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Tj 1 0 0 1 416.64 486.96 Tm <646520> Tj 1 0 0 1 428.40 486.72 Tm <6368616D612E20> Tj 1 0 0 1 459.84 489.84 Tm <6C6C> Tj 0.48 Tc 1 0 0 1 100.08 477.12 Tm <4E6F20> Tj 1 0 0 1 116.40 477.36 Tm <70726F636573736F20> Tj 1 0 0 1 155.52 476.64 Tm <646520> Tj 1 0 0 1 168.72 476.64 Tm <666F726D61E7E36F20> Tj 1 0 0 1 210.48 476.16 Tm <646120> Tj 1 0 0 1 223.92 476.16 Tm <6368616D6120> Tj 1 0 0 1 253.92 475.92 Tm <646966757369766120> Tj 1 0 0 1 289.92 475.68 Tm <656D20> Tj 1 0 0 1 306.24 475.68 Tm <756D6120> Tj 1 0 0 1 327.36 475.68 Tm <76656C6120> Tj 1 0 0 1 348.24 475.44 Tm <6170726573656E74616D2D736520> Tj 1 0 0 1 408.72 475.20 Tm <636F6D6F20> Tj 1 0 0 1 434.88 474.96 Tm <636F6D62757374ED76656920> Tj 1 0 0 1 487.92 474.72 Tm <6520> Tj 1 0 0 1 496.08 474.72 Tm <6F786964616E746520> Tj 1 0 0 1 534.00 474.48 Tm <61> Tj 0.48 Tc 1 0 0 1 57.36 466.08 Tm <7061726166696E6120> Tj 1 0 0 1 94.56 465.60 Tm <6520> Tj 1 0 0 1 102.96 465.60 Tm <6F20> Tj 1 0 0 1 112.08 465.36 Tm <6F786967EA6E696F20> Tj 1 0 0 1 150.72 465.36 Tm <726573706563746976616D656E74652E20> Tj 1 0 0 1 222.24 462.96 Tm <5175616E646F20> Tj 1 0 0 1 258.00 464.64 Tm <6120> Tj 1 0 0 1 266.64 464.64 Tm <76656C6120> Tj 1 0 0 1 287.28 464.16 Tm Tj 1 0 0 1 295.92 464.16 Tm <61636573612C20> Tj 1 0 0 1 324.00 464.16 Tm <6F20> Tj 1 0 0 1 333.36 464.16 Tm <63616C6F7220> Tj 1 0 0 1 357.12 464.16 Tm <76696E646F20> Tj 1 0 0 1 384.00 464.40 Tm <28444120> Tj 1 0 0 1 405.12 463.68 Tm <4348414D4120> Tj 1 0 0 1 448.08 463.44 Tm <4F552920> Tj 1 0 0 1 470.64 463.44 Tm <646520> Tj 1 0 0 1 483.84 463.44 Tm <756D6120> Tj 1 0 0 1 504.96 463.20 Tm <666F6E746520> Tj 1 0 0 1 528.96 463.20 Tm <6465> Tj 0.48 Tc 1 0 0 1 57.60 454.32 Tm <69676E69E7E36F20> Tj 1 0 0 1 90.00 454.80 Tm <28756D20> Tj 1 0 0 1 108.48 454.08 Tm <66F373666F726F2C20> Tj 1 0 0 1 142.08 454.08 Tm <706F7220> Tj 1 0 0 1 158.40 453.60 Tm <6578656D706C6F292C20> Tj 1 0 0 1 201.12 453.36 Tm <6465727265746520> Tj 1 0 0 1 231.36 453.12 Tm <6120> Tj 1 0 0 1 238.08 453.60 Tm <7061726166696E612C20> Tj 1 0 0 1 276.00 452.88 Tm <756D20> Tj 1 0 0 1 291.36 452.64 Tm <686964726F636172626F6E65746F20> Tj 1 0 0 1 354.48 452.88 Tm <70657361646F2C20> Tj 1 0 0 1 387.84 452.88 Tm <28454D505245474E41444120> Tj 1 0 0 1 465.60 451.92 Tm <4E4F20> Tj 1 0 0 1 483.36 451.92 Tm <504156494F20> Tj 1 0 0 1 520.32 451.44 Tm <4F5529> Tj 0.48 Tc 1 0 0 1 57.36 442.80 Tm <6E6120> Tj 1 0 0 1 69.60 442.56 Tm <6261736520> Tj 1 0 0 1 90.24 442.32 Tm <646F20> Tj 1 0 0 1 102.72 442.80 Tm <706176696F2E20> Tj 1 0 0 1 130.32 442.08 Tm <436F6D6F20> Tj 1 0 0 1 156.96 442.08 Tm <6F20> Tj 1 0 0 1 164.40 442.32 Tm <706176696F20> Tj 1 0 0 1 189.84 441.60 Tm Tj 1 0 0 1 196.32 441.60 Tm <756D20> Tj 1 0 0 1 211.92 441.60 Tm <6D6174657269616C20> Tj 1 0 0 1 247.20 441.84 Tm <706F726F736F2C20> Tj 1 0 0 1 280.08 441.12 Tm <6120> Tj 1 0 0 1 287.28 441.12 Tm <6365726120> Tj 1 0 0 1 306.48 440.88 Tm <6CED717569646120> Tj 1 0 0 1 336.96 440.64 Tm <736F626520> Tj 1 0 0 1 357.36 441.12 Tm <706F7220> Tj 1 0 0 1 373.92 440.64 Tm <61E7E36F20> Tj 1 0 0 1 394.56 440.40 Tm <646120> Tj 1 0 0 1 406.32 440.40 Tm <636170696C6172696461646520> Tj 1 0 0 1 457.92 440.16 Tm <656D20> Tj 1 0 0 1 472.80 440.16 Tm <746F726E6F20> Tj 1 0 0 1 496.32 439.92 Tm <646F20> Tj 1 0 0 1 508.56 440.16 Tm <766F6C756D65> Tj 0.48 Tc 1 0 0 1 57.60 431.04 Tm <646573746520> Tj 1 0 0 1 82.56 431.04 Tm <652C20> Tj 1 0 0 1 93.84 430.80 Tm <656E74E36F2C20> Tj 1 0 0 1 122.16 430.80 Tm <7661706F72697A612D736520> Tj 1 0 0 1 172.56 430.80 Tm <284E7B4A4D4120> Tj 1 0 0 1 211.20 430.08 Tm <5441584120> Tj 1 0 0 1 243.60 429.84 Tm <50524F504F5243494F4E414C20> Tj 1 0 0 1 330.00 429.12 Tm <414F20> Tj 1 0 0 1 349.44 429.12 Tm <464C55584F20> Tj 1 0 0 1 388.56 428.88 Tm <444520> Tj 1 0 0 1 406.32 428.88 Tm <43414C4F5220> Tj 1 0 0 1 446.88 428.64 Tm <50524F56454E49454E544520> Tj 1 0 0 1 523.92 428.16 Tm <4441> Tj 0.48 Tc 1 0 0 1 57.60 419.76 Tm <4348414D412920> Tj 1 0 0 1 103.20 417.60 Tm <5B706F7220> Tj 1 0 0 1 124.56 419.28 Tm <61E7E36F20> Tj 1 0 0 1 147.36 419.04 Tm <646F20> Tj 1 0 0 1 160.80 419.04 Tm <63616C6F7220> Tj 1 0 0 1 185.04 418.80 Tm <636564EC646F20> Tj 1 0 0 1 214.08 419.04 Tm <70656C6120> Tj 1 0 0 1 235.92 418.56 Tm <6368616D615D2E20> Tj 1 0 0 1 272.64 418.32 Tm <4573736520> Tj 1 0 0 1 294.24 418.08 Tm <63616C6F7220> Tj 1 0 0 1 317.76 417.84 Tm <6C6962657261646F20> Tj 1 0 0 1 354.00 417.60 Tm <61756D656E746120> Tj 1 0 0 1 390.96 417.60 Tm <6120> Tj 1 0 0 1 398.40 417.60 Tm <74656D706572617475726120> Tj 1 0 0 1 449.52 417.12 Tm <646F7320> Tj 1 0 0 1 467.04 417.36 Tm <676173657320> Tj 1 0 0 1 492.00 416.88 Tm <6520> Tj 1 0 0 1 499.68 416.88 Tm <726564757A20> Tj 1 0 0 1 525.12 416.64 Tm <737561> Tj 0.48 Tc 1 0 0 1 57.36 408.00 Tm <64656E7369646164652C20> Tj 1 0 0 1 105.60 407.76 Tm <73757267696E646F20> Tj 1 0 0 1 145.20 407.52 Tm <656E74E36F20> Tj 1 0 0 1 172.08 407.04 Tm <4C4D4120> Tj 1 0 0 1 201.12 407.04 Tm <434F4E56454343414F20> Tj 1 0 0 1 276.72 406.56 Tm <4E4154492E2C2C2752414C20> Tj 1 0 0 1 331.20 404.16 Tm <5B666C7574756162697469646164656C20> Tj 1 0 0 1 400.32 406.32 Tm <2874656E64EA6E63696120> Tj 1 0 0 1 446.88 405.36 Tm <617363656E73696F6E616C20> Tj 1 0 0 1 498.00 405.12 Tm <646F7320> Tj 1 0 0 1 516.72 405.36 Tm <6761736573> Tj 0.48 Tc 1 0 0 1 57.36 396.96 Tm <7175656E74657320> Tj 1 0 0 1 94.08 396.72 Tm <71756520> Tj 1 0 0 1 114.24 396.24 Tm <6465636F7272652C20> Tj 1 0 0 1 151.92 396.24 Tm <7072696E636970616C6D656E74652C20> Tj 1 0 0 1 220.32 395.52 Tm <646120> Tj 1 0 0 1 235.20 395.28 Tm <6D656E6F7220> Tj 1 0 0 1 266.88 395.04 Tm <64656E73696461646520> Tj 1 0 0 1 312.72 394.56 Tm <64657374657320> Tj 1 0 0 1 342.72 394.56 Tm <656D20> Tj 1 0 0 1 360.48 394.56 Tm <72656C61E7E36F20> Tj 1 0 0 1 395.04 394.32 Tm Tj 1 0 0 1 404.88 394.08 Tm <64656E73696461646520> Tj 1 0 0 1 450.48 393.84 Tm <646F20> Tj 1 0 0 1 466.56 393.84 Tm <617220> Tj 1 0 0 1 479.76 393.60 Tm <63697263756C616E7465292E20> Tj 1 0 0 1 531.12 393.36 Tm <41> Tj 0.48 Tc 1 0 0 1 57.60 385.68 Tm <28434F4E56454343414F20> Tj 1 0 0 1 134.88 384.72 Tm <4E41545552414C2920> Tj 1 0 0 1 196.08 382.08 Tm <5B666C7574756162696C69646164654A20> Tj 1 0 0 1 269.28 383.52 Tm <6573746162656C65636520> Tj 1 0 0 1 318.96 383.04 Tm <554D20> Tj 1 0 0 1 344.40 383.04 Tm <4553434F414D454E544F20> Tj 1 0 0 1 424.32 380.88 Tm <49636F7272656E74657320> Tj 1 0 0 1 474.96 382.32 Tm <636C6520> Tj 1 0 0 1 493.20 382.08 Tm <636F6E742C6563E7E36F66> Tj 0.48 Tc 1 0 0 1 57.12 373.68 Tm <415343454E44454E544520> Tj 1 0 0 1 128.64 371.28 Tm <51554520> Tj 1 0 0 1 152.64 372.96 Tm <444120> Tj 1 0 0 1 169.44 372.72 Tm <4120> Tj 1 0 0 1 179.76 372.72 Tm <464F524D4120> Tj 1 0 0 1 220.08 372.48 Tm <444120> Tj 1 0 0 1 237.36 372.24 Tm <4348414D4120> Tj 1 0 0 1 278.88 372.00 Tm <4520> Tj 1 0 0 1 288.24 371.76 Tm <554D20> Tj 1 0 0 1 307.68 371.76 Tm <4E4120> Tj 1 0 0 1 324.72 371.76 Tm <4449524543414F20> Tj 1 0 0 1 374.40 371.28 Tm <52414449414C20> Tj 