Asignación 2 - Ejercicio.docx
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Transcript of Asignación 2 - Ejercicio.docx
La ecuacin obtenida, es una ecuacin trascendental que debe ser resuelta para , lo que equivale a encontrar las races de la ecuacin.
Para determinar las raices de la ecuacin se supone un valor de y se realiza una iteracin con la ecuacin anterior tomando un tamao de paso 0.00125. En la Figura 1, f()=0 vs supuestto , se observa el punto donde la funcin f() corta el eje x (cambia de signo), este valor representa la raz de la ecuacin (). Para realizar la iteracin de la funcin, se expreso la ecuacin de la siguiente forma:Prueba Error[ (()/) ] *E = 0
Y se calcularon los trminos A, B, C, D y E, como se presenta en las tablas 1, 2, 3, 4 y 5.Tabla 1. Clculo del trmino A y BAB
exp(-^2)/(erf())(1-Tm*)/(Tm*)(k(A))/(k(B))((B)/(A))^0.5(1-Tm*)/(Tm*)*(k(A))/(k(B))*((B)/(A))^0.5
0.001250000708.98301741.0000.27165392.8235123910.767018148
0.002500000354.49372431.0000.27165392.8235123910.767018148
0.003750000236.33161131.0000.27165392.8235123910.767018148
0.005000000177.25129341.0000.27165392.8235123910.767018148
0.006250000141.80369351.0000.27165392.8235123910.767018148
0.007500000118.17245261.0000.27165392.8235123910.767018148
0.008750000101.29341701.0000.27165392.8235123910.767018148
0.01000000088.634509651.0000.27165392.8235123910.767018148
0.01125000078.789021181.0000.27165392.8235123910.767018148
0.01250000070.912925951.0000.27165392.8235123910.767018148
0.01375000064.469116741.0000.27165392.8235123910.767018148
0.01500000059.099522091.0000.27165392.8235123910.767018148
0.01625000054.556246361.0000.27165392.8235123910.767018148
0.01750000050.662221241.0000.27165392.8235123910.767018148
0.01875000047.287596631.0000.27165392.8235123910.767018148
0.02000000044.334984981.0000.27165392.8235123910.767018148
0.02125000041.729913441.0000.27165392.8235123910.767018148
0.02250000039.414458691.0000.27165392.8235123910.767018148
0.02375000037.342891791.0000.27165392.8235123910.767018148
0.02500000035.478629611.0000.27165392.8235123910.767018148
0.02625000033.792057211.0000.27165392.8235123910.767018148
0.02750000032.258944211.0000.27165392.8235123910.767018148
0.02875000030.859274191.0000.27165392.8235123910.767018148
0.03000000029.576366811.0000.27165392.8235123910.767018148
0.03125000028.396210581.0000.27165392.8235123910.767018148
0.03250000027.306949651.0000.27165392.8235123910.767018148
0.03375000026.298484561.0000.27165392.8235123910.767018148
0.03500000025.362158661.0000.27165392.8235123910.767018148
0.03625000024.490509291.0000.27165392.8235123910.767018148
0.03750000023.677068851.0000.27165392.8235123910.767018148
0.03875000022.916204231.0000.27165392.8235123910.767018148
0.04000000022.20298651.0000.27165392.8235123910.767018148
0.04125000021.533084151.0000.27165392.8235123910.767018148
0.04250000020.902675261.0000.27165392.8235123910.767018148
0.04375000020.308374731.0000.27165392.8235123910.767018148
0.04500000019.747173541.0000.27165392.8235123910.767018148
0.04625000019.216388011.0000.27165392.8235123910.767018148
0.04750000018.713616941.0000.27165392.8235123910.767018148
0.04875000018.236705391.0000.27165392.8235123910.767018148
0.05000000017.783713941.0000.27165392.8235123910.767018148
0.05125000017.352892381.0000.27165392.8235123910.767018148
0.05250000016.942657161.0000.27165392.8235123910.767018148
0.05375000016.551572081.0000.27165392.8235123910.767018148
0.05500000016.178331461.0000.27165392.8235123910.767018148
0.05625000015.821745721.0000.27165392.8235123910.767018148
0.05750000015.480728711.0000.27165392.8235123910.767018148
0.05875000015.154286701.0000.27165392.8235123910.767018148
0.06000000014.841508791.0000.27165392.8235123910.767018148
0.06125000014.541558451.0000.27165392.8235123910.767018148
0.06250000014.253666041.0000.27165392.8235123910.767018148
0.06375000013.977122331.0000.27165392.8235123910.767018148
0.06500000013.711272591.0000.27165392.8235123910.767018148
0.06625000013.455511561.0000.27165392.8235123910.767018148
0.06750000013.209278791.0000.27165392.8235123910.767018148
0.06875000012.972054571.0000.27165392.8235123910.767018148
0.07000000012.743356361.0000.27165392.8235123910.767018148
0.07125000012.522735441.0000.27165392.8235123910.767018148
0.07250000012.309774051.0000.27165392.8235123910.767018148
0.07375000012.104082771.0000.27165392.8235123910.767018148
0.07500000011.905298131.0000.27165392.8235123910.767018148
0.07625000011.713080481.0000.27165392.8235123910.767018148
0.07750000011.527112111.0000.27165392.8235123910.767018148
0.07875000011.347095461.0000.27165392.8235123910.767018148
0.08000000011.172751591.0000.27165392.8235123910.767018148
0.08125000011.00381871.0000.27165392.8235123910.767018148
0.08250000010.840050881.0000.27165392.8235123910.767018148
0.08375000010.681216891.0000.27165392.8235123910.767018148
0.08500000010.52709911.0000.27165392.8235123910.767018148
0.08625000010.377492491.0000.27165392.8235123910.767018148
0.08750000010.232203751.0000.27165392.8235123910.767018148
0.08875000010.091050481.0000.27165392.8235123910.767018148
0.0900000009.9538604071.0000.27165392.8235123910.767018148
0.0912500009.8204706851.0000.27165392.8235123910.767018148
0.0925000009.6907272841.0000.27165392.8235123910.767018148
0.0937500009.5644843871.0000.27165392.8235123910.767018148
0.0950000009.441603851.0000.27165392.8235123910.767018148
0.0962500009.3219547091.0000.27165392.8235123910.767018148
0.0975000009.2054127131.0000.27165392.8235123910.767018148
0.0987500009.0918599041.0000.27165392.8235123910.767018148
0.1000000008.9811842241.0000.27165392.8235123910.767018148
0.1012500008.8732791461.0000.27165392.8235123910.767018148
0.1025000008.7680433431.0000.27165392.8235123910.767018148
0.1037500008.665380371.0000.27165392.8235123910.767018148
0.1050000008.5651983761.0000.27165392.8235123910.767018148
