Solução Numérica da Eq. de Difusão de Calor 1D em Regime Permanente com Propriedades Constantes Dados de entrada 13 = Nx: número de volumes de controle (direção x, incluindo fictícios) 13 = Ny: número de volumes de controle (direção y, incluindo fictícios) 1.0000000000E+00 = k: condutividade térmica [W/m.K] 1.0000000000E+00 = Lx: comprimento do domínio (direção x) [m] 1.0000000000E+00 = Ly: comprimento do domínio (direção y) [m] 500 = itmax: número máximo de iterações do processo iterativo -1.0000000000E-12 = tol: tolerância empregada Comportamento da norma L1 Iteração Norma L1/NormaL1(inicial) 1 1.000000000000000E+00 2 3.461329477135798E-01 3 2.460883393161785E-01 4 1.976065358334586E-01 5 1.656107860571104E-01 6 1.439378448302387E-01 7 1.277170304875992E-01 8 1.145417011126343E-01 9 1.037056328784977E-01 10 9.453008895026309E-02 11 8.664835545715463E-02 12 7.976995558971334E-02 13 7.368614247230276E-02 14 6.823188409818654E-02 15 6.328283021759111E-02 16 5.874596725958657E-02 17 5.455424131674473E-02 18 5.065981379850939E-02 19 4.702883290663056E-02 20 4.363692917663524E-02 21 4.046598781027659E-02 22 3.750181306024523E-02 23 3.473258890306838E-02 24 3.214787003781623E-02 25 2.973798284337441E-02 26 2.749368248402816E-02 27 2.540598393303907E-02 28 2.346609436083228E-02 29 2.166540497520264E-02 30 1.999551237995840E-02 31 1.844825219605658E-02 32 1.701573437505203E-02 33 1.569037468661410E-02 34 1.446491973638161E-02 35 1.333246470494147E-02 36 1.228646399779626E-02 37 1.132073552820753E-02 38 1.042945957785140E-02 39 9.607173230152487E-03 40 8.848761322208291E-03 41 8.149444764117572E-03 42 7.504766958197867E-03 43 6.910578932343683E-03 44 6.363023690817114E-03 45 5.858520186522529E-03 46 5.393747232865342E-03 47 4.965627600550876E-03 48 4.571312484215780E-03 49 4.208166474237604E-03 50 3.873753129015803E-03 51 3.565821210983873E-03 52 3.282291624324819E-03 53 3.021245072626281E-03 54 2.780910439517232E-03 55 2.559653883842258E-03 56 2.355968632396570E-03 57 2.168465447095391E-03 58 1.995863739178551E-03 59 1.836983300264726E-03 60 1.690736618427559E-03 61 1.556121746721843E-03 62 1.432215691516716E-03 63 1.318168288438378E-03 64 1.213196534530434E-03 65 1.116579346325966E-03 66 1.027652714790081E-03 67 9.458052294727043E-04 68 8.704739456584080E-04 69 8.011405697827539E-04 70 7.373279398544867E-04 71 6.785967790806020E-04 72 6.245427023026290E-04 73 5.747934562131125E-04 74 5.290063756277409E-04 75 4.868660393279138E-04 76 4.480821101638795E-04 77 4.123873452136497E-04 78 3.795357628358123E-04 79 3.493009544283136E-04 80 3.214745296180332E-04 81 2.958646844536776E-04 82 2.722948829678040E-04 83 2.506026432109841E-04 84 2.306384195407451E-04 85 2.122645735879906E-04 86 1.953544269015310E-04 87 1.797913888266096E-04 88 1.654681536655726E-04 89 1.522859616410573E-04 90 1.401539186065982E-04 91 1.289883698535194E-04 92 1.187123237171945E-04 93 1.092549210392245E-04 94 1.005509468375218E-04 95 9.254038083848525E-05 96 8.516798378098500E-05 97 7.838291664721096E-05 98 7.213839020866314E-05 99 6.639134246846629E-05 100 6.110214178957288E-05 101 5.623431365837971E-05 102 5.175428920938466E-05 103 4.763117377204183E-05 104 4.383653385531325E-05 105 4.034420109229979E-05 