conductividad buena explicacion,+--
DESCRIPTION
tema de conductividadTRANSCRIPT
RESUMEN
RESUMEN
La presente experiencia corresponde a la prctica Conductividad Trmica se realiz bajo las siguientes condiciones ambientales:
P = 756 mmHg
T= C
Se tomaron datos de tiempo y temperatura para dos slidos cilndricos (aluminio y cobre ); asi como tambin las dimensiones de ellos.
En el caso de la barra de aluminio se efectuaron 3 corridas, obtenindose como resultados el valor promedio de K = W/m.k.
Para el caso de la barra de cobre se efectuaron 3 corridas, obtenindose un valor promedio de K = W/m.k
De dicha prctica se concluye bsicamente que la conductividad trmica del cobre y del aluminio se mantienen constantes dentro de un amplio rango de temperaturas.
INTRODUCCIN
En la prctica se desarrolla el fenmeno de conduccin transitoria donde se desarrolla el modelo para sistema con resistencia interna despreciable la que se justifica cuando la resistencia trmica externa entre la superficie del sistema y el medio que lo rodea es grande, comparada con la resistencia interna del sistema que controla el proceso de transferencia de calor.
El objetivo de esta experiencia es la determinacin de la conductividad trmica de un slido cilndrico de cobre y de aluminio cuya densidad y capacidad calorfica son conocidas.
FUNDAMENTO TEORICO
METODO DE LA RESISTENCIA INTERNA DESPRECIABLE:
La conduccin transitoria es aquel en que un slido experimenta un cambio sbito en su ambiente trmico. Considere una pieza forjada de metal caliente que inicialmente est a una temperatura uniforme Ti y que se templa por inmersin en un lquido de temperatura ms baja T( < Ti (figura 1) . Si decimos que el templado comienza en el tiempo t = 0, la temperatura del slido disminuir en el tiempo t > 0, hasta que finalmente alcance T(. Esta reduccin se debe a la transferencia de calor por conveccin en la interfaz slido-lquido.
La esencia del mtodo de resistencia interna despreciable es la suposicin de que la temperatura del slido es espacialmente uniforme en cualquier instante durante el proceso transitorio. Esta suposicin implica que los gradientes de temperatura dentro del slido son insignificantes.
NUMERO DE BIOT:
Es la razn de la resistencia trmica interna de un slido a la resistencia trmica de la capa limite.
Bi = h x L K
Proporciona una medida de la cada de temperatura en el slido en relacin con la diferencia de temperaturas entre la superficie y el fluido.
NUMERO DE FOURIER:
Es la razn de la rapidez de conduccin de calor a la rapidez de almacenamiento de energa trmica en un slido.
Fo = x t
L2
Es un tiempo adimensional que caracteriza a la conduccin transitoria.
DIFUSIVIDAD TERMICA:
Mide la capacidad de un material para conducir energa trmica en relacin con su capacidad para almacenar energa trmica. Materiales de grande respondern rpidamente a cambios en su medio termico, mientras que los materiales de pequeos respondern mas lentamente y tardan ms en alcanzar una nueva condicin de equilibrio.
= k / x Cp
DETALLES EXPERIMENTALES
EQUIPO:
1 Horno elctrico.
1 Barra cilndrica de aluminio.
1 Barra cilndrica de cobre.
1 Termmetro digital.
1 Termmetro de vidrio.
1 Cronmetro.
1 Tanque con agua.
Aceite.
Pinzas de metal.
PROCEDIMIENTO:
1. Tomar las dimensiones de las barras.
2. Llenar los orificios de las barras con aceite en la cual se introducir el termmetro.
3. Introducir las barras en el horno y calentarlas hasta la temperatura establecida.
4. Sacar una de las barras y tomar la temperatura a la que se encuentra en ese instante.
5. Enseguida introducir completamente la barra en el tanque con agua y anotar las temperaturas cada 5 segundos.
6. Repetir el procedimiento, efectuando tres corridas para cada barra.
TABLAS DE DATOS Y RESULTADOS
Tabla N1: Condiciones Experimentales
Presin Atmosfrica (mm Hg)758.8
Temperatura (C)24
Tabla N2 : Dimensiones de las Barras
CobreAluminio
Dimetro (m)0.0510.051
Altura (m)0.15720.1590
Tabla N3: Propiedades de los Materiales
CobreAluminio
Densidad (Kg/m3)89332702
Capacidad Calorfica (J/Kg.K)385903
Conductividad Termica (W/mK)401237
Tabla 4 Datos del tiempo y temperatura primera toma de datos del aluminio
tT(t)
0116.900
1091.800
2074.500
3062.800
4054.600
5047.800
6043.100
7039.100
8036.000
9032.000
10030.000
11028.700
12027.400
13026.200
14025.200
15024.300
16023.400
17022.800
18022.200
19021.600
20021.200
21020.800
22020.500
23020.200
24019.900
25019.700
26019.500
27019.400
28019.200
29019.000
30018.900
31018.800
32018.700
33018.600
34018.500
35018.400
36018.400
37018.400
38018.300
39018.300
40018.300
41018.300
42018.300
43018.200
44018.200
45018.200
46018.200
47018.200
48018.100
49018.100
50018.100
51018.100
52018.100
53018.100
54018.100
55018.100
56018.100
Tabla 5 Datos del tiempo y temperatura segunda toma de datos del aluminio
tT(t)
0.000117.400
10.000113.900
20.00099.900
30.00082.400
40.00067.500
50.00058.500
60.00049.800
70.00043.100
80.00038.300
90.00035.300
100.00032.500
110.00030.000
120.00028.200
130.00026.900
140.00025.500
150.00024.400
160.00023.600
170.00023.100
180.00022.200
190.00021.700
200.00021.300
210.00020.900
220.00020.600
230.00020.100
240.00019.900
250.00019.700
260.00019.600
270.00019.500
280.00019.300
290.00019.200
300.00019.100
310.00019.000
320.00018.900
330.00018.800
340.00018.700
350.00018.700
360.00018.700
370.00018.700
380.00018.600
390.00018.600
400.00018.600
410.00018.600
420.00018.500
430.00018.500
440.00018.500
450.00018.500
460.00018.500
470.00018.500
480.00018.500
490.00018.500
500.00018.500
510.00018.400
Tabla 6 Datos del tiempo y temperatura segunda toma de datos del aluminio
tT(t)
0.000114.600
10.000104.000
20.00092.400
30.00079.900
40.00069.200
50.00059.500
60.00053.300
70.00048.900
80.00044.000
90.00040.300
100.00037.400
110.00034.500
120.00032.200
130.00030.400
140.00028.800
150.00027.300
160.00026.200
170.00025.200
180.00024.100
190.00023.500
200.00022.900
210.00022.400
220.00022.000
230.00021.600
240.00021.300
250.00020.900
260.00020.600
270.00020.300
280.00020.000
290.00019.700
300.00019.500
310.00019.400
320.00019.300
330.00019.200
340.00019.000
350.00018.900
360.00018.800
370.00018.800
380.00018.700
390.00018.700
400.00018.600
410.00018.500
420.00018.500
430.00018.500
440.00018.400
450.00018.400
460.00018.400
470.00018.400
480.00018.400
490.00018.400
500.00018.300
510.00018.300
Tabla 7 Datos del tiempo y temperatura segunda toma de datos del aluminio
Cilindro de Cobre
Corrida N 2
tT(t)
0.000116.700