0.1062500008.4674098311.0000.27165392.8235123910.767018148
0.1075000008.3719312781.0000.27165392.8235123910.767018148
0.1087500008.2786830991.0000.27165392.8235123910.767018148
0.1100000008.1875892921.0000.27165392.8235123910.767018148
0.1112500008.0985772741.0000.27165392.8235123910.767018148
0.1125000008.0115776861.0000.27165392.8235123910.767018148
0.1137500007.9265242221.0000.27165392.8235123910.767018148
0.1150000007.8433534551.0000.27165392.8235123910.767018148
0.1162500007.7620046881.0000.27165392.8235123910.767018148
0.1175000007.6824198091.0000.27165392.8235123910.767018148
0.1187500007.6045431511.0000.27165392.8235123910.767018148
0.1200000007.5283213681.0000.27165392.8235123910.767018148
0.1212500007.4537033121.0000.27165392.8235123910.767018148
0.1225000007.3806399281.0000.27165392.8235123910.767018148
0.1237500007.3090841371.0000.27165392.8235123910.767018148
0.1250000007.238990751.0000.27165392.8235123910.767018148
0.1262500007.1703163621.0000.27165392.8235123910.767018148
0.1275000007.1030192761.0000.27165392.8235123910.767018148
0.1287500007.037059411.0000.27165392.8235123910.767018148
0.1300000006.9723982271.0000.27165392.8235123910.767018148
0.1312500006.9089986581.0000.27165392.8235123910.767018148
0.1325000006.8468250321.0000.27165392.8235123910.767018148
0.1337500006.7858430121.0000.27165392.8235123910.767018148
0.1350000006.7260195351.0000.27165392.8235123910.767018148
Tabla 2. Clculo del trmino CC
((B)/(A))^2(^2)((B)/(A))((B)/(A))^2*(^2)*((B)/(A))exp(-((B)/(A))^2*(^2)*((B)/(A)))
0.84640.00000156257.9722222-0.00001054330.9999894568
0.84640.00000625007.9722222-0.00004217310.9999578278
0.84640.00001406257.9722222-0.00009488940.9999051151
0.84640.00002500007.9722222-0.00016869220.9998313220
0.84640.00003906257.9722222-0.00026358160.9997364531
0.84640.00005625007.9722222-0.00037955750.9996205145
0.84640.00007656257.9722222-0.00051661990.9994835135
0.84640.00010000007.9722222-0.00067476890.9993254587
0.84640.00012656257.9722222-0.00085400440.9991463602
0.84640.00015625007.9722222-0.00105432640.9989462292
0.84640.00018906257.9722222-0.00127573490.9987250785
0.84640.00022500007.9722222-0.00151823000.9984829219
0.84640.00026406257.9722222-0.00178181160.9982197749
0.84640.00030625007.9722222-0.00206647970.9979356540
0.84640.00035156257.9722222-0.00237223440.9976305771
0.84640.00040000007.9722222-0.00269907560.9973045637
0.84640.00045156257.9722222-0.00304700330.9969576341
0.84640.00050625007.9722222-0.00341601750.9965898104
0.84640.00056406257.9722222-0.00380611830.9962011158
0.84640.00062500007.9722222-0.00421730560.9957915748
0.84640.00068906257.9722222-0.00464957940.9953612132
0.84640.00075625007.9722222-0.00510293970.9949100582
0.84640.00082656257.9722222-0.00557738660.9944381381
0.84640.00090000007.9722222-0.00607292000.9939454829
0.84640.00097656257.9722222-0.00658953990.9934321235
0.84640.00105625007.9722222-0.00712724640.9928980922
0.84640.00113906257.9722222-0.00768603940.9923434227
0.84640.00122500007.9722222-0.00826591890.9917681499
0.84640.00131406257.9722222-0.00886688490.9911723100
0.84640.00140625007.9722222-0.00948893750.9905559404
0.84640.00150156257.9722222-0.01013207660.9899190800
0.84640.00160000007.9722222-0.01079630220.9892617687
0.84640.00170156257.9722222-0.01148161440.9885840478
0.84640.00180625007.9722222-0.01218801310.9878859599
0.84640.00191406257.9722222-0.01291549830.9871675489
0.84640.00202500007.9722222-0.01366407000.9864288597
0.84640.00213906257.9722222-0.01443372830.9856699386
0.84640.00225625007.9722222-0.01522447310.9848908333
0.84640.00237656257.9722222-0.01603630440.9840915926
0.84640.00250000007.9722222-0.01686922220.9832722664
0.84640.00262656257.9722222-0.01772322660.9824329060
0.84640.00275625007.9722222-0.01859831750.9815735640
0.84640.00288906257.9722222-0.01949449490.9806942940
0.84640.00302500007.9722222-0.02041175890.9797951509
0.84640.00316406257.9722222-0.02135010940.9788761908
0.84640.00330625007.9722222-0.02230954640.9779374712
0.84640.00345156257.9722222-0.02329006990.9769790504
0.84640.00360000007.9722222-0.02429168000.9760009883
0.84640.00375156257.9722222-0.02531437660.9750033456
0.84640.00390625007.9722222-0.02635815970.9739861845
0.84640.00406406257.9722222-0.02742302940.9729495682
0.84640.00422500007.9722222-0.02850898560.9718935611
0.84640.00438906257.9722222-0.02961602830.9708182288
0.84640.00455625007.9722222-0.03074415750.9697236379
0.84640.00472656257.9722222-0.03189337330.9686098563
0.84640.00490000007.9722222-0.03306367560.9674769530
0.84640.00507656257.9722222-0.03425506440.9663249981
0.84640.00525625007.9722222-0.03546753970.9651540629
0.84640.00543906257.9722222-0.03670110160.9639642197
0.84640.00562500007.9722222-0.03795575000.9627555419
0.84640.00581406257.9722222-0.03923148490.9615281041
0.84640.00600625007.9722222-0.04052830640.9602819820
0.84640.00620156257.9722222-0.04184621440.9590172523
0.84640.00640000007.9722222-0.04318520890.9577339928
0.84640.00660156257.9722222-0.04454528990.9564322824
0.84640.00680625007.9722222-0.04592645750.9551122009
0.84640.00701406257.9722222-0.04732871160.9537738295
0.84640.00722500007.9722222-0.04875205220.9524172502
0.84640.00743906257.9722222-0.05019647940.9510425459
0.84640.00765625007.9722222-0.05166199310.9496498008
0.84640.00787656257.9722222-0.05314859330.9482391001
0.84640.00810000007.9722222-0.05465628000.9468105297
0.84640.00832656257.9722222-0.05618505330.9453641770
0.84640.00855625007.9722222-0.05773491310.9439001299
0.84640.00878906257.9722222-0.05930585940.9424184775
0.84640.00902500007.9722222-0.06089789220.9409193101
0.84640.00926406257.9722222-0.06251101160.9394027184
0.84640.00950625007.9722222-0.06414521750.9378687947
0.84640.00975156257.9722222-0.06580050990.9363176317
0.84640.01000000007.9722222-0.06747688890.9347493235
