL and MATLAB, 611–614 installation, 606 MATLAB Command Window, 607 M Materials properties guidelines and considerations, 65–66 multipane window model Add Physics window, 70 geometry building, 74–77 material definition, 77 from newly built material, 77–81 parameter setting, 72–74 saved Initial Model Build, 72 Select Study Type window, 71 user defined direct entry, 84–86 user defined parameters, 82–84 set boundary conditions meshing and solution computations, 87–88 sources, 66–69 Meshing, 32 Microwave cancer therapy theory, 574 bioheat transfer models, 575 2D axisymmetric model, 574–575 building, 575–576 domains, 579 electromagnetic waves, frequency domain, 590–593 heat transfer (ht), 593–595 materials, 584–590Index • 619 mesh type, 595–597 parameters, 577–579 results, 598–600 settings union, 580 study settings, 597–598 union operation, 580–581 vector coordinates, 582 Modeling methodology Desktop Display, 5 Geometric coordinate systems, 6 Model Wizard window, 5 1D heat flow model, 35 1 pane window heat flow model, 13–35 2 pane window heat flow model, 35–48 3 pane window heat flow model, 49–59 First Principles Analysis, 60–61 hardware considerations installation, 3 platform, 2–3 rules, 2 problem formulation and implicit assumptions, 12–13 Right-Hand-Rule, 4 Select Space Dimension 1D button, 9 Desktop Display, 11 Physics Interface, 11 Select Physics page, 10 sources of modeling errors, 62–63 Mutual-inductance, 97 N Newton’s Law of Cooling, 276–277 O Ohm’s Law, 91, 252 1D Cartesian Coordinate Geometry, 7 1D modeling considerations, 130 First Principles Analysis, 223–224 KdV Equation animation, 146–147 build, 133–139 mesh type, 139–141 nonlinear partial differential equations, 131 results, 144–146 solver type, 142–144 in standard notation, 131 time dependent study type, 141–142 silicon inversion layer model Add Physics window, 207 analytic doping model window, 196 build, 187–188 DG and SP theory methodologies, 187 ECC settings, 204–205 Electron Concentration Plot Settings, 206 electrostatics, 210–213, 215 Geometry 1, 188–190 Global Definitions, 190–192 materials, 192–194 Mesh 1, 199–202 metal contact model window, 197 multiphysics, 213 Parametric sweep settings, 216 results, 221 Schrodinger equation, 207–210 Schrodinger-Poisson Coupling Settings, 214 Schrodinger-Poisson modified settings, 221 semiconductor material model window, 195 semiconductor window, 194 Study 1 and 2 settings, 202, 217 thin insulator gate window values, 198 spherically symmetric transport model animation, 184–185620 • Index build, 171–173 1D Plot Group 1, 181–183 1D Plot Group 2, 183–184 Geometry 1 window, 174–175 Global Definitions, 173–174 Initial Values 1, 176–179 Mesh Type, 179–180 PDE, 175–176 results, 181 study step, 180 time-dependent heat conduction, 168–170 Telegraph Equation Model animation, 165–166 build, 150–152 default solver, 158–159 differential equations for Voltage and Current, 148 1D Plot Group 2, 159–165 Geometry 1 Window, 153 initial values coefficients, 155 lumped-constant circuit, 148 Mesh Type, 156–157 PDE, 153–154 results, 159 study step, 157 Zero Flux 1, 155 1D 1 pane window heat flow model control button array, 17 Desktop Display, 16–17 with built geometry, 21 Geometry 1 entry, 19 Global Definitions Parameters 1 selection menu, 16 initial model build, 15 materials selection button add material library, 22–23 Domain-boundary selection window, 32 expanded built-in material list, 23 expanded Heat Transfer in Solids, 27 Function List, 22 Heat Transfer in Solids Selection window, 28–29 Initial Boundaries Heat Flux window, 29 meshed 1D domain, 32 scrolled list with silica glass visible, 24 Solid 1 window Settings, 27 Twistie before built-in, 23 model wizard add physics window, 13 Done button, select study type window, 14 parameters entry table, 17–18 settings - interval window, 20–21 1D 2 pane window heat flow model, 35–48 1D 3 pane window heat flow model, 49–59 P Perfectly matched layer (PML) models 2D concave metallic mirror boundary selection, 506 computed solution, 516–517 electromagnetic waves (emw), 513 energy concentration systems, 517 general extrusion, 507–513 geometry, 500–505 in Graphics window, 505 materials, 506–507 mesh type, 514 parameters, 498 study settings, 514–516 variables, 499–500 2D energy concentrator boundaries selection, 526–529 computed solution, 538–539 difference, 525 domain, 522 electromagnetic waves (emw), 529–531 far-field calculation, 533–534 formation, 523–524Index • 621 general extrusion, 535 geometry, 521 impedance boundary condition, 532 materials, 527–528 mesh type, 535–536 parameters, 518–519 rectangle, 524–525 study settings, 