106 3.713009180357044E-05 107 3.417204092977096E-05 108 3.144964919203606E-05 109 2.894414242771773E-05 110 2.663824212741526E-05 111 2.451604628872821E-05 112 2.256291975781675E-05 113 2.076539330672383E-05 114 1.911107075124059E-05 115 1.758854346629652E-05 116 1.618731171291687E-05 117 1.489771223048621E-05 118 1.371085159843268E-05 119 1.261854490706518E-05 120 1.161325931207079E-05 121 1.068806208806212E-05 122 9.836572818300644E-06 123 9.052919395459044E-06 124 8.331697525113317E-06 125 7.667933457396948E-06 126 7.057049686718771E-06 127 6.494833384649824E-06 128 5.977407346115880E-06 129 5.501203252819814E-06 130 5.062937063953486E-06 131 4.659586369316403E-06 132 4.288369545567400E-06 133 3.946726573937123E-06 134 3.632301385165208E-06 135 3.342925611423736E-06 136 3.076603633420212E-06 137 2.831498816549111E-06 138 2.605920846812114E-06 139 2.398314072434937E-06 140 2.207246776353865E-06 141 2.031401302433662E-06 142 1.869564968806831E-06 143 1.720621704782902E-06 144 1.583544353927461E-06 145 1.457387590388085E-06 146 1.341281400298037E-06 147 1.234425081060618E-06 148 1.136081720312135E-06 149 1.045573113280496E-06 150 9.622750860129261E-07 151 8.856131909594894E-07 152 8.150587448223545E-07 153 7.501251836636155E-07 154 6.903647064098856E-07 155 6.353651874988982E-07 156 5.847473337615094E-07 157 5.381620697991241E-07 158 4.952881297609746E-07 159 4.558298424410939E-07 160 4.195150919390138E-07 161 3.860934409085208E-07 162 3.553344038684334E-07 163 3.270258574508362E-07 164 3.009725775453322E-07 165 2.769948932910226E-07 166 2.549274472248712E-07 167 2.346180558276477E-07 168 2.159266595285821E-07 169 1.987243572440936E-07 170 1.828925164909959E-07 171 1.683219563827303E-07 172 1.549121940251274E-07 173 1.425707517380362E-07 174 1.312125192504809E-07 175 1.207591669675799E-07 176 1.111386054816417E-07 177 1.022844886278077E-07 178 9.413575545665802E-08 179 8.663621041755953E-08 180 7.973413399865933E-08 181 7.338192775170691E-08 182 6.753578477133422E-08 183 6.215538853444184E-08 184 5.720363423864900E-08 185 5.264637281950284E-08 186 4.845217622168951E-08 187 4.459212034727864E-08 188 4.103958474033877E-08 189 3.777007030411958E-08 190 3.476102940988037E-08 191 3.199171055352558E-08 192 2.944301626292548E-08 193 2.709736935390339E-08 194 2.493859426756206E-08 195 2.295180264790563E-08 196 2.112329361863519E-08 197 1.944045698484920E-08 198 1.789168753858745E-08 199 1.646630437384671E-08 200 1.515447768267585E-08 201 1.394716083610291E-08 202 1.283602767046139E-08 203 1.181341548212742E-08 204 1.087227204193740E-08 205 1.000610703441096E-08 206 9.208947156522637E-09 207 8.475294853124551E-09 208 7.800090650537916E-09 209 7.178678193292304E-09 210 6.606771871189795E-09 211 6.080428087402088E-09 212 5.596016524685186E-09 213 5.150196681921947E-09 214 4.739894239208629E-09 215 4.362279450788223E-09 216 4.014748339203286E-09 217 3.694903956907884E-09 218 3.400540877708180E-09 219 3.129628924551080E-09 220 2.880299619747796E-09 221 2.650833797555523E-09 222 2.439648960809511E-09 223 2.245288675832454E-09 224 2.066412433879495E-09 225 1.901786695555570E-09 226 1.750276477806436E-09 227 1.610836648021128E-09 228 1.482505580283375E-09 229 