0.84640.01025156257.9722222-0.06917435440.9331639647
0.84640.01050625007.9722222-0.07089290640.9315616511
0.84640.01076406257.9722222-0.07263254490.9299424793
0.84640.01102500007.9722222-0.07439327000.9283065469
0.84640.01128906257.9722222-0.07617508160.9266539523
0.84640.01155625007.9722222-0.07797797970.9249847947
0.84640.01182656257.9722222-0.07980196440.9232991744
0.84640.01210000007.9722222-0.08164703560.9215971923
0.84640.01237656257.9722222-0.08351319330.9198789504
0.84640.01265625007.9722222-0.08540043750.9181445513
0.84640.01293906257.9722222-0.08730876830.9163940985
0.84640.01322500007.9722222-0.08923818560.9146276965
0.84640.01351406257.9722222-0.09118868940.9128454504
0.84640.01380625007.9722222-0.09316027970.9110474662
0.84640.01410156257.9722222-0.09515295660.9092338505
0.84640.01440000007.9722222-0.09716672000.9074047110
0.84640.01470156257.9722222-0.09920156990.9055601559
0.84640.01500625007.9722222-0.10125750640.9037002943
0.84640.01531406257.9722222-0.10333452940.9018252360
0.84640.01562500007.9722222-0.10543263890.8999350914
0.84640.01593906257.9722222-0.10755183490.8980299719
0.84640.01625625007.9722222-0.10969211750.8961099894
0.84640.01657656257.9722222-0.11185348660.8941752566
0.84640.01690000007.9722222-0.11403594220.8922258867
0.84640.01722656257.9722222-0.11623948440.8902619939
0.84640.01755625007.9722222-0.11846411310.8882836929
0.84640.01788906257.9722222-0.12070982830.8862910989
0.84640.01822500007.9722222-0.12297663000.8842843280
Tabla 3. Clculo del trmino D y EDE
((B)/(A))((B)/(A))^0.5*((B)/(A))*((B)/(A))^0.5erfc(*((B)/(A))*((B)/(A))^0.5)(()^(0.5) * H)/(C(B)*(Tm-T1))
0.00125000000.922.82351239100.00324703920.996336121456.3472178280
0.00250000000.922.82351239100.00649407850.992672320156.3472178280
0.00375000000.922.82351239100.00974111770.989008673356.3472178280
0.00500000000.922.82351239100.01298815700.985345258356.3472178280
0.00625000000.922.82351239100.01623519620.981682152256.3472178280
0.00750000000.922.82351239100.01948223550.978019432356.3472178280
0.00875000000.922.82351239100.02272927470.974357175856.3472178280
0.01000000000.922.82351239100.02597631400.970695459956.3472178280
0.01125000000.922.82351239100.02922335320.967034361556.3472178280
0.01250000000.922.82351239100.03247039250.963373957956.3472178280
0.01375000000.922.82351239100.03571743170.959714326156.3472178280
0.01500000000.922.82351239100.03896447100.956055543156.3472178280
0.01625000000.922.82351239100.04221151020.952397685756.3472178280
0.01750000000.922.82351239100.04545854950.948740830956.3472178280
0.01875000000.922.82351239100.04870558870.945085055556.3472178280
0.02000000000.922.82351239100.05195262800.941430436256.3472178280
0.02125000000.922.82351239100.05519966720.937777049756.3472178280
0.02250000000.922.82351239100.05844670650.934124972656.3472178280
0.02375000000.922.82351239100.06169374570.930474281456.3472178280
0.02500000000.922.82351239100.06494078500.926825052656.3472178280
0.02625000000.922.82351239100.06818782420.923177362456.3472178280
0.02750000000.922.82351239100.07143486350.919531287156.3472178280
0.02875000000.922.82351239100.07468190270.915886902956.3472178280
0.03000000000.922.82351239100.07792894200.912244285756.3472178280
0.03125000000.922.82351239100.08117598120.908603511456.3472178280
0.03250000000.922.82351239100.08442302050.904964656056.3472178280
0.03375000000.922.82351239100.08767005970.901327795056.3472178280
0.03500000000.922.82351239100.09091709900.897693004056.3472178280
0.03625000000.922.82351239100.09416413820.894060358456.3472178280
0.03750000000.922.82351239100.09741117750.890429933656.3472178280
0.03875000000.922.82351239100.10065821670.886801804656.3472178280
0.04000000000.922.82351239100.10390525600.883176046556.3472178280
0.04125000000.922.82351239100.10715229520.879552734156.3472178280
0.04250000000.922.82351239100.11039933450.875931942156.3472178280
0.04375000000.922.82351239100.11364637370.872313745156.3472178280
0.04500000000.922.82351239100.11689341300.868698217456.3472178280
0.04625000000.922.82351239100.12014045220.865085433256.3472178280
0.04750000000.922.82351239100.12338749150.861475466756.3472178280
0.04875000000.922.82351239100.12663453070.857868391656.3472178280
0.05000000000.922.82351239100.12988157000.854264281756.3472178280
0.05125000000.922.82351239100.13312860920.850663210456.3472178280
0.05250000000.922.82351239100.13637564850.847065251156.3472178280
0.05375000000.922.82351239100.13962268770.843470476856.3472178280
0.05500000000.922.82351239100.14286972700.839878960556.3472178280
0.05625000000.922.82351239100.14611676620.836290774956.3472178280
0.05750000000.922.82351239100.14936380550.832705992456.3472178280
0.05875000000.922.82351239100.15261084470.829124685456.3472178280
0.06000000000.922.82351239100.15585788400.825546926056.3472178280
0.06125000000.922.82351239100.15910492320.821972786056.3472178280
0.06250000000.922.82351239100.16235196250.818402337056.3472178280
0.06375000000.922.82351239100.16559900170.814835650556.3472178280
0.06500000000.922.82351239100.16884604100.811272797556.3472178280
0.06625000000.922.82351239100.17209308020.807713849156.3472178280
0.06750000000.922.82351239100.17534011950.804158875856.3472178280
0.06875000000.922.82351239100.17858715870.800607948256.3472178280
0.07000000000.922.82351239100.18183419800.797061136556.3472178280
0.07125000000.922.82351239100.18508123720.793518510456.3472178280
0.07250000000.922.82351239100.18832827650.789980139956.3472178280
0.07375000000.922.82351239100.19157531570.786446094156.3472178280
0.07500000000.922.82351239100.19482235500.782916442356.3472178280
0.07625000000.922.82351239100.19806939420.779391253456.3472178280
0.07750000000.922.82351239100.20131643350.775870596056.3472178280
0.07875000000.922.82351239100.20456347270.772354538356.3472178280
0.08000000000.922.82351239100.20781051200.768843148456.3472178280