536–538 variables, 520 discovery, 494 First Principles Analysis, 539 wave equation solution, 496 R Resonance, 125–126 S Schrodinger equation, 207–210 Self-inductance, 97 Sensors, 253 Series-parallel resistive circuit, 94 Series-resistor parallel-inductor-capacitor circuit model, 118–125 Shared memory parallelism, 2 Spherically symmetric transport model animation, 184–185 build, 171–173 1D Plot Group 1, 181–183 1D Plot Group 2, 183–184 Geometry 1 window, 174–175 Global Definitions, 173–174 Initial Values 1, 176–179 Mesh Type, 179–180 PDE, 175–176 results, 181 study step, 180 time-dependent heat conduction, 168–170 T Telegraph equation model, 1D modeling animation, 165–166 build, 150–152 default solver, 158–159 differential equations for Voltage and Current, 148 1D Plot Group 2, 159–165 Geometry 1 Window, 153 initial values coefficients, 155 lumped-constant circuit, 148 Mesh Type, 156–157 PDE, 153–154 results, 159 study step, 157 Zero Flux 1, 155 Thermodynamics, 276 2D axisymmetric heat conduction in cylinder model, 277 building, 278–282 computed results, 287–288 default contour plot, 288 heat flux edit windows, 285 heat transfer in solids, 282 mesh type, 285–286 stationary study type, 286–287 2D axisymmetric tumor laser irradiation model bioheat transfer, 558 boolean operations, 551–552 computed solution, 571–573 domains, 550–551, 558–565 domains formation, 553–554 geometry, 550 heat flux, 567–569 heat source, 566–567 initial values, 566 mesh type, 569–570 parameters, 548–550 study settings, 570–571 variables, 554–558 2D Cartesian Coordinate Geometry, 7622 • Index 2D complex mixed mode modeling axisymmetric transient modeling of a coaxial cable, 405–430 coordinate system, 369 First Principles Analysis, 431 radio frequency waves, 370 two (2) wire, parallel-wire, air-dielectric, transmission line model, 370–381 coaxial cables, 389–404 electromagnetic waves, frequency domain (emw), 382–389 2D metal layer on a diamond block model building, 353–354 computed results, 362–363 geometry, 354–356 heat transfer in solids (ht) interface, 358–361 materials, 356–358 mesh type, 361 study settings, 361–362 2D metal layer on a dielectric block model building, 332–333 computed results, 340–341 Fick’s First Law, 330 Fick’s Second Law, 331 geometry, 333–334 heat transfer in solids (ht) interface, 335–339 materials, 334–335 mesh type, 339 second study computed results, 350–351 geometry, 342–344 heat transfer 2 (ht2) interface, 346–349 materials, 344–346 mesh type, 349 study settings, 349–350 vs. study 1 results, 351–353 study settings, 339–340 2D modeling coordinate system, 229 electrochemical polishing theory, 229–232 (see also Electrochemical polishing model) 2D simple mixed mode modeling coordinate system, 309–310 electrical impedance theory, 310–313 electric impedance sensor model building, 313–316 computed results, 325–329 electric currents (ec) interface, 318–321 geometry, 317–318 mesh type, 321–322 study settings, 322–325 First Principles Analysis, 363–364 out-of-plane thickness, 309–310 3D Cartesian Coordinate Geometry, 6 3D modeling considerations coordinate system, 435–436 inductance theory, 436–438 First Principles Analysis, 489 heat transfer in solids, 477–488 linear microresistor beam model building, 457–458 electric currents (ec), 473–474 electric potential boundary specification, 475–476 extrude, 462–463, 467–468 fillets, 466–467 form union, 469 geometry, 459–460 intersection, 468–469 materials, 471–473 parameters, 458–459 polygon settings, 460–462, 465–466 selections, 469–471 Settings Ground window, 475 work plane, 460 Work Plane 2, 463–465 multiphysics thermal linear elastic 1, 476–477Index • 623 spiral coil microinductor model building, 438–439 color and style plot settings, 450 3D Plot Group 2, 451–454 environment, 442–443 geometry, 439–441 inductance calculation, 454–455 magnetic and electric fields, 445–449 materials, 443–445 selected spiral coil boundaries, 451 Z 0D electrical circuit interface modeling electrical circuit interface model setup, 99–104 electrical / electronic circuit considerations connection sequences, 91–92 Kirchhoff law, 94–96 Maxwell-Faraday formulation, 97 Ohm’s law, 91 parallel resistive circuit, 93 self-inductance and mutual-inductance, 97 series-parallel resistive circuit, 94 First Principles Analysis, 126–127 inductor-resistor series circuit model, 112–118 problem formulation and implicit assumptions, 104 resistor-capacitor series circuit model, 105–111 series-resistor parallel-inductor-capacitor circuit model, 118–125 0D Space Dimension, 9 #ماتلاب,#متلاب,#Matlab,#مات_لاب,#مت_لاب,
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