1.364398333299027E-09 230 1.255700349202877E-09 231 1.155662138083176E-09 232 1.063593503747175E-09 233 9.788599493170320E-10 234 9.008765777350420E-10 235 8.291064032182869E-10 236 7.630534501854620E-10 237 7.022632533060195E-10 238 6.463157722259771E-10 239 5.948253821557373E-10 240 5.474372956364295E-10 241 5.038243665333996E-10 242 4.636860725639633E-10 243 4.267452683725369E-10 244 3.927477041206997E-10 245 3.614586185860995E-10 246 3.326620494192785E-10 247 3.061597975876950E-10 248 2.817689008993408E-10 249 2.593211156229890E-10 250 2.386616851588417E-10 251 2.196481354027400E-10 252 2.021493334045790E-10 253 1.860447103850131E-10 254 1.712228991910350E-10 255 1.575821187758741E-10 256 1.450280591738118E-10 257 1.334738669653048E-10 258 1.228404311295653E-10 259 1.130540967485335E-10 260 1.040474006382933E-10 261 9.575827152966522E-11 262 8.812938908321827E-11 263 8.110835037687368E-11 264 7.464664490391306E-11 265 6.869977082113462E-11 266 6.322654239745475E-11 267 5.818957870671367E-11 268 5.355369010203554E-11 269 4.928728214298793E-11 270 4.536075425948843E-11 271 4.174682868440217E-11 272 3.842103874517251E-11 273 3.536011833156342E-11 274 3.254305926938332E-11 275 2.995043839579964E-11 276 2.756432877623695E-11 277 2.536840897826074E-11 278 2.334735695795063E-11 279 2.148743574446445E-11 280 1.977549713748531E-11 281 1.819999498256079E-11 282 1.675008194113790E-11 283 1.541570308776427E-11 284 1.418757399976417E-11 285 1.305726907744617E-11 286 1.201692720513000E-11 287 1.105970452336443E-11 288 1.017853942728046E-11 289 9.367606548040414E-12 290 8.621309371684533E-12 291 7.934475210155546E-12 292 7.302301567294144E-12 293 6.720570242822632E-12 294 6.185311456334815E-12 295 5.692455287985613E-12 296 5.238975983740148E-12 297 4.821506976015605E-12 298 4.437412823141668E-12 299 4.083885300483981E-12 300 3.758524394347344E-12 301 3.459160180298905E-12 302 3.183529846475599E-12 303 2.929869457491713E-12 304 2.696511236510553E-12 305 2.481663011602006E-12 306 2.283953381636942E-12 307 2.102048655931320E-12 308 1.934715067222705E-12 309 1.780449412981821E-12 310 1.638577966173313E-12 311 1.508018480226555E-12 312 1.387922130671299E-12 313 1.277317518660947E-12 314 1.175572947950827E-12 315 1.081983338140435E-12 316 9.957292739691555E-13 317 9.164695407141072E-13 318 8.434800793137968E-13 319 7.763315399952814E-13 320 7.144241044924292E-13 321 6.575629869382942E-13 322 6.051758958400837E-13 323 5.568070964571362E-13 324 5.125643196927324E-13 325 4.716467277722986E-13 326 4.342262087311465E-13 327 3.995610518100808E-13 328 3.676712231776556E-13 329 3.384615517924165E-13 330 3.114635578942077E-13 331 2.866544670898406E-13 332 2.638344942553281E-13 333 2.427215825427798E-13 334 2.234029103543063E-13 335 2.057665498794810E-13 336 1.891589871283942E-13 337 1.742605530932331E-13 338 1.603960394772974E-13 339 1.474983883450876E-13 340 1.358509835077827E-13 341 1.250454905877804E-13 342 1.150201286431248E-13 343 1.058501951255503E-13 344 9.735482185283763E-14 345 8.977712084333242E-14 346 8.236942543284562E-14 347 7.591853227277912E-14 348 6.986353706693427E-14 349 6.435707145313009E-14 350 5.922055086038829E-14 351 5.456784725465146E-14 352 5.010869513140573E-14 