0.08125000000.922.82351239100.21105755120.765336494156.3472178280
0.08250000000.922.82351239100.21430459050.761834642756.3472178280
0.08375000000.922.82351239100.21755162970.758337661656.3472178280
0.08500000000.922.82351239100.22079866900.754845617456.3472178280
0.08625000000.922.82351239100.22404570820.751358576956.3472178280
0.08750000000.922.82351239100.22729274750.747876606256.3472178280
0.08875000000.922.82351239100.23053978670.744399771256.3472178280
0.09000000000.922.82351239100.23378682600.740928137756.3472178280
0.09125000000.922.82351239100.23703386520.737461770956.3472178280
0.09250000000.922.82351239100.24028090450.734000735956.3472178280
0.09375000000.922.82351239100.24352794370.730545097256.3472178280
0.09500000000.922.82351239100.24677498300.727094919356.3472178280
0.09625000000.922.82351239100.25002202220.723650266156.3472178280
0.09750000000.922.82351239100.25326906150.720211201356.3472178280
0.09875000000.922.82351239100.25651610070.716777788256.3472178280
0.10000000000.922.82351239100.25976314000.713350089956.3472178280
0.10125000000.922.82351239100.26301017920.709928169056.3472178280
0.10250000000.922.82351239100.26625721850.706512087756.3472178280
0.10375000000.922.82351239100.26950425770.703101908056.3472178280
0.10500000000.922.82351239100.27275129700.699697691656.3472178280
0.10625000000.922.82351239100.27599833620.696299499556.3472178280
0.10750000000.922.82351239100.27924537550.692907392856.3472178280
0.10875000000.922.82351239100.28249241470.689521431956.3472178280
0.11000000000.922.82351239100.28573945400.686141676956.3472178280
0.11125000000.922.82351239100.28898649320.682768187656.3472178280
0.11250000000.922.82351239100.29223353250.679401023456.3472178280
0.11375000000.922.82351239100.29548057170.676040243356.3472178280
0.11500000000.922.82351239100.29872761100.672685905956.3472178280
0.11625000000.922.82351239100.30197465020.669338069556.3472178280
0.11750000000.922.82351239100.30522168950.665996791956.3472178280
0.11875000000.922.82351239100.30846872870.662662130556.3472178280
0.12000000000.922.82351239100.31171576800.659334142656.3472178280
0.12125000000.922.82351239100.31496280720.656012884656.3472178280
0.12250000000.922.82351239100.31820984650.652698413056.3472178280
0.12375000000.922.82351239100.32145688570.649390783656.3472178280
0.12500000000.922.82351239100.32470392500.646090051956.3472178280
0.12625000000.922.82351239100.32795096420.642796273056.3472178280
0.12750000000.922.82351239100.33119800350.639509501456.3472178280
0.12875000000.922.82351239100.33444504270.636229791556.3472178280
0.13000000000.922.82351239100.33769208200.632957197256.3472178280
0.13125000000.922.82351239100.34093912120.629691771756.3472178280
0.13250000000.922.82351239100.34418616050.626433568156.3472178280
0.13375000000.922.82351239100.34743319970.623182639156.3472178280
0.13500000000.922.82351239100.35068023900.619939036756.3472178280
=0.1175En la Tabla 4, se observa el cambio de signo en f()=0, lo que indica que el valor de se encuentra en el rando de 0.1175 y 0.11875. El valor de empleado para el clculo de los perfiles de temperatura es de 0.1175.Tabla 4. Supuesto y f()=0 SupuestoEvaluando la Funcin
0.001250000708.142752760
0.002500000353.580208724
0.003750000235.344840428
0.005000000176.191262802
0.006250000140.670398846
0.007500000116.965889574
0.008750000100.013581146
0.01000000087.281396651
0.01125000077.362626704
0.01250000069.413245680
0.01375000062.896146371
0.01500000057.453257313
0.01625000052.836682880
0.01750000048.869354776
0.01875000045.421422920
0.02000000042.395499759
0.02125000039.717112461
0.02250000037.328337717
0.02375000035.183446602
0.02500000033.245855982
0.02625000031.485950940
0.02750000029.879501097
0.02875000028.406490051
0.03000000027.050237474
0.03125000025.796731893
0.03250000024.634117448
0.03375000023.552294707
0.03500000022.542607016
0.03625000021.597591745
0.03750000020.710781284
0.03875000019.876542556
0.04000000019.089946621
0.04125000018.346661987
0.04250000017.642866755
0.04375000016.975175814
0.04500000016.340580179
0.04625000015.736396164
0.04750000015.160222576
0.04875000014.609904503
0.05000000014.083502525
0.05125000013.579266433
0.05250000013.095612712
0.05375000012.631105146
0.05500000012.184438092
0.05625000011.754421961
0.05750000011.339970612
0.05875000010.940090339
0.06000000010.553870251
0.06125000010.180473814
0.0625000009.819131419
0.0637500009.469133821
0.0650000009.129826332
0.0662500008.800603677
0.0675000008.480905417
0.0687500008.170211875
0.0700000007.868040493
0.0712500007.573942581
0.0725000007.287500391
0.0737500007.008324500
0.0750000006.736051449
0.0762500006.470341612
0.0775000006.210877275
0.0787500005.957360899
0.0800000005.709513542
0.0812500005.467073429
0.0825000005.229794651
0.0837500004.997445980
0.0850000004.769809794
0.0862500004.546681085
0.0875000004.327866563
0.0887500004.113183825
0.0900000003.902460608
0.0912500003.695534083
0.0925000003.492250230
0.0937500003.292463239
0.0950000003.096034978
0.0962500002.902834491
0.0975000002.712737540
0.0987500002.525626175
0.1000000002.341388348
0.1012500002.159917544
0.1025000001.981112444
0.1037500001.804876614
0.1050000001.631118213
0.1062500001.459749721
0.1075000001.290687691
0.1087500001.123852514
0.1100000000.959168200
0.1112500000.796562174
0.1125000000.635965089
0.1137500000.477310646
0.1150000000.320535431
0.1162500000.165578755
0.1175000000.012382516
0.118750000-0.139108942
0.120000000-0.288948957
0.121250000-0.437188665
0.122500000-0.583877114
0.123750000-0.729061369
0.125000000-0.872786614
0.126250000-1.015096241
0.127500000-1.156031939
0.128750000-1.295633779
0.130000000-1.433940288
0.131250000-1.570988528
0.132500000-1.706814157
0.133750000-1.841451504
0.135000000-1.974933623
En la Figura 1 se observa el corte en el eje x, correspondiente a la raz de la ecuacin ().