10.000101.100
20.00086.200
30.00074.100
40.00064.600
50.00058.100
60.00052.000
70.00047.500
80.00041.700
90.00037.600
100.00035.100
110.00033.000
120.00031.100
130.00029.300
140.00028.200
150.00027.100
160.00026.300
170.00025.400
180.00024.500
190.00024.100
200.00023.400
210.00023.000
220.00022.500
230.00022.100
240.00021.700
250.00021.400
260.00020.800
270.00020.400
280.00020.200
290.00020.200
300.00019.900
310.00019.800
320.00019.600
330.00019.500
340.00019.400
350.00019.400
360.00019.300
370.00019.200
380.00019.200
390.00019.200
400.00019.100
410.00019.100
420.00019.000
430.00019.000
440.00018.900
450.00018.900
460.00018.900
470.00018.900
480.00018.800
490.00018.800
500.00018.800
510.00018.800
520.00018.800
530.00018.800
540.00018.800
550.00018.800
560.00018.700
570.00018.700
580.00018.700
590.00018.700
600.00018.700
610.00018.700
620.00018.700
630.00018.700
640.00018.700
650.00018.700
ClculosTabla 8Cilindro de Aluminio Toma de Datos N 1T infinita H2O 17.9 C T inicial 116.9 CtT(t)T(t)-TinfTini-TinfLnT(t)-Tinf- Tini Tinf
0116.9001.0000.000
1091.8000.746-0.292
2074.5000.572-0.559
3062.8000.454-0.791
4054.6000.371-0.992
5047.8000.302-1.197
6043.1000.255-1.368
7039.1000.214-1.541
8036.0000.183-1.699
9032.0000.142-1.949
10030.0000.122-2.102
11028.7000.109-2.216
12027.4000.096-2.344
13026.2000.084-2.479
14025.2000.074-2.607
15024.3000.065-2.739
16023.4000.056-2.890
17022.8000.049-3.006
18022.2000.043-3.137
19021.6000.037-3.287
20021.2000.033-3.401
21020.8000.029-3.530
22020.5000.026-3.640
23020.2000.023-3.762
24019.9000.020-3.902
25019.7000.018-4.007
26019.5000.016-4.125
27019.4000.015-4.190
28019.2000.013-4.333
29019.0000.011-4.500
30018.9000.010-4.595
31018.8000.009-4.700
32018.7000.008-4.818
33018.6000.007-4.952
34018.5000.006-5.106
35018.4000.005-5.288
36018.4000.005-5.288
37018.4000.005-5.288
38018.3000.004-5.511
39018.3000.004-5.511
40018.3000.004-5.511
41018.3000.004-5.511
42018.3000.004-5.511
43018.2000.003-5.799
44018.2000.003-5.799
45018.2000.003-5.799
46018.2000.003-5.799
47018.2000.003-5.799
48018.1000.002-6.205
49018.1000.002-6.205
50018.1000.002-6.205
51018.1000.002-6.205
52018.1000.002-6.205
53018.1000.002-6.205
54018.1000.002-6.205
55018.1000.002-6.205
56018.1000.002-6.205
Tabla 5 Cilindro de Aluminio
Toma de Datos N 2T inicial 117.400 T Infinita H2O 17.900tT(t)T(t)-TinfTini-TinfLn(T(t)-Tinf/Tini-Tinf)
0.000117.4001.0000.000
10.000113.9000.965-0.036
20.00099.9000.824-0.193
30.00082.4000.648-0.433
40.00067.5000.498-0.696
50.00058.5000.408-0.896
60.00049.8000.321-1.138
70.00043.1000.253-1.373
80.00038.3000.205-1.585
90.00035.3000.175-1.744
100.00032.5000.147-1.919
110.00030.0000.122-2.107
120.00028.2000.104-2.268
130.00026.9000.090-2.403
140.00025.5000.076-2.572
150.00024.4000.065-2.728
160.00023.6000.057-2.860
170.00023.1000.052-2.951
180.00022.2000.043-3.142
190.00021.7000.038-3.265
200.00021.3000.034-3.376
210.00020.9000.030-3.502
220.00020.6000.027-3.607
230.00020.1000.022-3.812
240.00019.9000.020-3.907
250.00019.7000.018-4.012
260.00019.6000.017-4.070
270.00019.5000.016-4.130
280.00019.3000.014-4.264
290.00019.2000.013-4.338
300.00019.1000.012-4.418
310.00019.0000.011-4.505
320.00018.9000.010-4.600
330.00018.8000.009-4.706
340.00018.7000.008-4.823