1 0 0 1 416.16 371.52 Tm <71756520> Tj 1 0 0 1 433.20 371.04 Tm <617272617374616D20> Tj 1 0 0 1 470.40 370.56 Tm <6F786967EA6E696F20> Tj 1 0 0 1 510.00 370.80 Tm <70752E7520> Tj 1 0 0 1 529.92 370.32 Tm <7569> Tj 0.48 Tc 1 0 0 1 57.12 362.16 Tm <76697A696E68616EE7617320> Tj 1 0 0 1 108.00 361.68 Tm <646120> Tj 1 0 0 1 120.72 361.68 Tm <6368616D612E20> Tj 1 0 0 1 152.40 361.44 Tm <4573736520> Tj 1 0 0 1 174.00 361.20 Tm <6F786967EA6E696F20> Tj 1 0 0 1 212.40 360.96 Tm Tj 1 0 0 1 220.08 361.44 Tm <285452414E53504F525441444F20> Tj 1 0 0 1 310.56 360.00 Tm <5052494E434950414C4D454E544520> Tj 1 0 0 1 405.36 360.00 Tm <70656C4F20> Tj 1 0 0 1 429.36 361.92 Tm <70524F434553534F20> Tj 1 0 0 1 486.48 359.04 Tm <444120> Tj 1 0 0 1 504.24 358.80 Tm <6469667573616F29> Tj 0.24 Tc 1 0 0 1 57.12 348.96 Tm <5B61727261737461646F20> Tj 1 0 0 1 106.32 350.88 Tm <706F73746572EC6F726D656E74655D20> Tj 1 0 0 1 176.16 349.92 Tm <6174E920> Tj 1 0 0 1 190.08 349.92 Tm <6120> Tj 1 0 0 1 197.76 349.92 Tm <6368616D6120> Tj 1 0 0 1 227.04 350.16 Tm <284F4E444520> Tj 1 0 0 1 262.56 349.20 Tm <524541474520> Tj 1 0 0 1 301.68 348.96 Tm <434F4D20> Tj 1 0 0 1 329.52 348.96 Tm <4120> Tj 1 0 0 1 340.08 348.96 Tm <5041524146494E412920> Tj 1 0 0 1 401.76 348.48 Tm <2E20> Tj 1 0 0 1 407.28 346.56 Tm <5B2C20> Tj 1 0 0 1 417.12 348.48 Tm <726573756C7463746E646F20> Tj 1 0 0 1 463.44 348.00 Tm <656D20> Tj 1 0 0 1 478.08 347.76 Tm <73756120> Tj 1 0 0 1 495.36 347.76 Tm <636F6E7462757374636A6F> Tj 0.48 Tc 1 0 0 1 57.12 339.36 Tm <434F4D20> Tj 1 0 0 1 81.36 339.36 Tm <4120> Tj 1 0 0 1 92.40 337.20 Tm <5041547166694E414A2E20> Tj 1 0 0 1 141.36 336.96 Tm <5B4120> Tj 1 0 0 1 156.72 336.96 Tm <666F54E76120> Tj 1 0 0 1 186.72 338.64 Tm <64655D20> Tj 1 0 0 1 207.60 338.88 Tm <284120> Tj 1 0 0 1 225.12 338.16 Tm <434F4E56454343414F20> Tj 1 0 0 1 297.60 337.68 Tm <4E41545552414C2C20> Tj 1 0 0 1 356.88 337.44 Tm <50524F44555A49444120> Tj 1 0 0 1 424.32 336.96 Tm <50454C4120> Tj 1 0 0 1 457.92 336.48 Tm <4449464552454E434120> Tj 1 0 0 1 523.92 336.24 Tm <4445> Tj 0.48 Tc 1 0 0 1 57.12 327.84 Tm <44454E5349444144455320> Tj 1 0 0 1 125.52 327.60 Tm <4520> Tj 1 0 0 1 135.60 327.60 Tm <464F52434120> Tj 1 0 0 1 174.72 327.12 Tm <444120> Tj 1 0 0 1 192.96 326.88 Tm <4752415649444144452920> Tj 1 0 0 1 261.12 324.48 Tm <5B6573636F616D656E746F2E666C757475616E746520> Tj 1 0 0 1 355.44 325.68 Tm <646570656E646520> Tj 1 0 0 1 392.16 325.44 Tm <636C6F20> Tj 1 0 0 1 405.60 325.44 Tm <6EED742C656C20> Tj 1 0 0 1 427.92 325.68 Tm <677261742C69746163696F6E616C20> Tj 1 0 0 1 486.00 324.72 Tm <6520> Tj 1 0 0 1 494.16 324.72 Tm Tj 1 0 0 1 502.08 324.72 Tm <657370657261646F> Tj 0.24 Tc 1 0 0 1 57.12 316.80 Tm <7175654A20> Tj 1 0 0 1 79.20 316.80 Tm <284445544552C027CD494E412920> Tj 1 0 0 1 150.96 315.84 Tm <6120> Tj 1 0 0 1 158.64 315.84 Tm <666F726D612C20> Tj 1 0 0 1 188.16 315.60 Tm <6F20> Tj 1 0 0 1 196.32 315.36 Tm <74616D616E686F20> Tj 1 0 0 1 233.76 315.36 Tm <6520> Tj 1 0 0 1 241.44 315.12 Tm <6120> Tj 1 0 0 1 249.12 315.12 Tm <7461786120> Tj 1 0 0 1 269.04 314.88 Tm <646520> Tj 1 0 0 1 281.76 315.12 Tm <717565696D6120> Tj 1 0 0 1 314.40 314.64 Tm <646120> Tj 1 0 0 1 327.12 314.64 Tm <6368616D6120> Tj 1 0 0 1 356.64 312.48 Tm <5B6972E36F20> Tj 1 0 0 1 378.00 314.16 Tm <76617269617220> Tj 1 0 0 1 404.16 314.16 Tm <636F6D20> Tj 1 0 0 1 424.32 313.92 Tm <6120> Tj 1 0 0 1 432.00 314.40 Tm <6772617669646164655D2E20> Tj 1 0 0 1 480.72 313.44 Tm <4F20> Tj 1 0 0 1 490.80 313.92 Tm <70726F63E873736F20> Tj 1 0 0 1 528.48 313.20 Tm <6465> Tj 0.48 Tc 1 0 0 1 57.12 305.04 Tm <7661706F72697A61E7E36F20> Tj 1 0 0 1 108.72 304.56 Tm <65736672696120> Tj 1 0 0 1 133.44 304.32 Tm <6F20> Tj 1 0 0 1 140.88 304.80 Tm <706176696F20> Tj 1 0 0 1 166.08 304.08 Tm <6578706F73746F20> Tj 1 0 0 1 199.68 304.08 Tm <70726F746567656E646F2D6F20> Tj 1 0 0 1 256.08 303.36 Tm <646F20> Tj 1 0 0 1 269.04 303.12 Tm <73757065726171756563696D656E746F2E20> Tj 1 0 0 1 347.52 300.72 Tm <5B4120> Tj 1 0 0 1 360.24 302.64 Tm <6368616D612C20> Tj 1 0 0 1 391.20 302.88 Tm <706F7220> Tj 1 0 0 1 407.28 302.40 Tm <73756120> Tj 1 0 0 1 423.12 302.40 Tm <76657A2C20> Tj 1 0 0 1 442.56 302.16 Tm <666F6D65636520> Tj 1 0 0 1 475.20 301.92 Tm <6120> Tj 1 0 0 1 482.40 301.92 Tm <7265616C696D656E7461C7E36F> Tj 0.48 Tc 1 0 0 1 57.12 293.04 Tm <646F20> Tj 1 0 0 1 70.08 293.04 Tm <63616C6F7220> Tj 1 0 0 1 92.16 293.28 Tm <7061726120> Tj 1 0 0 1 112.32 292.80 Tm <636F6D706C6574617220> Tj 1 0 0 1 154.32 292.32 Tm <6F20> Tj 1 0 0 1 162.00 292.56 Tm <6369636C6F2E5D20> Tj 1 0 0 1 189.84 295.68 Tm <74326C> Tj 0.48 Tc 1 0 0 1 99.84 281.28 Tm <447572616E746520> Tj 1 0 0 1 136.08 281.04 Tm <6120> Tj 1 0 0 1 144.48 281.52 Tm <717565696D6120> Tj 1 0 0 1 177.84 280.80 Tm <646120> Tj 1 0 0 1 191.04 280.56 Tm <76656C6120> Tj 1 0 0 1 211.68 280.56 Tm <74616D62E96D20> Tj 1 0 0 1 247.68 280.56 Tm <706F646520> Tj 1 0 0 1 271.44 280.08 Tm <73657220> Tj 1 0 0 1 287.04 279.84 Tm <6F627365727661646120> Tj 1 0 0 1 331.68 279.60 Tm <6120> Tj 1 0 0 1 340.08 279.60 Tm <666F726D61E7E36F20> Tj 1 0 0 1 381.60 279.36 Tm <64617320> Tj 1 0 0 1 398.40 279.12 Tm <6368616D6164617320> Tj 1 0 0 1 441.84 279.36 Tm <22626F7264617320> Tj 1 0 0 1 477.12 278.64 Tm <646520> Tj 1 0 0 1 490.32 278.64 Tm <6368616D61222E20> Tj 1 0 0 1 526.80 278.40 Tm <4173> Tj 0.48 Tc 1 0 0 1 56.88 270.00 Tm <626F7264617320> Tj 1 0 0 1 88.08 269.76 Tm <646520> Tj 1 0 0 1 101.04 269.52 Tm <6368616D6120> Tj 1 0 0 1 130.80 269.52 Tm <73E36F20> Tj 1 0 0 1 147.60 269.52 Tm <6361726163746572ED73746963617320> Tj 1 0 0 1 207.84 268.80 Tm <636F6D756E7320> Tj 1 0 0 1 242.40 268.56 Tm <646520> Tj 1 0 0 1 255.60 268.32 Tm <636F6D62757374E36F20> Tj 1 0 0 1 302.88 267.84 Tm <64696675736976612E20> Tj 1 0 0 1 341.04 267.60 Tm <506F7220> Tj 1 0 0 1 359.04 267.60 Tm <6578656D706C6F2C20> Tj 1 0 0 1 398.64 267.36 Tm <756D6120> Tj 1 0 0 1 419.76 267.36 Tm <6368616D6120> Tj 1 0 0 1 449.04 267.36 Tm <70726F706167616E646F20> Tj 1 0 0 1 500.16 266.40 Tm <736F62726520> Tj 1 0 0 1 524.88 266.40 Tm <756D> Tj 0.48 Tc 1 0 0 1 57.12 258.48 Tm <6C6569746F20> Tj 1 0 0 1 80.16 258.24 Tm <636F6D62757374ED76656C20> Tj 1 0 0 1 133.68 258.24 Tm <284150524553454E544120> Tj 1 0 0 1 201.84 257.28 Tm <554D4120> Tj 1 0 0 1 230.40 257.04 Tm <424F52444120> Tj 1 0 0 1 271.68 256.80 Tm <4E4120> Tj 1 0 0 1 290.88 256.56 Tm <4652454E544520> Tj 1 0 0 1 336.24 256.08 Tm <444120> Tj 1 0 0 1 355.68 256.08 Tm <4348414D412920> Tj 1 0 0 1 402.00 253.92 Tm <66746572697220> Tj 1 0 0 1 426.96 255.60 Tm <636F6E636C757AED646F20> Tj 1 0 0 1 472.80 255.36 Tm <637420> Tj 1 0 0 1 482.88 255.12 Tm <626F72636C6120> Tj 1 0 0 1 510.96 255.12 Tm <637420> Tj 1 0 0 1 521.04 255.12 Tm <4C726D6374> Tj 0.48 Tc 1 0 0 1 55.92 247.20 Tm <706F73EDE7E36F20> Tj 1 0 0 1 91.68 246.48 Tm <656D20> Tj 1 0 0 1 105.84 246.48 Tm <616C67756D20> Tj 1 0 0 1 133.92 246.24 Tm <6C7567617220> Tj 1 0 0 1 158.16 246.00 Tm <6163696D6120> Tj 1 0 0 1 185.28 245.76 Tm <646F20> Tj 