Figura 1:supuesttovs Funcin f()=0
En las ecuaciones 10 y xx , se obtuvieron los perfiles de temperatura para el slido y el lquido. Por regla de fases se puede asumir que la temperatura en la interfase es continua y por tanto Perfil de temperatura para el slido,
Perfil de temperatura para el lquido,
Como , es equivalente a decir que . Para ello se realiz una iteracin con un tamao de paso de de 0.0000025, hasta obtener un valor absoluto de la cercano a cero. Esta iteracin se realiz para valores de tiempo iguales a t=1, 5, 10 y 50 s. El valor de donde la diferencia es cercana a cero, representa la distancia a la cual se esta formando la interfase para cada tiempo. Este valor es importante de determinar porque nos indica el punto donde cambia la funcin de perfil de temperatura del slido al lquido, es decir que para valores de se debe usar la funcin de perfil de temperatura de la fase slida (), mientras que para valores de se usa la funcin de perfil de temperatura de la fase lquida.
En la tabla 5, se presenta el resumen para cada tiempo del valor de es decir donde se forma la interfase.Tabla 5. Datos para la iteracinFase Lquida (A)Fase Slida (B)
TM0.5
0.1175
K (J/(m s K)0.60282.219
(kg/m3)1000920
Cp (J/(Kg K))41872100
1.440E-071.148E-06
Tabla 6. Valor de para t=1 st=1 s
=*erf
0.000000000.000000000000.038985773200.038985773
0.000002500.004987305740.042408560330.037421255
5.00E-060.009974597910.045832118180.035857520
0.000007500.014961862920.049256372620.034294510
0.000010000.019949087210.052681249470.032732162
0.000012500.024936257190.056106674500.031170417
0.000015000.029923359300.059532573440.029609214
0.000017500.034910379950.062958872020.028048492
0.000020000.039897305580.066385495920.026488190
0.000022500.044884122610.069812370790.024928248
0.000025000.049870817470.073239422280.023368605
0.000027500.054857376580.076666576030.021809199
0.000030000.059843786380.080093757660.020249971
0.000032500.064830033310.083520892810.018690860
0.000035000.069816103780.086947907090.017131803
0.000037500.074801984240.090374726150.015572742
0.000040000.079787661120.093801275640.014013615
0.000042500.084773120860.097227481220.012454360
0.000045000.089758349890.100653268580.010894919
0.000047500.094743334670.104078563440.009335229
0.000050000.099728061630.107503291550.007775230
0.000052500.104712517210.110927378700.006214861
0.000055000.109696687870.114350750700.004654063
0.000057500.114680560040.117773333440.003092773
0.000060000.119664120200.121195052840.001530933
0.000062500.124647354780.12461583488-0.000031520
0.000065000.129630250260.12803560561-0.001594645
Tabla 7. Valor de para t=5 s=*erf
0.000000000.000000000000.038985773200.038985773
0.000002500.002230391740.040516390130.038285998
5.00E-060.004460782270.042047169400.037586387
0.000007500.006691170370.043578104380.036886934
0.000010000.008921554830.045109188440.036187634
0.000012500.011151934430.046640414950.035488481
0.000015000.013382307960.048171777270.034789469
0.000017500.015612674200.049703268780.034090595
0.000020000.017843031940.051234882830.033391851
0.000022500.020073379970.052766612790.032693233
0.000025000.022303717070.054298452020.031994735
0.000027500.024534042030.055830393870.031296352
0.000030000.026764353630.057362431700.030598078
0.000032500.028994650660.058894558870.029899908
0.000035000.031224931910.060426768740.029201837
0.000037500.033455196150.061959054650.028503858
0.000040000.035685442190.063491409970.027805968
0.000042500.037915668790.065023828030.027108159
0.000045000.040145874760.066556302210.026410427
0.000047500.042376058870.068088825830.025712767
0.000050000.044606219910.069621392260.025015172
0.000052500.046836356670.071153994840.024317638
0.000055000.049066467930.072686626930.023620159
0.000057500.051296552480.074219281870.022922729
0.000060000.053526609110.075751953000.022225344
0.000062500.055756636590.077284633680.021527997
0.000065000.057986633730.078817317260.020830684
0.000067500.060216599300.080349997070.020133398
0.000070000.062446532090.081882666480.019436134
0.000072500.064676430890.083415318830.018738888
0.000075000.066906294480.084947947460.018041653
0.000077500.069136121660.086480545730.017344424
0.000080000.071365911200.088013106980.016647196
0.000082500.073595661890.089545624560.015949963
0.000085000.075825372530.091078091820.015252719
0.000087500.078055041890.092610502120.014555460
0.000090000.080284668770.094142848800.013858180
0.000092500.082514251940.095675125220.013160873
0.000095000.084743790210.097207324730.012463535
0.000097500.086973282350.098739440680.011766158
0.000100000.089202727160.100271466430.011068739
0.000102500.091432123410.101803395340.010371272
0.000105000.093661469900.103335220760.009673751
0.000107500.095890765420.104866936050.008976171
0.000110000.098120008750.106398534570.008278526
0.000112500.100349198670.107930009680.007580811
0.000115000.102578333990.109461354750.006883021
0.000117500.104807413480.110992563150.006185150
0.000120000.107036435930.112523628230.005487192
0.000122500.109265400140.114054543370.004789143
0.000125000.111494304880.115585301950.004090997
0.000127500.113723148950.117115897320.003392748
0.000130000.115951931140.118646322870.002694392
0.000132500.118180650230.120176571970.001995922
0.000135000.120409305010.121706638000.001297333
0.000137500.122637894280.123236514350.000598620
0.000140000.124866416810.12476619440-0.000100222
0.000142500.127094871400.12629567154-0.000799200
Tabla 7. Valor de para t=10 s=*erf
0.000000000.000000000000.038985773200.038985773
0.000002500.001577125200.040068065710.038490941
5.00E-060.003154249970.041150440350.037996190
0.000007500.004731373870.042232894790.037501521
0.000010000.006308496500.043315426680.037006930
0.000012500.007885617400.044398033680.036512416
0.000015000.009462736160.045480713450.036017977
0.000017500.011039852340.046563463640.035523611
0.000020000.012616965520.047646281900.035029316
0.000022500.014194075260.048729165900.034535091
0.000025000.015771181140.049812113270.034040932
0.000027500.017348282720.050895121680.033546839
0.000030000.018925379590.051978188790.033052809
0.000032500.020502471300.053061312230.032558841
0.000035000.022079557430.054144489670.032064932
0.000037500.023656637550.055227718750.031571081
0.000040000.025233711230.056310997140.031077286
0.000042500.026810778040.057394322470.030583544
0.000045000.028387837550.058477692400.030089855
0.000047500.029964889340.059561104580.029596215
0.000050000.031541932970.060644556670.029102624
0.000052500.033118968020.061728046310.028609078
0.000055000.034695994040.062811571140.028115577
0.000057500.036273010630.063895128830.027622118