350.00018.7000.008-4.823
360.00018.7000.008-4.823
370.00018.7000.008-4.823
380.00018.6000.007-4.957
390.00018.6000.007-4.957
t (s)T (C)Ln(T(o)-Too)/(To-Too))t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)
0111.30.000020029.1-2.531940023.6-4.022060022.7-4.8487
5106.2-0.058820528.8-2.575140523.5-4.086560522.6-5.0028
1097.2-0.171921028.5-2.620241023.5-4.086561022.6-5.0028
1589.1-0.285821528.3-2.651541523.5-4.086561522.6-5.0028
2082.2-0.394322028-2.700242023.4-4.155562022.6-5.0028
2576.1-0.501222527.8-2.734142523.4-4.155562522.6-5.0028
3070.9-0.602223027.6-2.769243023.4-4.155563022.6-5.0028
3566.5-0.696523527.4-2.805643523.3-4.229663522.6-5.0028
4062.8-0.783324027.1-2.862844023.3-4.229664022.6-5.0028
4559.4-0.870324526.9-2.902844523.2-4.309764522.5-5.1851
5056.4-0.953925026.8-2.923445023.2-4.309765022.5-5.1851
5553.8-1.032525526.6-2.965945523.2-4.309765522.5-5.1851
6051.4-1.111026026.4-3.010446023.2-4.309766022.5-5.1851
6549.4-1.181526526.2-3.056946523.1-4.396766522.5-5.1851
7047.6-1.249427026.1-3.081047023.1-4.396767022.5-5.1851
7546-1.313927525.9-3.131047523.1-4.396767522.5-5.1851
8044.5-1.378528025.7-3.183748023.1-4.396768022.5-5.1851
8543.2-1.438028525.5-3.239248523-4.4920
9042-1.496329025.3-3.298149023-4.4920
9540.9-1.552829525.1-3.360649523-4.4920
10039.9-1.607230025-3.393450022.9-4.5974
10538.9-1.664730524.9-3.427350522.9-4.5974
11038-1.719431024.7-3.498751022.9-4.5974
11537.2-1.770731524.7-3.498751522.9-4.5974
12036.5-1.817932024.5-3.575752022.9-4.5974
12535.7-1.874632524.5-3.575752522.9-4.5974
13035.1-1.919433024.4-3.616553022.8-4.7151
13534.4-1.974333524.3-3.659153522.8-4.7151
14033.9-2.015534024.2-3.703554022.8-4.7151
14533.4-2.058434524.1-3.750154522.8-4.7151
15032.8-2.112535024.1-3.750155022.8-4.7151
15532.4-2.150235524-3.798955522.8-4.7151
16031.9-2.199536023.9-3.850156022.7-4.8487
16531.5-2.240736523.9-3.850156522.7-4.8487
17031.1-2.283737023.9-3.850157022.7-4.8487
17530.8-2.317237523.8-3.904257522.7-4.8487
18030.5-2.351938023.8-3.904258022.7-4.8487
18530.1-2.400138523.7-3.961458522.7-4.8487
19029.7-2.450839023.7-3.961459022.7-4.8487
19529.5-2.477139523.6-4.022059522.7-4.8487
Tabla N5: Datos de la Barra de Cobre (2ra Corrida)
t (s)T (C)Ln(T(o)-Too)/(To-Too))t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)
0125.40.000020030.5-2.498540024.3-3.805760022.9-4.7440
5122.7-0.026520530.1-2.546740524.2-3.850160522.9-4.7440
10120.3-0.050621029.8-2.584541024.2-3.850161022.9-4.7440
15114.9-0.107121529.5-2.623741524.1-3.896761522.8-4.8617
20105.3-0.216222029.2-2.664542024.1-3.896762022.8-4.8617
2597.2-0.318522528.8-2.721742524-3.945562522.8-4.8617
3089.8-0.422023028.6-2.751543024-3.945563022.8-4.8617
3583.2-0.524523528.4-2.782343523.9-3.996863522.8-4.8617
4077.2-0.627624028.1-2.830344023.9-3.996864022.8-4.8617
4572.2-0.722624527.9-2.863744523.8-4.050864522.8-4.8617
5067.7-0.816525027.7-2.898145023.8-4.050865022.7-4.9953
5564-0.900925527.5-2.933945523.7-4.108065522.7-4.9953
6061.2-0.969926027.3-2.970946023.7-4.108066022.7-4.9953
6557.6-1.066326527.1-3.009446523.7-4.108066522.7-4.9953
7054.9-1.145127026.9-3.049447023.6-4.168667022.7-4.9953
7552-1.237427526.8-3.070047523.6-4.168667522.7-4.9953
8050.2-1.299328026.6-3.112548023.5-4.233168022.7-4.9953