1 0 0 1 198.48 245.76 Tm <6C6569746F6C20> Tj 1 0 0 1 222.96 246.00 Tm <284669672E3120> Tj 1 0 0 1 249.84 245.28 Tm <61292E20> Tj 1 0 0 1 263.28 245.52 Tm <284E4F20> Tj 1 0 0 1 284.40 244.80 Tm <4341534F20> Tj 1 0 0 1 314.88 244.56 Tm <444520> Tj 1 0 0 1 331.68 244.56 Tm <554D412920> Tj 1 0 0 1 361.68 242.64 Tm <5B556D614A20> Tj 1 0 0 1 391.68 244.32 Tm <76656C6120> Tj 1 0 0 1 410.88 244.56 Tm <717565696D616E646F20> Tj 1 0 0 1 458.16 243.60 Tm <656D20> Tj 1 0 0 1 473.04 243.60 Tm <6D6963726F6772617669646164652E> Tj 0.48 Tc 1 0 0 1 57.36 235.68 Tm <284120> Tj 1 0 0 1 72.24 234.96 Tm <4348414D412920> Tj 1 0 0 1 121.20 234.48 Tm <746572E120> Tj 1 0 0 1 140.16 234.48 Tm <756D6120> Tj 1 0 0 1 161.76 234.48 Tm <666F726D6120> Tj 1 0 0 1 189.84 234.00 Tm <657366E97269636120> Tj 1 0 0 1 224.88 233.76 Tm <636F6D20> Tj 1 0 0 1 246.24 233.52 Tm <756D6120> Tj 1 0 0 1 267.84 233.28 Tm <626F72646120> Tj 1 0 0 1 295.20 233.04 Tm <63697263756C617220> Tj 1 0 0 1 329.76 232.80 Tm <62656D20> Tj 1 0 0 1 351.36 232.80 Tm <646566696E69646120> Tj 1 0 0 1 388.32 233.28 Tm <284669672E20> Tj 1 0 0 1 412.08 232.56 Tm <3120> Tj 1 0 0 1 420.24 232.32 Tm <622920> Tj 1 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MOURAENIZETE A. GONALVESLUIZ EDUARDO M. LIMAFERNANDO F. FACHINIInstituto Nacional de Pesquisas Espacias (INPE), I2630-000, Cachoeira Puulistct, So Paulo, Bt.ctsil.SumrioEste trabalho tem por objetivo estudar a influncia do nmero de Grashof em chamas difusivas atrar's daobservao experimental da queima de uma r,ela. Tambem ser analisada a ordem de magnitude dos termos dasequaes de consenao. E apresentado que a diminui;c gradatira do;omprimento do pavio da vela resura nadiminuio da altura da chama e dc efeitc do nmero de Grashof Conro c..nseqncra. a uma cerra altura do par,io (4mm) o efeittr d.r fluru:bild.ade e Lesr:ezadc. tenl.l-se a mudaia ,ja tbnla lt lh,rnta elipri,'a Fara quase eslrica. quaseno apresentanJ.- Ic:=a;r c::.11:sen. srnulan,j.--se assi:T as;..rlres de i:i;ic-graridade. Portanto. foi concludoque o .'.'ni.e;:r:e :.:; J, :L:';i:.':: J3 :32.. cr:ri Nras Je empur.' e 1.'rJf,: \ l:.'..sa:. repres:nradas pelo nnrero deGrashof. e de granie tnpcnn;ra e rr1 no processo da combusro.IntroduoAs chamas podem ser divididas em duas classes: chamas pre-misturadas, nas quais combustvel e oxidanteso pre-misturados antes que a ignio ocorra, e em chamas nas quais combustvel e oxidante encontram-se na zona dereao. Para essa segunda classe de chamas aplicado o termo "chamas difusivas". A chama de um fsforo" delmpadas a 1eo, do queimador tipo turbina a gs e de uma vela exemplifiam essa classe de chama. llNo processo de formao da chama difusiva em uma vela apresentam-se como combustvei e oxidante aparafina e o oxignio respectivamente. Quando a vela acesa, o calor vindo (DA CHAMA OU) de uma fonte deignio (um fsforo, por exemplo), derrete a parafina, um hidrocarboneto pesado, (EMPREGNADA NO PAVIO OU)na base do pavio. Como o pavio um material poroso, a cera lquida sobe por ao da capilaridade em torno do volumedeste e, ento, vaporiza-se (N{JMA TAXA PROPORCIONAL AO FLUXO DE CALOR PROVENIENTE DACHAMA) [por ao do calor ceddo pela chama]. Esse calor liberado aumenta a temperatura dos gases e reduz suadensidade, surgindo ento LMA CONVECCAO NATI.,,'RAL [flutuabitidadel (tendncia ascensional dos gasesquentes que decorre, principalmente, da menor densidade destes em relao densidade do ar circulante). A(CONVECCAO NATURAL) [flutuabilidadeJ estabelece UM ESCOAMENTO Icorrentes cle cont,ecofASCENDENTE QUE DA A FORMA DA CHAMA E UM NA DIRECAO RADIAL que arrastam oxignio pu.u uivizinhanas da chama. Esse oxignio (TRANSPORTADO PRINCIPALMENTE pelO pROCESSO DA difusao)[arrastado posterormente] at a chama (ONDE REAGE COM A PARAFINA) . [, resultctndo em sua contbustcjoCOM A PATqfiNAJ. [A foTa de] (A CONVECCAO NATURAL, PRODUZIDA PELA DIFERENCA DEDENSIDADES E FORCA DA GRAVIDADE) [escoamento.flutuante depende clo nt,el grat,itacional e esperadoqueJ (DETER'INA) a forma, o tamanho e a taxa de queima da chama [iro variar com a gravidade]. O procsso devaporizao esfria o pavio exposto protegendo-o do superaquecimento. [A chama, por sua vez, fomece a realimentaodo calor para completar o ciclo.] t2lDurante a queima da vela tambm pode ser observada a formao das chamadas "bordas de chama". Asbordas de chama so caractersticas comuns de combusto difusiva. Por exemplo, uma chama propagando sobre umleito combustvel (APRESENTA UMA BORDA NA FRENTE DA CHAMA) fterir concluzdo ct borcla ct Lrmctposo em algum lugar acima do leitol (Fig.1 a). (NO CASO DE UMA) [UmaJ vela queimando em microgravidade.(A CHAMA) ter uma forma esfrica com uma borda circular bem definida (Fig. 1 b) t3l (J) ) qu.. n.*ru,condies, a nica conveco presente o escoamento Stefan, gerado pelo processo de mudana de fase expalsotrmica do combustvel, (QUE TFM SIMETRIA ESFERICA). O oxignio chega zona de reao por in-,raomolecular. Esse processo lento muda a forma, cor, temperatura e o limite de extino da chama. lll tPQ OPROCESSO DE DIFUSAO FAZ TUDO ISSO?I endstream endobj 7 0 obj 4051 endobj 8 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 9 0 obj << /Length 44 >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj2 Do Q endstream endobj 10 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj2 2 0 R >> /Subtype 6 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 8 0 R 9 0 R 3 0 R ] >> endobj 13 0 obj << /Type /XObject /Subtype /Image /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 76684 >> stream ejˣ C;K h$B=*.Ⱥ0) a""taL]JdU.YҐ!  K|w"uVv0! ` taA!B.#u,HKH]"E bGC]A",! ! 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<74594320> Tj 1 0 0 1 352.80 636.00 Tm <5C43485C20> Tj 1 0 0 1 384.00 634.32 Tm <51554520> Tj 1 0 0 1 408.48 636.00 Tm <4F20> Tj 1 0 0 1 420.00 636.00 Tm <4F584947454E494F20> Tj 1 0 0 1 472.80 636.24 Tm <434F4E5449444F20> Tj 1 0 0 1 521.76 636.24 Tm <4E41> Tj 1.44 Tc 1 0 0 1 56.16 624.24 Tm <41545C6C4F534645525C20> Tj 1 0 0 1 123.84 624.24 Tm <4520> Tj 1 0 0 1 136.80 624.24 Tm Tj 1 0 0 1 211.68 624.24 Tm <505C525C20> Tj 1 0 0 1 245.04 623.52 Tm <4F4C45CC5C495C5220> Tj 1 0 0 1 300.00 624.48 Tm <5C20> Tj 1 0 0 1 312.72 624.48 Tm <505C525C46495C5C20> Tj 1 0 0 1 369.84 624.48 Tm <434F5C5449442E5C20> Tj 1 0 0 1 421.44 624.72 Tm <5C555C312E5C20> Tj 1 0 0 1 459.12 624.72 Tm <5C27495D4920> Tj 1 0 0 1 478.56 624.72 Tm <2D5C5D20> Tj 1 0 0 1 497.28 624.48 Tm <534520> Tj 1 0 0 1 515.52 624.72 Tm <545541> Tj 1.20 Tc 1 0 0 1 56.40 612.72 Tm <524553504F53545C20> Tj 1 0 0 1 113.04 612.72 Tm <4643295220> Tj 1 0 0 1 141.12 612.72 Tm Tj 1 0 0 1 196.56 612.72 Tm <5C2E20> Tj 1 0 0 1 213.36 612.96 Tm <5C20> Tj 1 0 0 1 226.08 612.96 Tm <46525C534520> Tj 1 0 0 1 265.68 612.96 Tm <5C5C544552494F5220> Tj 1 0 0 1 321.84 612.96 Tm <4553542E5C20> Tj 1 0 0 1 353.76 612.96 Tm <434329525245547B20> Tj 1 0 0 1 409.92 612.96 Tm <534520> Tj 1 0 0 1 428.64 613.20 Tm <464F5220> Tj 1 0 0 1 454.80 612.96 