353 4.617239740354368E-14 354 4.247871794024556E-14 355 3.907342154516798E-14 356 3.603868736338010E-14 357 3.318380299663654E-14 358 3.061347510630408E-14 359 2.816331454263302E-14 360 2.585822501199617E-14 361 2.372233873048219E-14 362 2.184996267042730E-14 363 2.015194341459349E-14 364 1.858939785265890E-14 365 1.691316548244989E-14 366 1.564350849199535E-14 367 1.447420695770488E-14 368 1.343726229656561E-14 369 1.207363778949989E-14 370 1.142879535038417E-14 371 1.044949644327763E-14 372 9.639987117909932E-15 373 8.835045015024482E-15 374 8.008377745736969E-15 375 7.580293216859998E-15 376 6.850370829206664E-15 377 6.370071837897465E-15 378 5.930476673980764E-15 379 5.322665768504923E-15 380 4.984259270259185E-15 381 4.619714681185967E-15 382 4.238567621197537E-15 383 3.922966375751689E-15 384 3.465102321905982E-15 385 3.343145137785322E-15 386 3.053867140835153E-15 387 2.737556124327874E-15 388 2.692963985903189E-15 389 2.550145704498732E-15 390 2.209548173845968E-15 391 2.132985478045523E-15 392 1.936008578692746E-15 393 1.773995619018286E-15 394 1.620037017910500E-15 395 1.648859894926870E-15 396 1.485828568077314E-15 397 1.346435703534545E-15 398 1.209881923237500E-15 399 1.131344212309595E-15 400 1.021329697787795E-15 401 9.430697233621895E-16 402 1.020897663228663E-15 403 9.474826477876081E-16 404 9.787434341019373E-16 405 8.998971270603668E-16 406 8.375915717112745E-16 407 7.584675281674050E-16 408 7.085366769763047E-16 409 7.041854717736192E-16 410 6.983838648367052E-16 411 5.771981710002092E-16 412 6.237344649409875E-16 413 5.615832076487280E-16 414 5.489924862111699E-16 415 4.930131511922232E-16 416 4.429588615556567E-16 417 4.003108786470655E-16 418 4.338861358138870E-16 419 4.085812544933046E-16 420 3.330677854793230E-16 421 4.085503948819381E-16 422 3.769810124539433E-16 423 3.254763210831483E-16 424 4.000331421447665E-16 425 3.603785415387320E-16 426 3.200758890939997E-16 427 3.843873191819186E-16 428 3.759626452788467E-16 429 3.154469473890151E-16 430 3.851588094660827E-16 431 3.728149649194572E-16 432 3.066210985381779E-16 433 3.667973407029773E-16 434 3.658098331392472E-16 435 3.037511546810874E-16 436 3.659332715847135E-16 437 3.656863946937810E-16 438 3.037202950697208E-16 439 3.659332715847135E-16 440 3.656863946937810E-16 441 3.037202950697208E-16 442 3.659332715847135E-16 443 3.656863946937810E-16 444 3.037202950697208E-16 445 3.659332715847135E-16 446 3.656863946937810E-16 447 3.037202950697208E-16 448 3.659332715847135E-16 449 3.656863946937810E-16 450 3.037202950697208E-16 451 3.659332715847135E-16 452 3.656863946937810E-16 453 3.037202950697208E-16 454 3.659332715847135E-16 455 3.656863946937810E-16 456 3.037202950697208E-16 457 3.659332715847135E-16 458 3.656863946937810E-16 459 3.037202950697208E-16 460 3.659332715847135E-16 461 3.656863946937810E-16 462 3.037202950697208E-16 463 3.659332715847135E-16 464 3.656863946937810E-16 465 3.037202950697208E-16 466 3.659332715847135E-16 467 3.656863946937810E-16 468 3.037202950697208E-16 469 3.659332715847135E-16 470 3.656863946937810E-16 471 3.037202950697208E-16 472 3.659332715847135E-16 473 3.656863946937810E-16 474 3.037202950697208E-16 475 3.659332715847135E-16 476 3.656863946937810E-16 