0.000060000.037850017340.064978717020.027128700
0.000062500.039427013750.066062333360.026635320
0.000065000.041003999430.067145975500.026141976
0.000067500.042580973940.068229641090.025648667
0.000070000.044157936870.069313327770.025155391
0.000072500.045734887770.070397033200.024662145
0.000075000.047311826230.071480755020.024168929
0.000077500.048888751810.072564490880.023675739
0.000080000.050465664080.073648238440.023182574
0.000082500.052042562620.074731995330.022689433
0.000085000.053619446990.075815759210.022196312
0.000087500.055196316770.076899527730.021703211
0.000090000.056773171520.077983298520.021210127
0.000092500.058350010820.079067069250.020717058
0.000095000.059926834240.080150837560.020224003
0.000097500.061503641350.081234601090.019730960
0.000100000.063080431720.082318357500.019237926
0.000102500.064657204920.083402104440.018744900
0.000105000.066233960520.084485839540.018251879
0.000107500.067810698090.085569560470.017758862
0.000110000.069387417210.086653264860.017265848
0.000112500.070964117450.087736950370.016772833
0.000115000.072540798370.088820614640.016279816
0.000117500.074117459550.089904255330.015786796
0.000120000.075694100550.090987870090.015293770
0.000122500.077270720960.092071456550.014800736
0.000125000.078847320330.093155012380.014307692
0.000127500.080423898250.094238535220.013814637
0.000130000.082000454280.095322022720.013321568
0.000132500.083576988000.096405472530.012828485
0.000135000.085153498970.097488882300.012335383
0.000137500.086729986760.098572249680.011842263
0.000140000.088306450960.099655572320.011349121
0.000142500.089882891120.100738847870.010855957
0.000145000.091459306820.101822073990.010362767
0.000147500.093035697640.102905248330.009869551
0.000150000.094612063130.103988368530.009376305
0.000152500.096188402880.105071432260.008883029
0.000155000.097764716460.106154437150.008389721
0.000157500.099341003430.107237380880.007896377
0.000160000.100917263370.108320261080.007402998
0.000162500.102493495850.109403075410.006909580
0.000165000.104069700430.110485821530.006416121
0.000167500.105645876710.111568497100.005922620
0.000170000.107222024230.112651099760.005429076
0.000172500.108798142580.113733627170.004935485
0.000175000.110374231330.114816076990.004441846
0.000177500.111950290040.115898446880.003948157
0.000180000.113526318300.116980734490.003454416
0.000182500.115102315660.118062937490.002960622
0.000185000.116678281710.119145053520.002466772
0.000187500.118254216010.120227080250.001972864
0.000190000.119830118140.121309015330.001478897
0.000192500.121405987670.122390856440.000984869
0.000195000.122981824170.123472601220.000490777
0.000197500.124557627200.12455424734-0.000003380
0.000200000.126133396360.12563579246-0.000497604
Tabla 8. Valor de para t=50 s=*erf
0.000000000.000000000000.038985773200.038985773
0.000002500.000705311860.039469778820.038764467
0.000005000.001410623670.039953801130.038543177
0.000007500.002115935410.040437839910.038321904
0.000010000.002821247040.040921894960.038100648
0.000012500.003526558510.041405966070.037879408
0.000015000.004231869790.041890053030.037658183
0.000017500.004937180840.042374155630.037436975
0.000020000.005642491620.042858273650.037215782
0.000022500.006347802090.043342406900.036994605
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0.000027500.007758421960.044310718210.036552296
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0.000035000.009874348510.045763294090.035888946
0.000037500.010579656330.046247514260.035667858
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0.000045000.012695576190.047700256410.035004680
0.000047500.013400881480.048184530330.034783649
0.000050000.014106186040.048668817150.034562631
0.000052500.014811489840.049153116680.034341627
0.000055000.015516792820.049637428700.034120636
0.000057500.016222094960.050121753000.033899658
0.000060000.016927396220.050606089370.033678693
0.000062500.017632696560.051090437610.033457741
0.000065000.018337995930.051574797510.033236802
0.000067500.019043294310.052059168840.033015875
0.000070000.019748591650.052543551410.032794960
0.000072500.020453887920.053027945000.032574057
0.000075000.021159183070.053512349410.032353166
0.000077500.021864477070.053996764420.032132287
0.000080000.022569769880.054481189820.031911420
0.000082500.023275061460.054965625410.031690564
0.000085000.023980351770.055450070960.031469719
0.000087500.024685640780.055934526290.031248886
0.000090000.025390928450.056418991160.031028063
0.000092500.026096214730.056903465380.030807251
0.000095000.026801499590.057387948730.030586449
0.000097500.027506782990.057872441010.030365658
0.000100000.028212064900.058356941990.030144877
0.000102500.028917345270.058841451480.029924106
0.000105000.029622624060.059325969260.029703345
0.000107500.030327901250.059810495130.029482594
0.000110000.031033176780.060295028860.029261852
0.000112500.031738450620.060779570260.029041120
0.000115000.032443722730.061264119110.028820396
0.000117500.033148993080.061748675200.028599682
0.000120000.033854261620.062233238330.028378977
0.000122500.034559528320.062717808270.028158280
0.000125000.035264793140.063202384820.027937592
0.000127500.035970056040.063686967780.027716912
0.000130000.036675316980.064171556930.027496240
0.000132500.037380575930.064656152050.027275576
0.000135000.038085832830.065140752950.027054920
0.000137500.038791087670.065625359400.026834272
0.000140000.039496340390.066109971210.026613631
0.000142500.040201590970.066594588150.026392997
0.000145000.040906839350.067079210020.026172371
0.000147500.041612085510.067563836620.025951751
0.000150000.042317329400.068048467720.025731138
0.000152500.043022570990.068533103110.025510532
0.000155000.043727810240.069017742600.025289932
0.000157500.044433047110.069502385960.025069339
0.000160000.045138281550.069987032990.024848751
0.000162500.045843513540.070471683480.024628170
0.000165000.046548743040.070956337210.024407594
0.000167500.047253970000.071440993980.024187024
0.000170000.047959194390.071925653570.023966459
0.000172500.048664416170.072410315780.023745900
0.000175000.049369635290.072894980400.023525345
0.000177500.050074851730.073379647210.023304795
0.000180000.050780065450.073864316000.023084251
0.000182500.051485276400.074348986570.022863710
0.000185000.052190484550.074833658700.022643174
0.000187500.052895689850.075318332180.022422642
0.000190000.053600892280.075803006810.022202115
0.000192500.054306091790.076287682370.021981591
0.000195000.055011288340.076772358650.021761070
0.000197500.055716481900.077257035440.021540554