Tm <5C462D474154495C225C2E20> Tj 1 0 0 1 515.52 613.20 Tm <545541> Tj 0.96 Tc 1 0 0 1 56.40 601.20 Tm <524553502820> Tj 1 0 0 1 85.20 602.88 Tm <2953692C5C20> Tj 1 0 0 1 110.88 601.44 Tm <61533A20> Tj 1 0 0 1 130.08 603.12 Tm <722C20> Tj 1 0 0 1 140.64 601.44 Tm <61522E525C445C20> Tj 1 0 0 1 191.76 601.20 Tm <3A3A2E2D20> Tj 1 0 0 1 216.72 603.84 Tm <6A2D2D20> Tj 1 0 0 1 231.36 601.44 Tm <3B3A726C2E2D3A2E2D20> Tj 1 0 0 1 268.08 601.44 Tm <726A2E20> Tj 1 0 0 1 287.04 601.44 Tm <3320> Tj 1 0 0 1 296.16 601.44 Tm <743A696E5C2E2E6DEC33643320> Tj 1 0 0 1 353.28 601.44 Tm <3A757420> Tj 1 0 0 1 370.08 601.44 Tm <43302C2E20> Tj 1 0 0 1 394.32 601.44 Tm <686172656E64E7722E20> Tj 1 0 0 1 435.36 601.92 Tm <7074723174E26C31746F2E20> Tj 1 0 0 1 475.68 601.68 Tm <6120> Tj 1 0 0 1 485.04 601.68 Tm <6962726E7261E7E06F20> Tj 1 0 0 1 526.80 601.68 Tm <6465> Tj 0.96 Tc 1 0 0 1 56.40 589.68 Tm <2E2D6C3A612D3A2D2D20> Tj 1 0 0 1 95.04 587.76 Tm <3A3A3A3AEC3A3A20> Tj 1 0 0 1 129.36 591.60 Tm <692D292E20> Tj 1 0 0 1 143.28 589.68 Tm <3A3A2D20> Tj 1 0 0 1 156.96 589.68 Tm <4A2D3A2D2E20> Tj 1 0 0 1 180.96 589.68 Tm <3B7220> Tj 1 0 0 1 193.68 589.68 Tm <2C2D3A272E742A3A3A692C2D2E20> Tj 1 0 0 1 239.52 589.92 Tm <3A3A3A2E2E6E726CEC61EF6120> Tj 1 0 0 1 286.32 589.68 Tm <3AE02E2E20> Tj 1 0 0 1 302.64 589.92 Tm <3A696571FC656E74656E6C2E72EC742E20> Tj 1 0 0 1 367.44 589.92 Tm <432E20> Tj 1 0 0 1 379.20 589.92 Tm <43274F2E20> Tj 1 0 0 1 398.40 589.92 Tm <434F3A20> Tj 1 0 0 1 418.32 589.92 Tm <6520> Tj 1 0 0 1 425.76 589.92 Tm <483B4F2E20> Tj 1 0 0 1 448.56 589.92 Tm <2E5C7373696E722E20> Tj 1 0 0 1 479.28 589.92 Tm <6120> Tj 1 0 0 1 486.72 589.92 Tm <746F726D61E7E06F20> Tj 1 0 0 1 526.80 589.92 Tm <6463> Tj 0.96 Tc 1 0 0 1 56.40 577.92 Tm Tj 1 0 0 1 90.96 577.68 Tm <6C2D20> Tj 1 0 0 1 101.28 577.92 Tm <4A3320> Tj 1 0 0 1 114.48 577.92 Tm <3A2E7220> Tj 1 0 0 1 130.08 577.92 Tm <3A3A3A2D3A3A3A333A3A696920> Tj 1 0 0 1 181.20 577.92 Tm <4A2E3A723A6120> Tj 1 0 0 1 207.36 577.92 Tm <4A2E2D496C724C27757369692E2C65CC20> Tj 1 0 0 1 259.44 577.92 Tm <6EE06F20> Tj 1 0 0 1 277.68 578.40 Tm <717565726E61646F20> Tj 1 0 0 1 320.88 578.16 Tm <5D726265726164272E20> Tj 1 0 0 1 357.12 577.92 Tm <4A3B20> Tj 1 0 0 1 370.32 577.92 Tm <3BCC722E726E727220> Tj 1 0 0 1 399.84 578.40 Tm <7061313320> Tj 1 0 0 1 420.96 578.16 Tm <6120> Tj 1 0 0 1 429.12 578.16 Tm <33746E6C6F7374E872612E20> Tj 1 0 0 1 474.72 578.16 Tm <74696571FC656E74656E6C656E7465> Tj 0.72 Tc 1 0 0 1 56.40 566.40 Tm <2E2D2774273A2E3A2D2720> Tj 1 0 0 1 83.04 566.40 Tm <33693A20> Tj 1 0 0 1 99.84 566.40 Tm <3A6C3B20> Tj 1 0 0 1 112.32 566.40 Tm <3A723A3A6C2D3A3A3A2D2D20> Tj 1 0 0 1 158.16 566.40 Tm <2E746520> Tj 1 0 0 1 170.64 566.40 Tm <686C643A2E2E3B65724C272E2E6E65746F732E20> Tj 1 0 0 1 240.24 566.40 Tm <4F20> Tj 1 0 0 1 250.32 566.88 Tm <70CD6F21276573736F20> Tj 1 0 0 1 288.24 566.40 Tm <646120> Tj 1 0 0 1 300.72 566.40 Tm <746F726D61E7E36F20> Tj 1 0 0 1 341.04 566.40 Tm <646520> Tj 1 0 0 1 353.76 566.64 Tm <74ECCC7267656E7220> Tj 1 0 0 1 387.36 566.40 Tm <636F6E736973746520> Tj 1 0 0 1 422.40 566.64 Tm <646120> Tj 1 0 0 1 434.88 566.88 Tm <706972F36C72736520> Tj 1 0 0 1 467.76 566.40 Tm <646F20> Tj 1 0 0 1 480.72 566.40 Tm <636F6E7262757374ED722E27656C20> Tj 1 0 0 1 531.84 566.64 Tm <63> Tj 0.72 Tc 1 0 0 1 56.40 555.12 Tm <7265612C2DF22D3A20> Tj 1 0 0 1 90.96 555.12 Tm <4A6520> Tj 1 0 0 1 104.88 554.88 Tm <72726C69613BE0722E20> Tj 1 0 0 1 148.08 554.88 Tm Tj 1 0 0 1 190.08 554.88 Tm <6C2E7220> Tj 1 0 0 1 204.72 555.36 Tm <7072696E726569726F20> Tj 1 0 0 1 243.60 555.12 Tm <616E65EC20> Tj 1 0 0 1 264.72 554.88 Tm <646520> Tj 1 0 0 1 278.64 554.88 Tm <62656E7A656E6F20> Tj 1 0 0 1 316.56 554.88 Tm <6520> Tj 1 0 0 1 325.44 555.36 Tm <706F7374656E6F7220> Tj 1 0 0 1 365.76 555.12 Tm <7462726E7261E7E06F20> Tj 1 0 0 1 407.76 554.88 Tm <646520> Tj 1 0 0 1 422.16 555.12 Tm <686964726F636172626F6E65746F7320> Tj 1 0 0 1 490.32 555.36 Tm <706F6C6963ED636C69636F73> Tj 0.72 Tc 1 0 0 1 56.40 543.36 Tm <61726F6E72E174722C2D6F732E20> Tj 1 0 0 1 105.12 543.36 Tm <61706172C863726E6C656E7472EC20> Tj 1 0 0 1 161.28 543.36 Tm <646120> Tj 1 0 0 1 173.04 543.60 Tm <7072696E726569726120> Tj 1 0 0 1 209.28 543.84 Tm <706172746963756C612E20> Tj 1 0 0 1 249.36 543.36 Tm <6372657363696D656E746F20> Tj 1 0 0 1 300.00 543.36 Tm <64617320> Tj 1 0 0 1 315.60 543.60 Tm <70617274ED63756C617320> Tj 1 0 0 1 357.12 543.36 Tm <646520> Tj 1 0 0 1 369.12 543.36 Tm <74EC6C6967656D20> Tj 1 0 0 1 402.48 543.36 Tm <64657269646F20> Tj 1 0 0 1 432.24 543.36 Tm Tj 1 0 0 1 443.04 543.36 Tm <726561E7D2657320> Tj 1 0 0 1 475.44 543.36 Tm <64617320> Tj 1 0 0 1 491.28 543.36 Tm <657370E96369657320> Tj 1 0 0 1 526.80 543.36 Tm <6461> Tj 0.72 Tc 1 0 0 1 56.40 531.84 Tm <74E0736520> Tj 1 0 0 1 75.12 533.28 Tm <6761736F73612E20> Tj 1 0 0 1 107.04 531.60 Tm <636F616C657363EA6E63696120> Tj 1 0 0 1 160.08 531.60 Tm <646120> Tj 1 0 0 1 172.08 532.08 Tm <70616E6963756C612E20> Tj 1 0 0 1 212.64 531.60 Tm <61676C6F6D657261E7E36F20> Tj 1 0 0 1 266.40 531.60 Tm <6520> Tj 1 0 0 1 273.84 531.60 Tm <6F78696461E7E36F2E6C20> Tj 1 0 0 1 318.24 531.60 Tm <4D454C484F524520> Tj 1 0 0 1 369.12 531.60 Tm <4120> Tj 1 0 0 1 379.20 531.60 Tm <4558504C4943414F20> Tj 1 0 0 1 431.52 531.84 Tm <444F5320> Tj 1 0 0 1 454.08 531.84 Tm <4ECD4543414E49534E6C4F5320> Tj 1 0 0 1 523.20 531.84 Tm <4445> Tj 0.48 Tc 1 0 0 1 56.40 520.32 Tm <464F525C7B41432E7B4F20> Tj 1 0 0 1 115.92 520.32 Tm <444520> Tj 1 0 0 1 132.48 520.32 Tm <46554C4947454D5D20> Tj 1 0 0 1 186.96 518.40 Tm <5175616E646F20> Tj 1 0 0 1 222.00 520.08 Tm <657373617320> Tj 1 0 0 1 245.28 520.56 Tm <70617274ED63756C617320> Tj 1 0 0 1 287.28 520.56 Tm <70617373616D20> Tj 1 0 0 1 320.16 520.08 Tm <6174726176E97320> Tj 1 0 0 1 351.60 520.08 Tm <646120> Tj 1 0 0 1 364.56 520.08 Tm <6368616D612C20> Tj 1 0 0 1 396.24 520.08 Tm <656C617320> Tj 1 0 0 1 415.20 520.32 Tm <697272616469616D20> Tj 1 0 0 1 452.16 520.08 Tm <636F6D6F20> Tj 1 0 0 1 477.60 520.08 Tm <636F72706F7320> Tj 1 0 0 1 507.36 520.32 Tm <6E6567726F732E> Tj 0.48 Tc 1 0 0 1 56.40 508.80 Tm <4973736F20> Tj 1 0 0 1 74.88 508.56 Tm <6520> Tj 1 0 0 1 81.84 508.80 Tm <726573706F6E73E176656C20> Tj 1 0 0 1 131.04 508.56 Tm <6EE06F20> Tj 1 0 0 1 148.32 508.56 Tm <73F320> Tj 1 0 0 1 159.36 509.04 Tm <70656C6120> Tj 1 0 0 1 178.56 508.56 Tm <6361726163746572ED737469636120> Tj 1 0 0 1 233.76 508.56 Tm <6C756D696E6F736120> Tj 1 0 0 1 272.64 508.56 Tm <636F6D6F20> Tj 1 0 0 1 297.12 508.56 Tm <74616D62E96D20> Tj 1 0 0 1 331.68 509.04 Tm <70656C6120> Tj 1 0 0 1 350.88 508.56 Tm <7472616E73666572EA6E63696120> Tj 1 0 0 1 404.88 508.56 Tm <646520> Tj 1 0 0 1 416.88 508.56 Tm <656E657267696120> Tj 1 0 0 1 448.32 508.56 Tm <72616469616E74652E20> Tj 1 0 0 1 485.76 512.16 Tm <742A6C> Tj 0.48 Tc 1 0 0 1 98.88 497.04 Tm <436F6D6F20> Tj 1 0 0 1 126.48 497.28 Tm <6E6120> Tj 1 0 0 1 139.44 497.52 Tm <717565696D6120> Tj 1 0 0 1 172.32 497.04 Tm <646520> Tj 1 0 0 1 185.04 497.04 Tm <756D6120> Tj 