477 3.037202950697208E-16 478 3.659332715847135E-16 479 3.656863946937810E-16 480 3.037202950697208E-16 481 3.659332715847135E-16 482 3.656863946937810E-16 483 3.037202950697208E-16 484 3.659332715847135E-16 485 3.656863946937810E-16 486 3.037202950697208E-16 487 3.659332715847135E-16 488 3.656863946937810E-16 489 3.037202950697208E-16 490 3.659332715847135E-16 491 3.656863946937810E-16 492 3.037202950697208E-16 493 3.659332715847135E-16 494 3.656863946937810E-16 495 3.037202950697208E-16 496 3.659332715847135E-16 497 3.656863946937810E-16 498 3.037202950697208E-16 499 3.659332715847135E-16 500 3.656863946937810E-16 Soluções numéricas - Campo de temperaturas 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 1.7734857499E-03 5.1767799815E-03 8.1606822865E-03 1.0483454646E-02 1.1956919858E-02 1.2461706533E-02 1.1956919858E-02 1.0483454646E-02 8.1606822865E-03 5.1767799815E-03 1.7734857499E-03 0.0000000000E+00 0.0000000000E+00 5.4641345178E-03 1.5949731871E-02 2.5143176805E-02 3.2299671086E-02 3.6839438110E-02 3.8394692950E-02 3.6839438110E-02 3.2299671086E-02 2.5143176805E-02 1.5949731871E-02 5.4641345178E-03 0.0000000000E+00 0.0000000000E+00 9.5974549678E-03 2.8014836180E-02 4.4162621976E-02 5.6732614784E-02 6.4706468545E-02 6.7438189048E-02 6.4706468545E-02 5.6732614784E-02 4.4162621976E-02 2.8014836180E-02 9.5974549678E-03 0.0000000000E+00 0.0000000000E+00 1.4508304141E-02 4.2349535906E-02 6.6759860134E-02 8.5761697530E-02 9.7815632237E-02 1.0194512615E-01 9.7815632237E-02 8.5761697530E-02 6.6759860134E-02 4.2349535906E-02 1.4508304141E-02 0.0000000000E+00 0.0000000000E+00 2.0594529832E-02 6.0115143168E-02 9.4765585124E-02 1.2173868297E-01 1.3884923672E-01 1.4471105109E-01 1.3884923672E-01 1.2173868297E-01 9.4765585124E-02 6.0115143168E-02 2.0594529832E-02 0.0000000000E+00 0.0000000000E+00 2.8349201849E-02 8.2750921812E-02 1.3044865423E-01 1.6757821249E-01 1.9113158060E-01 1.9920060475E-01 1.9113158060E-01 1.6757821249E-01 1.3044865423E-01 8.2750921812E-02 2.8349201849E-02 0.0000000000E+00 0.0000000000E+00 3.8400557601E-02 1.1209068800E-01 1.7669989749E-01 2.2699393216E-01 2.5889826843E-01 2.6982820672E-01 2.5889826843E-01 2.2699393216E-01 1.7669989749E-01 1.1209068800E-01 3.8400557601E-02 0.0000000000E+00 0.0000000000E+00 5.1562898152E-02 1.5051137510E-01 2.3726631557E-01 3.0479935023E-01 3.4763935424E-01 3.6231568526E-01 3.4763935424E-01 3.0479935023E-01 2.3726631557E-01 1.5051137510E-01 5.1562898152E-02 0.0000000000E+00 0.0000000000E+00 6.8902558056E-02 2.0112559869E-01 3.1705463946E-01 4.0729779894E-01 4.6454411304E-01 4.8415582586E-01 4.6454411304E-01 4.0729779894E-01 3.1705463946E-01 2.0112559869E-01 6.8902558056E-02 0.0000000000E+00 0.0000000000E+00 9.1824293434E-02 2.6803382215E-01 4.2252884465E-01 5.4279309303E-01 6.1908347313E-01 6.4521939207E-01 6.1908347313E-01 5.4279309303E-01 4.2252884465E-01 2.6803382215E-01 9.1824293434E-02 0.0000000000E+00 0.0000000000E+00 1.2218508697E-01 3.5665655181E-01 5.6223382395E-01 7.2226225541E-01 8.2377729439E-01 8.5855479617E-01 8.2377729439E-01 7.2226225541E-01 5.6223382395E-01 3.5665655181E-01 1.2218508697E-01 0.0000000000E+00 0.0000000000E+00 1.4231483827E-01 4.1541501300E-01 6.5486073395E-01 