0.000200000.056421672430.077741712540.021320040
0.000202500.057126859880.078226389730.021099530
0.000205000.057832044230.078711066790.020879023
0.000207500.058537225420.079195743530.020658518
0.000210000.059242403430.079680419730.020438016
0.000212500.059947578220.080165095170.020217517
0.000215000.060652749740.080649769660.019997020
0.000217500.061357917960.081134442970.019776525
0.000220000.062063082840.081619114910.019556032
0.000222500.062768244340.082103785250.019335541
0.000225000.063473402420.082588453790.019115051
0.000227500.064178557050.083073120310.018894563
0.000230000.064883708190.083557784620.018674076
0.000232500.065588855790.084042446490.018453591
0.000235000.066293999830.084527105720.018233106
0.000237500.066999140250.085011762090.018012622
0.000240000.067704277030.085496415400.017792138
0.000242500.068409410120.085981065430.017571655
0.000245000.069114539490.086465711980.017351172
0.000247500.069819665100.086950354840.017130690
0.000250000.070524786910.087434993780.016910207
0.000252500.071229904870.087919628620.016689724
0.000255000.071935018960.088404259120.016469240
0.000257500.072640129140.088888885090.016248756
0.000260000.073345235360.089373506320.016028271
0.000262500.074050337590.089858122580.015807785
0.000265000.074755435790.090342733680.015587298
0.000267500.075460529920.090827339400.015366809
0.000270000.076165619940.091311939540.015146320
0.000272500.076870705810.091796533870.014925828
0.000275000.077575787500.092281122200.014705335
0.000277500.078280864970.092765704310.014484839
0.000280000.078985938180.093250279990.014264342
0.000282500.079691007090.093734849030.014043842
0.000285000.080396071660.094219411220.013823340
0.000287500.081101131860.094703966350.013602834
0.000290000.081806187640.095188514210.013382327
0.000292500.082511238970.095673054590.013161816
0.000295000.083216285810.096157587280.012941301
0.000297500.083921328110.096642112070.012720784
0.000300000.084626365850.097126628750.012500263
0.000302500.085331398990.097611137110.012279738
0.000305000.086036427480.098095636940.012059209
0.000307500.086741451290.098580128030.011838677
0.000310000.087446470370.099064610170.011618140
0.000312500.088151484700.099549083140.011397598
0.000315000.088856494230.100033546750.011177053
0.000317500.089561498920.100518000770.010956502
0.000320000.090266498740.101002445000.010735946
0.000322500.090971493640.101486879230.010515386
0.000325000.091676483600.101971303250.010294820
0.000327500.092381468560.102455716850.010074248
0.000330000.093086448500.102940119810.009853671
0.000332500.093791423370.103424511940.009633089
0.000335000.094496393130.103908893010.009412500
0.000337500.095201357760.104393262820.009191905
0.000340000.095906317200.104877621160.008971304
0.000342500.096611271420.105361967820.008750696
0.000345000.097316220380.105846302590.008530082
0.000347500.098021164050.106330625250.008309461
0.000350000.098726102380.106814935610.008088833
0.000352500.099431035340.107299233440.007868198
0.000355000.100135962890.107783518540.007647556
0.000357500.100840884990.108267790700.007426906
0.000360000.101545801600.108752049710.007206248
0.000362500.102250712690.109236295360.006985583
0.000365000.102955618210.109720527440.006764909
0.000367500.103660518120.110204745740.006544228
0.000370000.104365412400.110688950050.006323538
0.000372500.105070301000.111173140160.006102839
0.000375000.105775183870.111657315860.005882132
0.000377500.106480061000.112141476950.005661416
0.000380000.107184932320.112625623200.005440691
0.000382500.107889797820.113109754410.005219957
0.000385000.108594657440.113593870380.004999213
0.000387500.109299511150.114077970890.004778460
0.000390000.110004358920.114562055730.004557697
0.000392500.110709200700.115046124700.004336924
0.000395000.111414036450.115530177580.004116141
0.000397500.112118866140.116014214160.003895348
0.000400000.112823689730.116498234240.003674545
0.000402500.113528507180.116982237600.003453730
0.000405000.114233318460.117466224040.003232906
0.000407500.114938123510.117950193340.003012070
0.000410000.115642922310.118434145300.002791223
0.000412500.116347714820.118918079710.002570365
0.000415000.117052501000.119401996350.002349495
0.000417500.117757280810.119885895030.002128614
0.000420000.118462054210.120369775520.001907721
0.000422500.119166821170.120853637620.001686816
0.000425000.119871581640.121337481120.001465899
0.000427500.120576335580.121821305820.001244970
0.000430000.121281082970.122305111490.001024029
0.000432500.121985823760.122788897940.000803074
0.000435000.122690557910.123272664950.000582107
0.000437500.123395285380.123756412320.000361127
0.000440000.124100006140.124240139830.000140134
0.000442500.124804720150.12472384728-0.000080873
0.000445000.125509427370.12520753445-0.000301893
Tabla 9. Datos de Y(B)=h, para los tiempos t=1, 5, 10 y 50 s.tY(B)=hT(B)T(A)T(A) - T(B)
10.0000625000.1246473550.124615835-0.000031520
50.0001400000.1248664170.124766194-0.000100222
100.0001975000.1245576270.124554247-0.000003380
500.0004425000.1248047200.124723847-0.000080873
Con los h obtenidos se realiz la evaluacin de la funcin T(B)*(Y(B ) entre ([0,Y(B)=h] )yT(A)*(Y(B )=([Y(B)=[h,T(A)* ]).Tabla 10. Perfiles de temperatura, para los tiempos t=1, 5, 10 y 50 s.t=1t=5t=10t=50
Y(B)T*Y(B)T*Y(B)T*Y(B)T*
0.000000000.000000000000.000000000.000000000000.000000000.000000000000.000000000.00000000000
0.000002500.004987305740.000002500.002230391740.00000250000.001577125200.00000250000.00070531186
5.00E-060.009974597915.00E-060.004460782270.00000500000.003154249970.00000500000.00141062367
0.000007500.014961862920.000007500.006691170370.00000750000.004731373870.00000750000.00211593541
0.000010000.019949087210.000010000.008921554830.00001000000.006308496500.00001000000.00282124704
0.000012500.024936257190.000012500.011151934430.00001250000.007885617400.00001250000.00352655851
0.000015000.029923359300.000015000.013382307960.00001500000.009462736160.00001500000.00423186979
0.000017500.034910379950.000017500.015612674200.00001750000.011039852340.00001750000.00493718084
0.000020000.039897305580.000020000.017843031940.00002000000.012616965520.00002000000.00564249162
0.000022500.044884122610.000022500.020073379970.00002250000.014194075260.00002250000.00634780209
0.000025000.049870817470.000025000.022303717070.00002500000.015771181140.00002500000.00705311222
0.000027500.054857376580.000027500.024534042030.00002750000.017348282720.00002750000.00775842196
0.000030000.059843786380.000030000.026764353630.00003000000.018925379590.00003000000.00846373129
0.000032500.064830033310.000032500.028994650660.00003250000.020502471300.00003250000.00916904015