1 0 0 1 206.16 497.04 Tm <76656C6120> Tj 1 0 0 1 226.08 497.04 Tm <74656D2D736520> Tj 1 0 0 1 256.08 497.04 Tm <756D6120> Tj 1 0 0 1 276.96 497.04 Tm <636F6E766563E7E36F20> Tj 1 0 0 1 322.32 497.04 Tm <6E61747572616C2C20> Tj 1 0 0 1 356.40 497.04 Tm <6973746F20> Tj 1 0 0 1 374.16 497.04 Tm <652C20> Tj 1 0 0 1 384.48 497.04 Tm <6F20> Tj 1 0 0 1 393.12 497.04 Tm <666C7569646F20> Tj 1 0 0 1 420.24 497.28 Tm <6D6F76696D656E74612D736520> Tj 1 0 0 1 480.24 497.52 Tm <706F7220> Tj 1 0 0 1 497.28 497.28 Tm <736920> Tj 1 0 0 1 507.12 497.52 Tm <7072F37072696F> Tj 0.72 Tc 1 0 0 1 56.88 483.84 Tm <49434F4D4F20> Tj 1 0 0 1 93.60 485.52 Tm <4F20> Tj 1 0 0 1 105.12 485.76 Tm <464C55CC444F20> Tj 1 0 0 1 146.16 485.52 Tm <534520> Tj 1 0 0 1 161.76 485.52 Tm <4D4F56494D454E544120> Tj 1 0 0 1 228.00 485.52 Tm <504F5220> Tj 1 0 0 1 252.00 485.52 Tm <534920> Tj 1 0 0 1 264.72 485.52 Tm <50524F5052494F272F5D20> Tj 1 0 0 1 319.20 485.52 Tm <696E666C75656E636961646F20> Tj 1 0 0 1 372.96 486.00 Tm <706F7220> Tj 1 0 0 1 390.72 485.52 Tm <65666569746F7320> Tj 1 0 0 1 421.44 486.00 Tm <6772617669746163696F6E61697320> Tj 1 0 0 1 481.44 485.52 Tm <6173736F636961646F7320> Tj 1 0 0 1 528.24 485.76 Tm Tj 0.48 Tc 1 0 0 1 56.40 474.00 Tm <6469666572656EE7617320> Tj 1 0 0 1 102.24 474.00 Tm <646520> Tj 1 0 0 1 116.40 474.00 Tm <64656E7369646164652C20> Tj 1 0 0 1 163.44 474.00 Tm <617320> Tj 1 0 0 1 176.64 474.00 Tm <666F72E7617320> Tj 1 0 0 1 205.68 474.00 Tm <646520> Tj 1 0 0 1 220.08 474.00 Tm <696EE97263696120> Tj 1 0 0 1 251.76 474.00 Tm <6EE36F20> Tj 1 0 0 1 271.20 474.00 Tm <73E36F20> Tj 1 0 0 1 289.20 474.00 Tm <696D706F7274616E74657320> Tj 1 0 0 1 341.52 472.08 Tm <5B505127CC20> Tj 1 0 0 1 366.24 474.00 Tm <4A5553544946495155455D2E20> Tj 1 0 0 1 432.24 474.00 Tm <506F7274616E746F2C20> Tj 1 0 0 1 473.52 474.00 Tm <6573736520> Tj 1 0 0 1 494.64 474.24 Tm <726567696D6520> Tj 1 0 0 1 527.04 474.24 Tm <6465> Tj 0.48 Tc 1 0 0 1 56.40 462.48 Tm <6573636F616D656E746F20> Tj 1 0 0 1 106.08 462.48 Tm <6520> Tj 1 0 0 1 113.76 462.48 Tm Tj 1 0 0 1 168.24 462.96 Tm <70656C6F20> Tj 1 0 0 1 188.16 462.48 Tm <6EFA6D65726F20> Tj 1 0 0 1 221.28 462.48 Tm <646520> Tj 1 0 0 1 233.04 462.48 Tm <47726173686F6620> Tj 1 0 0 1 267.60 462.96 Tm <71756520> Tj 1 0 0 1 284.40 462.48 Tm <6573746162656C65636520> Tj 1 0 0 1 328.08 462.48 Tm <6172617AE36F20> Tj 1 0 0 1 359.04 462.48 Tm <656E74726520> Tj 1 0 0 1 381.60 462.48 Tm <617320> Tj 1 0 0 1 392.16 462.48 Tm <666F72E7617320> Tj 1 0 0 1 419.04 462.48 Tm <646520> Tj 1 0 0 1 431.04 462.48 Tm <656D7075786F20> Tj 1 0 0 1 465.36 462.48 Tm <6520> Tj 1 0 0 1 472.32 462.72 Tm <666F72E7617320> Tj 1 0 0 1 499.20 462.72 Tm <766973636F7361733A> Tj 0.72 Tc 1 0 0 1 264.00 450.00 Tm <477220> Tj 1 0 0 1 276.96 452.64 Tm <2D20> Tj 1 0 0 1 285.12 450.48 Tm <70274C33676620> Tj 1 0 0 1 316.80 448.08 Tm <316620> Tj 1 0 0 1 326.88 448.56 Tm <2C> Tj 1.20 Tc 1 0 0 1 56.40 438.24 Tm <6F6E64656765616163656C657261E7E36F64616772617669646164652C706164656E7369646164652C7061766973636F73696461646563696E656DE174696361646F67E1732C4C656F636F6D7072696D656E746F6361726163746572ED737469636F> Tj 0.48 Tc 1 0 0 1 56.40 426.72 Tm <646120> Tj 1 0 0 1 68.40 427.20 Tm <67656F6D657472696120> Tj 1 0 0 1 110.64 426.72 Tm <656D20> Tj 1 0 0 1 125.28 426.72 Tm <65737475646F20> Tj 1 0 0 1 156.48 430.32 Tm <72276C> Tj 0.48 Tc 1 0 0 1 99.12 415.20 Tm <456D20> Tj 1 0 0 1 115.68 415.20 Tm <65737475646F20> Tj 1 0 0 1 144.72 414.96 Tm <616E746572696F7220> Tj 1 0 0 1 178.80 414.96 Tm <646520> Tj 1 0 0 1 191.28 414.96 Tm <6368616D6120> Tj 1 0 0 1 220.32 414.96 Tm <646966757369766120> Tj 1 0 0 1 255.36 414.96 Tm <61646A6163656E746520> Tj 1 0 0 1 296.16 414.96 Tm <6120> Tj 1 0 0 1 303.36 414.96 Tm <756D20> Tj 1 0 0 1 318.96 415.20 Tm <706176696F2C20> Tj 1 0 0 1 347.04 414.96 Tm <416C736169726166692C20> Tj 1 0 0 1 387.36 414.96 Tm <4C656520> Tj 1 0 0 1 405.12 414.96 Tm <6520> Tj 1 0 0 1 412.80 414.96 Tm <542769656E20> Tj 1 0 0 1 437.28 418.32 Tm <6C726C20> Tj 1 0 0 1 448.32 413.04 Tm <4920> Tj 1 0 0 1 454.32 414.96 Tm <41544520> Tj 1 0 0 1 476.88 414.96 Tm <4553544520> Tj 1 0 0 1 503.76 414.96 Tm <504F4E544F> Tj 0.72 Tc 1 0 0 1 56.40 403.44 Tm <444F20> Tj 1 0 0 1 74.16 403.44 Tm <544558544F20> Tj 1 0 0 1 110.40 403.44 Tm <564320> Tj 1 0 0 1 127.44 403.44 Tm <4EC04F20> Tj 1 0 0 1 152.64 403.20 Tm <55534F5520> Tj 1 0 0 1 183.12 403.20 Tm <4F20> Tj 1 0 0 1 193.68 403.44 Tm <4E4F4D4520> Tj 1 0 0 1 226.56 403.20 Tm <444F5320> Tj 1 0 0 1 250.08 403.20 Tm <4155544F52455320> Tj 1 0 0 1 299.28 403.20 Tm <444F5320> Tj 1 0 0 1 322.80 403.20 Tm <41525454474F532C20> Tj 1 0 0 1 371.76 405.60 Tm <705120> Tj 1 0 0 1 388.08 403.20 Tm <46415A20> Tj 1 0 0 1 410.16 403.20 Tm <7253534F20> Tj 1 0 0 1 435.12 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"t.1.1... ', "t::':;:;;4"',ir 'i "'':; ,' 4,ee1WM Figura l. (a) Charra estendida sob urn eito cornbustvel: (b) charna esrica ile urna rela enr concites de nricrngravidatlc.Na queima entre a paratna e o oxignio do ar. a quantidade de oxignio e apoximadamente r0%r e por isso aco.busto e incompleta. \esse caso. de\ido tlta de orignio tYC \CH\ QUE O OXIGENIO CONTIDO NAAT\lOSFER\ E \SLFICIE\TE P\R\ OLE\I\R \ P\R\FI\\ CO\TID.\ \U\1.\ \'I]I -\] SE TUARESPOST\ FC)R FIR\\TI\ \. \ FR\SE \\TERIOR EST.\ CC)RRET{ SE FOR \F-GATI\"\. TUARESP( )Si,\ aS: r, aR.R\D\ ::.- j-- ;:rl.-:.- rj. 3 t:in\..m3d3 :ut C0,. harendr. ptr1tl1to. a ibrnrao de.-l:a-:-- :::::: i-). ::- J-:-. ;r ,-:'.t*::i,-. :::..nrlaa :.. :ieqentenl.rt. C. C'O. CO: e H;O. .\ssinr. a tormao dc-;l:;e:: l- J3 :.r :::-:::3::ii J.:r:a J.-IlrL'usii.,e no quernado ]rberad'. J; ;r.rnrr pa13 a 3tnlostra. tieqentenlente.-'t':.:-' 3i: :l; :r::l-:::-- .te hld:..;erL'..netos. O po!'esso da tormao de trgenr consiste da pirlrse do conrbustr.'el crea,--: Je rrlia;r. ..mr3r l.r prinreiro ane de benzeno e postenor tbrnrao de hidrocarbonetos policclicosaronrtr,-os. aparcrnlentr da prinreira particula. crescimento das partculas de tligem derido s reaes das espcies datse gasosa. coalescncia da panicula. aglomerao e oxidao.l MELHORE A EXPLICAO DOS NECANISNlOS DEFOR\{AC.