8.4125353283E-01 9.5949297361E-01 1.0000000000E+00 9.5949297361E-01 8.4125353283E-01 6.5486073395E-01 4.1541501300E-01 1.4231483827E-01 0.0000000000E+00 Soluções numéricas - Temperatura em x = 0.5*Lx posição y T numérico T analítico Erro numérico 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 4.545454545454546E-02 1.246170653316575E-02 1.240702375349298E-02 -5.468277967277113E-05 1.363636363636364E-01 3.839469295019193E-02 3.823997226920157E-02 -1.547206809903584E-04 2.272727272727273E-01 6.743818904801149E-02 6.721329893624929E-02 -2.248901117622021E-04 3.181818181818182E-01 1.019451261521477E-01 1.017063779183065E-01 -2.387482338412489E-04 4.090909090909091E-01 1.447110510861208E-01 1.445518815521914E-01 -1.591695339293875E-04 5.000000000000000E-01 1.992006047493326E-01 1.992684076691934E-01 6.780291986077658E-05 5.909090909090909E-01 2.698282067177230E-01 2.703494371203276E-01 5.212304026046000E-04 6.818181818181819E-01 3.623156852642486E-01 3.636323515410094E-01 1.316666276760803E-03 7.727272727272727E-01 4.841558258565352E-01 4.867778161712052E-01 2.621990314670031E-03 8.636363636363637E-01 6.452193920741528E-01 6.498988960476447E-01 4.679503973491928E-03 9.545454545454546E-01 8.585547961701416E-01 8.663915704262905E-01 7.836774256148815E-03 1.000000000000000E+00 1.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 Soluções numéricas - Temperatura em y = 0.5*Ly posição x T numérico T analítico Erro numérico 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 4.545454545454546E-02 2.834920184884186E-02 2.835885121041630E-02 9.649361574447929E-06 1.363636363636364E-01 8.275092181192761E-02 8.277908816276315E-02 2.816635083553731E-05 2.272727272727273E-01 1.304486542284926E-01 1.304930556983562E-01 4.440146986367521E-05 3.181818181818182E-01 1.675782124874838E-01 1.676352519333529E-01 5.703944586912813E-05 4.090909090909091E-01 1.911315805967433E-01 1.911966370219403E-01 6.505642519696875E-05 5.000000000000000E-01 1.992006047493326E-01 1.992684076691934E-01 6.780291986077658E-05 5.909090909090909E-01 1.911315805967433E-01 1.911966370219403E-01 6.505642519696875E-05 6.818181818181819E-01 1.675782124874838E-01 1.676352519333529E-01 5.703944586912813E-05 7.727272727272727E-01 1.304486542284926E-01 1.304930556983563E-01 4.440146986370297E-05 8.636363636363637E-01 8.275092181192761E-02 8.277908816276314E-02 2.816635083552344E-05 9.545454545454546E-01 2.834920184884186E-02 2.835885121041631E-02 9.649361574458337E-06 1.000000000000000E+00 0.000000000000000E+00 2.440253581477619E-17 2.440253581477619E-17 Temperatura média numérica [°C]: 1.849133350827416E-01 Temperatura média analítica [°C]: 1.858539204602858E-01 Erro numérico para a temperatura média: 9.405853775442674E-04 Taxa de transferência de calor (face leste, numérica) [W]: 9.063250105305756E-01 Taxa de transferência de calor (face leste, analítica) [W]: 9.171523356672743E-01 Erro numérico para a taxa de transf. de calor (face leste) : 1.082732513669871E-02 Taxa de transferência de calor (face norte, numérica) [W]: -1.987778724214872E+00 Taxa de transferência de calor (face norte, analítica) [W]: -2.007483746394643E+00 Erro numérico para a taxa de transf. de calor (face norte) : -1.970502217977099E-02