0.000035000.069816103780.000035000.031224931910.00003500000.022079557430.00003500000.00987434851
0.000037500.074801984240.000037500.033455196150.00003750000.023656637550.00003750000.01057965633
0.000040000.079787661120.000040000.035685442190.00004000000.025233711230.00004000000.01128496358
0.000042500.084773120860.000042500.037915668790.00004250000.026810778040.00004250000.01199027021
0.000045000.089758349890.000045000.040145874760.00004500000.028387837550.00004500000.01269557619
0.000047500.094743334670.000047500.042376058870.00004750000.029964889340.00004750000.01340088148
0.000050000.099728061630.000050000.044606219910.00005000000.031541932970.00005000000.01410618604
0.000052500.104712517210.000052500.046836356670.00005250000.033118968020.00005250000.01481148984
0.000055000.109696687870.000055000.049066467930.00005500000.034695994040.00005500000.01551679282
0.000057500.114680560040.000057500.051296552480.00005750000.036273010630.00005750000.01622209496
0.000060000.119664120200.000060000.053526609110.00006000000.037850017340.00006000000.01692739622
0.000062500.124647354780.000062500.055756636590.00006250000.039427013750.00006250000.01763269656
0.000087500.158755866230.000065000.057986633730.00006500000.041003999430.00006500000.01833799593
0.000112500.192721342100.000067500.060216599300.00006750000.042580973940.00006750000.01904329431
0.000137500.226439914800.000070000.062446532090.00007000000.044157936870.00007000000.01974859165
0.000162500.259840828920.000072500.064676430890.00007250000.045734887770.00007250000.02045388792
0.000187500.292855366150.000075000.066906294480.00007500000.047311826230.00007500000.02115918307
0.000212500.325417268260.000077500.069136121660.00007750000.048888751810.00007750000.02186447707
0.000237500.357463134070.000080000.071365911200.00008000000.050465664080.00008000000.02256976988
0.000262500.388932786360.000082500.073595661890.00008250000.052042562620.00008250000.02327506146
0.000287500.419769605230.000085000.075825372530.00008500000.053619446990.00008500000.02398035177
0.000312500.449920825020.000087500.078055041890.00008750000.055196316770.00008750000.02468564078
0.000337500.479337792090.000090000.080284668770.00009000000.056773171520.00009000000.02539092845
0.000362500.507976181690.000092500.082514251940.00009250000.058350010820.00009250000.02609621473
0.000387500.535796172560.000095000.084743790210.00009500000.059926834240.00009500000.02680149959
0.000412500.562762578250.000097500.086973282350.00009750000.061503641350.00009750000.02750678299
0.000437500.588844935320.000100000.089202727160.00010000000.063080431720.00010000000.02821206490
0.000462500.614017548320.000102500.091432123410.00010250000.064657204920.00010250000.02891734527
0.000487500.638259492860.000105000.093661469900.00010500000.066233960520.00010500000.02962262406
0.000512500.661554577820.000107500.095890765420.00010750000.067810698090.00010750000.03032790125
0.000537500.683891268750.000110000.098120008750.00011000000.069387417210.00011000000.03103317678
0.000562500.705262574740.000112500.100349198670.00011250000.070964117450.00011250000.03173845062
0.000587500.725665901310.000115000.102578333990.00011500000.072540798370.00011500000.03244372273
0.000612500.745102872480.000117500.104807413480.00011750000.074117459550.00011750000.03314899308
0.000637500.763579125080.000120000.107036435930.00012000000.075694100550.00012000000.03385426162
0.000662500.781104078920.000122500.109265400140.00012250000.077270720960.00012250000.03455952832
0.000687500.797690686330.000125000.111494304880.00012500000.078847320330.00012500000.03526479314
0.000712500.813355164770.000127500.113723148950.00012750000.080423898250.00012750000.03597005604
0.000737500.828116716210.000130000.115951931140.00013000000.082000454280.00013000000.03667531698
0.000762500.841997236970.000132500.118180650230.00013250000.083576988000.00013250000.03738057593
0.000787500.855021021640.000135000.120409305010.00013500000.085153498970.00013500000.03808583283
0.000812500.867214464430.000137500.122637894280.00013750000.086729986760.00013750000.03879108767
0.000837500.878605761410.000140000.124866416810.00014000000.088306450960.00014000000.03949634039
0.000862500.889224616500.000165000.140050744830.00014250000.089882891120.00014250000.04020159097
0.000887500.899101954270.000190000.155308409470.00014500000.091459306820.00014500000.04090683935
0.000912500.908269641900.000215000.170532626700.00014750000.093035697640.00014750000.04161208551
0.000937500.916760222730.000240000.185716878260.00015000000.094612063130.00015000000.04231732940
0.000962500.924606663220.000265000.200854697630.00015250000.096188402880.00015250000.04302257099
0.000987500.931842115120.000290000.215939678340.00015500000.097764716460.00015500000.04372781024
0.001012500.938499694090.000315000.230965482000.00015750000.099341003430.00015750000.04443304711
0.001037500.944612275890.000340000.245925846380.00016000000.100917263370.00016000000.04513828155
0.001062500.950212310770.000365000.260814593180.00016250000.102493495850.00016250000.04584351354
0.001087500.955331656640.000390000.275625635670.00016500000.104069700430.00016500000.04654874304
0.001112500.960001431060.000415000.290352986160.00016750000.105645876710.00016750000.04725397000
0.001137500.964251882160.000440000.304990763220.00017000000.107222024230.00017000000.04795919439
0.001162500.968112277970.000465000.319533198670.00017250000.108798142580.00017250000.04866441617
0.001187500.971610813910.000490000.333974644380.00017500000.110374231330.00017500000.04936963529
0.001212500.974774537510.000515000.348309578810.00017750000.111950290040.00017750000.05007485173
0.001237500.977629289730.000540000.362532613190.00018000000.113526318300.00018000000.05078006545
0.001262500.980199661810.000565000.376638497590.00018250000.115102315660.00018250000.05148527640
0.001287500.982508966640.000590000.390622126540.00018500000.116678281710.00018500000.05219048455
0.001312500.984579223450.000615000.404478544470.00018750000.118254216010.00018750000.05289568985
0.001337500.986431154740.000640000.418202950780.00019000000.119830118140.00019000000.05360089228
0.001362500.988084194170.000665000.431790704640.00019250000.121405987670.00019250000.05430609179
0.001387500.989556504100.000690000.445237329410.00019500000.122981824170.00019500000.05501128834
0.001412500.990865001810.000715000.458538516810.00019750000.124557627200.00019750000.05571648190
0.001437500.992025392880.000740000.471690130670.00022250000.135364768150.00020000000.05642167243
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