{O DE FULIGEM] Quando essas partculas passam atravs da chama, elas irradiam como corpos negros.Isso e responsvel no s pela caracterstica luminosa como tambm pela transferncia de energia radiante. t*lComo na queima de uma vela tem-se uma conveco natural, isto e, o fluido movimenta-se por si prprioICOMO O FLUDO SE MOVIMENTA POR SI PROPRIO'/] influenciado por efeitos gravitacionais associados sdiferenas de densidade, as foras de inrcia no so importantes [PQ' JUSTIFIQUE]. Portanto, esse regime deescoamento e aracerizado pelo nmero de Grashof que estabelece arazo entre as foras de empuxo e foras viscosas:Gr - p'L3gf 1f ,ondegeaaceleraodagravidade,padensidade,paviscosidadecinemticadogs,Leocomprimentocaractersticoda geometria em estudo r'lEm estudo anterior de chama difusiva adjacente a um pavio, Alsairafi, Lee e T'ien lrl I ATE ESTE PONTODO TEXTO VC NO USOU O NOME DOS AUTORES DOS ARTTGOS, pQ FAZ rSSO AGORA' VC PRECTSAMANTER A COERENCIA NA CITACAO DAS REFERENCIASI apresentaram um modelo em que as equaes demomento de Navier-Stokes completas, com termos de foras de corpo, esto includas, permitindo o estudo do eito dagravidade na chama estabilizada no pavio (com gravidade zero o aso limitante). IPQ VC USOU O PORTANTO. SEVC NAO ESTA'CONCLUIDO NADA ANTERIORMENTE CITADO?I Portanto, o calor detalhado [O QUE CALORDETALHADO'/] e o fenmeno de transferncia de massa dentro do pavio poroso no so tratados. Ao invs disto. assumido que uma camada fina de combustvel lquido cobre toda a superficie do pavio durante o processo de queima.INAO ENTENDI A LIGACAO COM A FRASE ANTERIOR] Esse o caso limitante no qual o processo detransferncia de massa no pavio muito mais rpido que o processo de evaporao na superficie do pavio. trlO objetivo deste trabalho e estudar o efeito do nmero de Grashof em hamas difusivas, tendo em r,'ista arelao da variao no comprimento do pavio com a combusto, utilizando-se a queima de uma vela comum.Formulao do ModeloA configurao considerada no desenvolvimento do modelo mostrada na Figura 2. O modelo consiste deum pavio cilndrico poroso apoiado sobre o topo de um corpo cilndrico inerte. O experimento foi realizado emcondies atmosfricas (ar ilimitado e gravidade no sentido negativo da direo z). ,-r-t*s"*".1"f-f o-:'{ *{{ ""d '*c'trt:r. . 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162.72 728.88 Tm <6720> Tj 1 0 0 1 169.92 728.40 Tm <2F20> Tj 1 0 0 1 175.68 726.24 Tm <6C2E2C7420> Tj 1 0 0 1 198.24 728.88 Tm <286EFA6D65726F20> Tj 1 0 0 1 234.48 727.92 Tm <646520> Tj 1 0 0 1 246.48 727.92 Tm <47726173686FCD29> Tj 0.24 Tc 1 0 0 1 120.00 717.12 Tm <526520> Tj 1 0 0 1 133.20 719.52 Tm <2D20> Tj 1 0 0 1 141.60 717.36 Tm <7020> Tj 1 0 0 1 149.04 717.12 Tm <4C20> Tj 1 0 0 1 157.20 716.88 Tm <752C20> Tj 1 0 0 1 166.80 717.12 Tm <2F20> Tj 1 0 0 1 172.56 717.36 Tm <707220> Tj 1 0 0 1 198.24 717.36 Tm <286EFA6D65726F20> Tj 1 0 0 1 234.48 716.64 Tm <646520> Tj 1 0 0 1 246.24 716.64 Tm <5265796E6F6C647329> Tj 0.48 Tc 1 0 0 1 99.36 705.84 Tm <417320> Tj 1 0 0 1 113.04 705.84 Tm <65717561E7F5657320> Tj 1 0 0 1 151.92 705.60 Tm <646520> Tj 1 0 0 1 163.92 705.60 Tm <636F6E7365727661E7E36F20> Tj 1 0 0 1 215.76 705.36 Tm <64617320> Tj 1 0 0 1 231.60 705.12 Tm <657370E96369657320> Tj 1 0 0 1 267.12 705.12 Tm <6520> Tj 1 0 0 1 274.08 705.12 Tm <656E657267696120> Tj 1 0 0 1 306.00 704.88 Tm <6164696D656E73696F6E616C697A6164617320> Tj 1 0 0 1 386.40 705.12 Tm <706F64656D20> Tj 1 0 0 1 416.16 704.64 Tm <73657220> Tj 1 0 0 1 430.32 704.64 Tm <657363726974617320> Tj 1 0 0 1 462.72 704.64 Tm <636F6D6F3A> Tj 1.50 Tc /F3 11.0 Tf 1 0 0 1 126.96 675.36 Tm <4972EC592D2A722C2E592CEC5F20> Tj 1 0 0 1 232.56 680.40 Tm <7C20> Tj 1 0 0 1 243.84 675.36 Tm <5B2720> Tj 1 0 0 1 265.92 680.16 Tm <2EED52E828766F20> Tj 1 0 0 1 326.88 680.16 Tm <4C2C2C6CEC5F2E72285D2C20> Tj 1 0 0 1 400.80 679.92 Tm <722C2C296C5F2E3B> Tj 1.50 Tc 1 0 0 1 125.76 667.68 Tm <5C20> Tj 1 0 0 1 146.64 668.40 Tm <615220> Tj 1 0 0 1 189.84 668.16 Tm <617A6C20> Tj 1 0 0 1 228.24 667.92 Tm <506520> Tj 1 0 0 1 243.84 664.80 Tm <666E616E7220> Tj 1 0 0 1 312.72 667.44 Tm <615220> Tj 1 0 0 1 347.52 668.64 Tm <2920> Tj 1 0 0 1 380.64 667.44 Tm <697A2720> Tj 1 0 0 1 418.80 664.32 Tm <5D20> Tj 1 0 0 1 436.08 671.76 Tm <22> Tj 1.50 Tc /F3 28.0 Tf 1 0 0 1 337.92 759.60 Tm <2D2329> Tj 1.50 Tc /F3 12.0 Tf 1 0 0 1 381.12 762.48 Tm <2C20> Tj 1 0 0 1 392.40 765.12 Tm <6174722731> Tj 1.50 Tc 1 0 0 1 379.44 759.60 Tm <2D20> Tj 1 0 0 1 390.72 752.64 Tm <612C20> Tj 1 0 0 1 397.92 752.88 Tm <7A2E20> Tj 1 0 0 1 415.92 750.24 Tm <29> Tj 1.20 Tc /F3 10.0 Tf 1 0 0 1 524.88 764.40 Tm <283729> Tj 1.44 Tc /F3 9.0 Tf 1 0 0 1 525.12 678.48 Tm <283829> Tj 0.00 Tc /F3 10.0 Tf 1 0 0 1 234.72 641.04 Tm Tj 0.00 Tc 1 0 0 1 231.84 631.92 Tm <2E> Tj 1.50 Tc /F3 5.0 Tf 1 0 0 1 361.20 590.40 Tm <2C3437> Tj 0.96 Tc /F3 9.0 Tf 1 0 0 1 56.64 563.52 Tm <4F6E696520> Tj 1 0 0 1 83.76 563.52 Tm <506520> Tj 1 0 0 1 96.24 565.68 Tm <2D20> Tj 1 0 0 1 104.64 563.28 Tm <4C752D20> Tj 1 0 0 1 124.80 563.28 Tm <44292E20> Tj 1 0 0 1 138.96 563.28 Tm <7B6E756E6C65726F20> Tj 1 0 0 1 174.96 563.04 Tm <646520> Tj 1 0 0 1 187.20 563.04 Tm <506563CC657472> Tj 0.48 Tc 1 0 0 1 112.80 554.64 Tm <272C273B4C> Tj 1.50 Tc 1 0 0 1 110.64 537.36 Tm <70726C> Tj 0.48 Tc 1 0 0 1 99.12 523.44 Tm <2E5C7320> Tj 1 0 0 1 118.08 523.20 Tm <636F6E6469E7F5657320> Tj 1 0 0 1 165.84 522.96 Tm <646520> Tj 1 0 0 1 183.12 522.96 Tm <636F6E746F726E6F20> Tj 1 0 0 1 226.80 522.72 Tm <646F20> Tj 1 0 0 1 244.56 522.96 Tm <70726F626C656D612C20> Tj 1 0 0 1 292.80 522.48 Tm <71756520> Tj 1 0 0 1 315.36 522.00 Tm <657374E06F20> Tj 1 0 0 1 343.92 522.00 Tm <72656C6163696F6E6164617320> Tj 1 0 0 1 401.52 521.76 Tm <636F6D20> Tj 1 0 0 1 426.72 521.76 Tm <6F20> Tj 1 0 0 1 439.92 521.52 Tm <636F6E6A756E746F20> Tj 1 0 0 1 482.64 521.28 Tm <6465> Tj 0.72 Tc 1 0 0 1 56.40 511.92 Tm <6164696D656E73696F6E616C697A6164617320> Tj 1 0 0 1 137.28 511.68 Tm <6C6F676F20> Tj 1 0 0 1 157.20 511.44 Tm <6163696D612C20> Tj 1 0 0 1 186.00 511.20 Tm <73E36F20> Tj 1 0 0 1 201.84 511.20 Tm <617320> Tj 1 0 0 1 212.64 511.20 Tm <73656775696E7465733A> Tj 0.48 Tc 1 0 0 1 98.88 502.32 Tm <2D20> Tj 1 0 0 1 104.40 500.40 Tm <4E6120> Tj 1 0 0 1 118.80 500.16 Tm <64697265E7E36F20> Tj 1 0 0 1 150.48 500.16 Tm <72616469616C> Tj 1.50 Tc 1 0 0 1 255.36 640.80 Tm <4920> Tj 1 0 0 1 269.04 640.56 Tm <722720> Tj 1 0 0 1 290.16 638.88 Tm <5E20> Tj 1 0 0 1 299.52 640.56 Tm <6128292E20> Tj 1 0 0 1 331.68 640.32 Tm <6C2C20> Tj 1 0 0 1 346.80 639.12 Tm <2927> Tj 1.50 Tc 1 0 0 1 253.68 628.32 Tm <523B5220> Tj 1 0 0 1 317.28 628.32 Tm <2752> Tj 1.50 Tc /F3 3.0 Tf 1 0 0 1 291.84 601.68 Tm <692C70> Tj 1.20 Tc /F3 12.0 Tf 1 0 0 1 525.12 638.88 Tm <286529> Tj 1.44 Tc /F3 10.0 Tf 1 0 0 1 519.60 599.04 Tm <2820> Tj 1 0 0 1 523.92 598.56 Tm <313029> Tj 1.50 Tc /F3 8.0 Tf 1 0 0 1 518.40 562.32 Tm <286C6C29> Tj 1.50 Tc /F3 9.0 Tf 1 0 0 1 519.12 546.00 Tm <2820> Tj 1 0 0 1 523.44 545.52 Tm <316C29> Tj 0.72 Tc 1 0 0 1 500.16 521.28 Tm <65717561E7F26573> Tj 1.50 Tc 1 0 0 1 518.16 486.96 Tm <2820> Tj 1 0 0 1 522.72 486.72 Tm <6C3329> Tj 1.44 Tc 1 0 0 1 518.64 464.40 Tm <2820> Tj 1 0 0 1 522.96 464.16 Tm <313429> Tj 1.50 Tc 1 0 0 1 517.44 430.32 Tm <2820> Tj 1 0 0 1 521.76 429.84 Tm <6C3529> Tj 1.50 Tc 1 0 0 1 518.16 406.80 Tm <2820> Tj 1 0 0 1 522.72 406.32 Tm <6C3629> Tj 1.50 Tc 1 0 0 1 56.40 489.12 Tm <656D523A31> Tj 0.72 Tc 1 0 0 1 56.40 466.32 Tm <656D20> Tj 1 0 0 1 71.04 466.56 Tm <5220> Tj 1 0 0 1 79.92 468.72 Tm <2D20> Tj 1 0 0 1 88.08 466.32 Tm <522A362C2C> Tj 1.50 Tc /F3 8.0 Tf 1 0 0 1 56.16 432.24 Tm <656D5A3A20> Tj 1 0 0 1 88.80 432.24 Tm <6C2C20> Tj 1 0 0 1 126.96 433.20 Tm <2B> Tj 0.00 Tc /F3 3.0 Tf 1 0 0 1 56.16 422.16 Tm <67> Tj 0.96 Tc /F3 7.0 Tf 1 0 0 1 56.16 408.96 Tm <656D5A3A20> Tj 1 0 0 1 87.36 408.96 Tm <32313131365E2C20> Tj 1 0 0 1 126.72 409.92 Tm <2B> Tj 1.50 Tc /F3 9.0 Tf 1 0 0 1 126.96 490.08 Tm <2B20> Tj 1 0 0 1 162.24 486.48 Tm <596F3A302C59723A59702C20> Tj 1 0 0 1 232.80 487.92 Tm <65303A313B> Tj 0.48 Tc 1 0 0 1 162.48 466.32 Tm <796F20> Tj 1 0 0 1 174.00 468.00 Tm <3A20> Tj 1 0 0 1 182.16 465.84 Tm <596F2D2C20> Tj 1 0 0 1 204.00 466.08 Tm <797220> Tj 1 0 0 1 214.80 467.76 Tm <3A20> Tj 1 0 0 1 222.96 465.36 Tm <302C20> Tj 1 0 0 1 233.04 465.36 Tm <3020> Tj 1 0 0 1 240.24 467.52 Tm <3A20> Tj 1 0 0 1 248.40 465.36 Tm <54222E20> Tj 1 0 0 1 261.60 465.12 Tm <2F20> Tj 1 0 0 1 266.88 465.12 Tm <54622C20> Tj 1 0 0 1 281.04 464.88 Tm <5520> Tj 1 0 0 1 290.64 467.28 Tm <3A20> Tj 1 0 0 1 299.04 464.88 Tm <3020> Tj 1 0 0 1 306.48 464.88 Tm <6520> Tj 1 0 0 1 313.44 464.88 Tm Tj 1 0 0 1 327.84 464.88 Tm <2F20> Tj 1 0 0 1 333.12 464.64 Tm Tj 1 0 0 1 347.04 467.04 Tm <2D20> Tj 1 0 0 1 355.44 464.64 Tm <30> Tj 0.48 Tc 1 0 0 1 103.92 443.28 Tm <4E6120> Tj 1 0 0 1 118.08 443.04 Tm <64697265E7E36F20> Tj 1 0 0 1 150.00 443.04 Tm <617869616C> Tj 1.50 Tc 1 0 0 1 162.00 429.60 Tm <596F3A302C59723A596E2C65303A6C> Tj 1.20 Tc 1 0 0 1 162.00 408.72 Tm <796F20> Tj 1 0 0 1 172.56 410.64 Tm <3A20> Tj 1 0 0 1 180.72 408.24 Tm <59652C2C2C20> Tj 1 0 0 1 202.32 408.24 Tm <79723A20> Tj 1 0 0 1 221.52 407.76 Tm <302C20> Tj 1 0 0 1 231.60 410.16 Tm <6720> Tj 1 0 0 1 238.56 410.16 Tm <3A542C20> Tj 1 0 0 1 259.92 407.76 Tm <4920> Tj 1 0 0 1 265.20 407.52 Tm <54362C563A20> Tj 1 0 0 1 297.36 407.28 Tm <3020> Tj 1 0 0 1 305.04 407.28 Tm <6520> Tj 1 0 0 1 311.76 407.28 Tm Tj 1 0 0 1 326.16 407.28 Tm <4920> Tj 1 0 0 1 331.68 407.04 Tm Tj 1 0 0 1 353.28 407.04 Tm <30> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 55.92 372.24 Tm <4D617465726961697320> Tj 1 0 0 1 108.00 372.00 Tm <6520> Tj 1 0 0 1 116.40 372.00 Tm <4DE9746F646F73> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 98.40 349.20 Tm <5061726120> Tj 1 0 0 1 119.28 348.96 Tm <6120> Tj 1 0 0 1 127.44 348.96 Tm <7265616C747A61E7E36F20> Tj 1 0 0 1 170.64 348.48 Tm <646573736520> Tj 1 0 0 1 195.36 348.24 Tm <6578706572696D656E746F20> Tj 1 0 0 1 248.40 348.00 Tm <666F72616D20> Tj 1 0 0 1 275.28 347.76 Tm <7574696C697A61646F733A20> Tj 1 0 0 1 320.16 347.52 Tm <76656C6120> Tj 1 0 0 1 340.08 347.28 Tm <636F6D756D20> Tj 1 0 0 1 373.20 347.04 Tm <646520> Tj 1 0 0 1 385.68 347.52 Tm <7061726166696E612E20> Tj 1 0 0 1 424.56 347.04 Tm <7375706F72746520> Tj 1 0 0 1 456.48 347.04 Tm <7061726120> Tj 1 0 0 1 477.36 346.56 Tm <6120> Tj 1 0 0 1 484.80 346.56 Tm <76656C612E20> Tj 1 0 0 1 506.88 346.32 Tm <7465736F757261> Tj 0.48 Tc 1 0 0 1 55.68 338.16 Tm <7061726120> Tj 1 0 0 1 75.60 337.44 Tm <636F7274617220> Tj 1 0 0 1 101.52 337.20 Tm <6F20> Tj 1 0 0 1 108.72 337.68 Tm <706176696F20> Tj 1 0 0 1 133.68 336.96 Tm <646120> Tj 1 0 0 1 145.44 336.96 Tm <76656C6120> Tj 1 0 0 1 164.40 336.96 Tm <6E6F7320> Tj 1 0 0 1 180.72 336.72 Tm <6469666572656E74657320> Tj 1 0 0 1 222.48 336.24 Tm <636F6D7072696D656E746F732C20> Tj 1 0 0 1 284.64 335.76 Tm <657363616C6120> Tj 1 0 0 1 311.76 335.76 Tm <6D6574E16C69636120> Tj 1 0 0 1 347.52 336.00 Tm <7061726120> Tj 1 0 0 1 367.68 335.52 Tm <6D6564697220> Tj 1 0 0 1 393.12 335.28 Tm <6120> Tj 1 0 0 1 400.32 335.28 Tm <616C7475726120> Tj 1 0 0 1 425.52 335.04 Tm <646F20> Tj 1 0 0 1 438.00 335.52 Tm <706176696F2C20> Tj 1 0 0 1 465.36 334.80 Tm Tj 1 0 0 1 500.16 334.56 Tm <6520> Tj 1 0 0 1 507.12 334.56 Tm <63E26D657261> Tj 0.48 Tc 1 0 0 1 55.68 325.92 Tm <6469676974616C20> Tj 1 0 0 1 83.52 326.40 Tm <7061726120> Tj 1 0 0 1 103.20 325.68 Tm <72656769737472617220> Tj 1 0 0 1 138.96 325.44 Tm <617320> Tj 1 0 0 1 149.76 325.20 Tm <65746170617320> Tj 1 0 0 1 177.12 325.20 Tm <646F20> Tj 1 0 0 1 189.60 325.68 Tm <70726573656E746520> Tj 1 0 0 1 225.36 324.72 Tm <65737475646F2E> Tj 0.48 Tc 1 0 0 1 98.16 314.64 Tm <4120> Tj 1 0 0 1 109.92 314.40 Tm <6D65746F646F6C6F67696120> Tj 1 0 0 1 165.12 313.92 Tm <7574746C697A61646120> Tj 1 0 0 1 203.76 313.68 Tm <636F6E73697374697520> Tj 1 0 0 1 243.84 313.44 Tm <646520> Tj 1 0 0 1 258.24 313.44 Tm <6F627365727661E7F5657320> Tj 1 0 0 1 311.52 312.96 Tm <6E6120> Tj 1 0 0 1 325.68 312.96 Tm <666F726D612C20> Tj 1 0 0 1 356.64 312.72 Tm <636F722C20> Tj 1 0 0 1 376.80 312.72 Tm <6C756D696E6F73696461646520> Tj 1 0 0 1 435.12 312.24 Tm <646120> Tj 1 0 0 1 449.28 312.24 Tm <6368616D6120> Tj 1 0 0 1 479.76 312.00 Tm <656D20> Tj 1 0 0 1 496.80 312.00 Tm <6469666572656E746573> Tj 0.48 Tc 1 0 0 1 55.68 303.12 Tm <636F6D7072696D656E746F7320> Tj 1 0 0 1 115.20 302.64 Tm <646520> Tj 1 0 0 1 126.96 303.12 Tm <706176696F2E> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 55.92 275.76 Tm <526573756C7461646F7320> Tj 1 0 0 1 114.48 275.28 Tm <6520> Tj 1 0 0 1 122.64 275.28 Tm <44697363757373E36F> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 97.92 252.24 Tm <447572616E746520> Tj 1 0 0 1 134.64 251.76 Tm <617320> Tj 1 0 0 1 147.36 251.52 Tm <65746170617320> Tj 1 0 0 1 176.64 251.28 Tm <646120> Tj 1 0 0 1 190.32 251.52 Tm <726561E7E36F2C20> Tj 1 0 0 1 223.68 251.04 Tm <6120> Tj 1 0 0 1 232.08 251.52 Tm <7061726166696E6120> Tj 1 0 0 1 269.52 250.56 Tm Tj 1 0 0 1 278.64 250.56 Tm <7375626D657469646120> Tj 1 0 0 1 324.00 250.32 Tm Tj 1 0 0 1 332.64 250.80 Tm <706972F36C6973652C20> Tj 1 0 0 1 369.84 250.08 Tm <666F726D616E646F20> Tj 1 0 0 1 413.04 249.84 Tm <6D6F6CE963756C617320> Tj 1 0 0 1 457.68 249.60 Tm <6D656E6F72657320> Tj 1 0 0 1 495.84 249.36 Tm <6520> Tj 1 0 0 1 504.72 249.36 Tm <7261646963616973> Tj 0.48 Tc 1 0 0 1 55.44 240.48 Tm <636F6E7374697475ED646F7320> Tj 1 0 0 1 106.80 240.24 Tm <646520> Tj 1 0 0 1 119.52 240.00 Tm <636172626F6E6F20> Tj 1 0 0 1 155.04 239.76 Tm <6520> Tj 1 0 0 1 162.48 239.76 Tm <686964726F67EA6E696F2E20> Tj 1 0 0 1 211.44 239.28 Tm <4F7320> Tj 1 0 0 1 225.60 239.28 Tm Tj 1 0 0 1 257.76 239.04 Tm <646520> Tj 1 0 0 1 270.24 239.04 Tm <686964726F67EA6E696F20> Tj 1 0 0 1 316.80 238.56 Tm <73E36F20> Tj 1 0 0 1 333.12 238.56 Tm <6D61697320> Tj 1 0 0 1 355.20 238.32 Tm <6C657665732C20> Tj 1 0 0 1 381.12 238.56 Tm <706F7274616E746F20> Tj 1 0 0 1 417.60 238.08 Tm <72656167656D20> Tj 1 0 0 1 450.24 237.60 Tm <636F6D20> Tj 1 0 0 1 470.40 237.60 Tm <6F20> Tj 1 0 0 1 478.80 237.60 Tm <6F786967EA6E696F20> Tj 1 0 0 1 516.72 237.60 Tm <6D616973> Tj 0.48 Tc 1 0 0 1 55.44 228.96 Tm <7261706964616D656E74652E20> Tj 1 0 0 1 111.60 228.24 Tm <4F7320> Tj 1 0 0 1 127.20 228.24 Tm Tj 1 0 0 1 160.56 228.00 Tm <646520> Tj 1 0 0 1 174.48 227.76 Tm <636172626F6E6F2C20> Tj 1 0 0 1 213.84 227.52 Tm <616C656D20> Tj 1 0 0 1 237.36 227.52 Tm <646520> Tj 1 0 0 1 251.52 227.28 Tm <6573746172656D20> Tj 1 0 0 1 287.04 227.04 Tm <656D20> Tj 1 0 0 1 303.84 226.80 Tm <6578636573736F2C20> Tj 1 0 0 1 341.76 226.56 Tm <73E36F20> Tj 1 0 0 1 359.52 226.56 Tm <6D61697320> Tj 1 0 0 1 382.56 227.04 Tm <70657361646F7320> Tj 1 0 0 1 419.04 226.32 Tm <6520> Tj 1 0 0 1 428.16 226.32 Tm <6C656E746F732E20> Tj 1 0 0 1 458.88 226.08 Tm <506F7274616E746F2C20> Tj 1 0 0 1 499.44 225.84 Tm <64657669646F20> Tj 1 0 0 1 531.12 225.60 Tm Tj 0.48 Tc 1 0 0 1 55.44 217.44 Tm <646566696369EA6E63696120> Tj 1 0 0 1 103.44 216.96 Tm <646520> Tj 1 0 0 1 117.12 216.96 Tm <6F786967EA6E696F2C20> Tj 1 0 0 1 158.64 217.20 Tm <706172746520> Tj 1 0 0 1 183.12 216.48 Tm <646F20> Tj 1 0 0 1 197.52 216.24 Tm <636172626F6E6F20> Tj 1 0 0 1 233.76 216.24 Tm <6EE36F20> Tj 1 0 0 1 252.72 216.00 Tm Tj 1 0 0 1 261.36 215.76 Tm <7472616E73666F726D61646120> Tj 1 0 0 1 318.24 215.52 Tm <656D20> Tj 1 0 0 1 334.80 215.28 Tm <434F322C20> Tj 1 0 0 1 358.80 215.28 Tm <7472616E73666F726D616E646F2D736520> Tj 1 0 0 1 432.72 214.80 Tm <656D20> Tj 1 0 0 1 449.28 214.56 Tm <6F757472617320> Tj 1 0 0 1 477.84 215.04 Tm <70617274ED63756C617320> Tj 1 0 0 1 521.04 214.80 Tm <717565> Tj 0.48 Tc 1 0 0 1 55.20 205.92 Tm <7265636562656D20> Tj 1 0 0 1 92.64 205.44 Tm <6F20> Tj 1 0 0 1 101.52 205.44 Tm <6E6F6D6520> Tj 1 0 0 1 126.96 205.20 Tm <646520> Tj 1 0 0 1 140.16 205.20 Tm <66756C6967656D2E20> Tj 1 0 0 1 177.12 204.96 Tm <457373617320> Tj 1 0 0 1 202.56 205.20 Tm <70617274ED63756C617320> Tj 1 0 0 1 245.28 204.48 Tm <666963616D20> Tj 1 0 0 1 271.44 204.24 Tm <696E63616E64657363656E74657320> Tj 1 0 0 1 334.80 203.76 Tm <656D20> Tj 1 0 0 1 350.64 203.76 Tm <636F6E7461746F20> Tj 1 0 0 1 383.52 203.52 Tm <636F6D20> Tj 1 0 0 1 404.16 203.28 Tm <6120> Tj 1 0 0 1 412.32 203.28 Tm <6368616D612E20> Tj 1 0 0 1 444.24 203.04 Tm <6361726163746572697A616E646F20> Tj 1 0 0 1 506.16 202.80 Tm <73756120> Tj 1 0 0 1 522.72 202.80 Tm <636F72> Tj 0.48 Tc 1 0 0 1 55.44 194.16 Tm <616D6172656C6164612E> Tj 0.48 Tc 1 0 0 1 97.92 180.72 Tm <5175616C7175657220> Tj 1 0 0 1 138.24 182.88 Tm <71756520> Tj 1 0 0 1 156.24 182.16 Tm <73656A6120> Tj 1 0 0 1 174.96 182.16 Tm <6120> Tj 1 0 0 1 182.64 182.40 Tm <706F7369E7E36F20> Tj 1 0 0 1 216.72 181.68 Tm <646120> Tj 1 0 0 1 229.20 181.68 Tm <76656C612C20> Tj 1 0 0 1 251.76 181.44 Tm <6F20> Tj 1 0 0 1 260.40 181.44 Tm <666F676F20> Tj 1 0 0 1 281.76 181.20 Tm <73656D70726520> Tj 1 0 0 1 314.16 180.96 Tm <736520> Tj 1 0 0 1 325.68 180.96 Tm <6D616E74E96D20> Tj 1 0 0 1 361.20 180.96 Tm <6E6F20> Tj 1 0 0 1 374.64 180.72 Tm <73656E7469646F20> Tj 1 0 0 1 406.56 180.72 Tm <686F72697A6F6E74616C2E20> Tj 1 0 0 1 452.88 180.24 Tm <4F7320> Tj 1 0 0 1 467.28 180.48 Tm <676173657320> Tj 1 0 0 1 492.48 180.48 Tm <7175656E74657320> Tj 1 0 0 1 526.08 180.00 Tm <6461> Tj 0.48 Tc 1 0 0 1 55.44 171.60 Tm <636F6D62757374E36F2E20> Tj 1 0 0 1 103.68 171.60 Tm <706F7220> Tj 1 0 0 1 120.24 171.12 Tm <736572656D20> Tj 1 0 0 1 146.64 170.88 Tm <6D656E6F7320> Tj 1 0 0 1 175.44 170.64 Tm <64656E736F7320> Tj 1 0 0 1 205.44 171.12 Tm <71756520> Tj 1 0 0 1 222.72 170.40 Tm <6F20> 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<696E766973ED76656C20> Tj 1 0 0 1 318.96 77.04 Tm <6E6F20> Tj 1 0 0 1 331.92 77.04 Tm <63656E74726F20> Tj 1 0 0 1 360.00 76.80 Tm <646120> Tj 1 0 0 1 372.48 76.80 Tm <6368616D6120> Tj 1 0 0 1 401.28 76.56 Tm <636F6E74656D20> Tj 1 0 0 1 433.92 76.32 Tm <756D6120> Tj 1 0 0 1 453.60 76.32 Tm <6E7576656D20> Tj 1 0 0 1 483.84 76.32 Tm <646520> Tj 1 0 0 1 496.56 77.52 Tm <716173657320> Tj 1 0 0 1 520.56 77.52 Tm <717565> Tj 0.48 Tc 1 0 0 1 55.20 67.44 Tm <7661706F72697A6172616D2C20> Tj 1 0 0 1 109.92 66.96 Tm <6D617320> Tj 1 0 0 1 128.40 66.72 Tm <61696E646120> Tj 1 0 0 1 152.40 66.72 Tm <6EE36F20> Tj 1 0 0 1 169.44 67.44 Tm <717565696D6172616D2E> Tj ET endstream endobj 23 0 obj 22608 endobj 24 0 obj << /Length 25 0 R >> stream (,,t/ ..,y I [r a (|U|=-|--|( R Z ) Re LR R \Onde: Gr: pt Lt g / l.,t (nmero de Grasho)Re - p L u, / pr (nmero de Reynolds) As equaes de conservao das espcies e energia adimensionalizadas podem ser escritas como:IrY-*r,.Y,_ | [' .R(vo L,,l_.r(], r,,)l_.;\ aR azl Pe fnanr aR ) iz' ] " -#) , atr'1- a, z. ) (7) (8) . ,47 Onie Pe - Lu- D). {nunlero de Pecetr',';Lprl.\s condies de contorno do problema, que esto relacionadas com o conjunto deadimensionalizadas logo acima, so as seguintes:- Na direo radial I r' ^ a(). l, )'R;R 'R i,p (e)( 10)(ll)( 1l)equaes( l3)( 14)( l5)( l6) emR:1em R - R*6,, emZ: l, +gemZ: 21116^, + + Yo:0,Yr:Yp, e0:1; yo : Yo-, yr : 0, 0 : T". / Tb, U : 0 e V / R - 0 Na direo axial Yo:0,Yr:Yn,e0:lyo : Ye,,, yr: 0, g :T, I T6,V: 0 e U I Z: 0 Materiais e MtodosPara a realtzao desse experimento foram utilizados: vela comum de parafina. suporte para a vela. tesourapara cortar o pavio da vela nos diferentes comprimentos, escala metlica para medir a altura do pavio, sforos e cmeradigital para registrar as etapas do presente estudo.A metodologia uttlizada consistiu de observaes na forma, cor, luminosidade da chama em diferentescomprimentos de pavio.Resultados e DiscussoDurante as etapas da reao, a parafina submetida pirlise, formando molculas menores e radicaisconstitudos de carbono e hidrognio. Os tomos de hidrognio so mais leves, portanto reagem com o oxignio maisrapidamente. Os tomos de carbono, alem de estarem em excesso, so mais pesados e lentos. Portanto, devido deficincia de oxignio, parte do carbono no transformada em CO2, transformando-se em outras partculas querecebem o nome de fuligem. Essas partculas ficam incandescentes em contato com a chama. caracterizando sua coramarelada.Qualquer que seja a posio da vela, o fogo sempre se mantm no sentido horizontal. Os gases quentes dacombusto. por serem menos densos que o ar, sofrem menor ao da fora da gravidade. portanto sobem e provocam oalongamento da chama, arastando tambm as partculas originadas (dixido de carbono. fuligen e \,apor de gua). O arfrio e atrado para a chama devido s correntes de conveco, realimentando o processo de combusto. Portanto. aconveco do ar ocorre graas ao efeito da gravidade. Sem ela, no h o movinreno constante do ar frio. carresandooxignio para a chanraAs cores na hama fornecem muitas inftrrmaes sobre o que est acontecendo no processo e pode serobsenrada na Figura 3. A combusto ocorre na estreita faixa que circula a superficie da chama e a regio mais quente.A parte amarela e branca no topo da chama indica a presena do carbono incandescente. O interior escuro denotatemperaturas mais frias e carncia de oxignio. 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Burke. S.P., Schumann, T. E. W.: Dffision.flames. Proceedings of the first and second symposiurn on combustion"The Combustion Institute. 1965, pp. 2-1 1.2. Alsairafi" A., Lee, S., T'ien, J.S. Modelng gravity efec't on difJsion.flames stablzed u'ouncl u c'.t'lntlrictl ticl,.saturated v'ith liqud fuel. Combust. Sci. and Tech, Vol. 176.2004,pp.2165-2191.3. Buckmaster, J.: Edge-.flumes antl ther stubilitl,. Combust. Sci, and Tech. 1996, pp. 115:41-68.1. vansuror'. Z. A.: Soot fonnutot n combustion 1rl.o(r,.\\e,\ . ConrhLrstton. Erplosiotr tnd Shotk ll'tn'as, Vol.,ll (6).2005. PP. 717-r-++ ( 1 8),i. \\'illians. F .\ C,,,r'",,.;;,,i'.''..,,,-..)' ed..\i,ir:rn-\\.e>1ei. \enlr Park. 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