8548.4-1.365228526.4-3.157048523.5-4.233168522.7-4.9953
9046.7-1.431829026.3-3.180049023.5-4.233169022.7-4.9953
9545.1-1.498829526.2-3.203549523.5-4.233169522.7-4.9953
10043.8-1.556730026-3.252350023.4-4.302170022.6-5.1494
10542.5-1.618230525.9-3.277650523.4-4.3021
11041.4-1.673331025.8-3.303651023.4-4.3021
11540.3-1.731731525.7-3.330351523.4-4.3021
12039.4-1.782132025.6-3.357752023.3-4.3762
12538.5-1.835232525.5-3.385852523.3-4.3762
13037.7-1.884933025.4-3.414853023.3-4.3762
13536.9-1.937233525.2-3.475553523.2-4.4563
14036.3-1.978334025.2-3.475554023.2-4.4563
14535.5-2.035934525.1-3.507254523.2-4.4563
15034.9-2.081435025-3.540055023.2-4.4563
15534.3-2.129035524.9-3.573955523.2-4.4563
16033.8-2.170536024.8-3.609056023.1-4.5433
16533.2-2.222736524.8-3.609056523.1-4.5433
17032.7-2.268437024.7-3.645457023.1-4.5433
17532.3-2.306537524.6-3.683157523.1-4.5433
18031.9-2.346138024.5-3.722358023.1-4.5433
18531.5-2.387338524.5-3.722358523.1-4.5433
19031.1-2.430339024.4-3.763159023-4.6386
19530.8-2.463939524.4-3.763159523-4.6386
Tabla N6: Datos de la Barra de Aluminio (1ra Corrida)
t (s)T (C)Ln(T(o)-Too)/(To-Too))t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)
0135.50.000019525-3.633239022.7-5.0885
590.2-0.509420024.9-3.667139522.7-5.0885
1081.1-0.652620524.8-3.702240022.6-5.2426
1573.2-0.796121024.7-3.738640522.6-5.2426
2066.8-0.929621524.5-3.815541022.6-5.2426
2561.7-1.050522024.4-3.856341522.5-5.4250
3057.4-1.165122524.3-3.898942022.5-5.4250
3553.5-1.281823024.2-3.943342522.5-5.4250
4049.6-1.414023524.1-3.989943022.5-5.4250
4547.5-1.493124024-4.038743522.5-5.4250
5045.1-1.592024523.9-4.089944022.4-5.6481
5543-1.687325023.8-4.144044522.4-5.6481
6041.2-1.776925523.7-4.201245022.4-5.6481
6539.6-1.863926023.7-4.201245522.4-5.6481
7035.7-2.114426523.6-4.261846022.4-5.6481
7534.7-2.190227023.5-4.326346522.3-5.9358
8033.9-2.255327523.5-4.326347022.3-5.9358
8533.1-2.324928023.4-4.395347522.3-5.9358
9032.3-2.399728523.4-4.395348022.3-5.9358
9531.6-2.470029023.3-4.469448522.3-5.9358
10031-2.534629523.3-4.469449022.2-6.3412
10530.5-2.591730023.2-4.5495
11029.9-2.664930523.2-4.5495
11529.4-2.730331023.1-4.6365
12028.9-2.800331523.1-4.6365
12528.5-2.860032023.1-4.6365
13028.1-2.923532523-4.7318
13527.8-2.973933023-4.7318
14027.5-3.027133522.9-4.8372
14527.1-3.102634022.9-4.8372
15026.9-3.142634522.9-4.8372
15526.6-3.205735022.8-4.9549
16026.4-3.250235522.8-4.9549
16526.1-3.320836022.8-4.9549
17025.9-3.370836522.8-4.9549
17525.7-3.423537022.8-4.9549
18025.5-3.479037522.7-5.0885
18525.4-3.508038022.7-5.0885
19025.2-3.568738522.7-5.0885
Tabla N7: Datos de la Barra de Aluminio (2ra Corrida)
t (s)T (C)Ln(T(o)-Too)/(To-Too))t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)
0127.60.000019527.1-3.030439023.1-4.5643
5125.3-0.022020026.8-3.091039523.1-4.5643
10118.2-0.093220526.6-3.133640023.1-4.5643
15110.2-0.180121026.4-3.178140523-4.6597
20101.1-0.288921526.1-3.248741023-4.6597
2592.7-0.401222026-3.273441523-4.6597
3084.9-0.518122525.8-3.324742022.9-4.7650
3577.8-0.637923025.6-3.378742522.9-4.7650
4071.8-0.751623525.4-3.435943022.9-4.7650
4565.6-0.884624025.3-3.465743522.9-4.7650
5062.1-0.968324525.2-3.496544022.8-4.8828
5558.2-1.070625025-3.561044522.8-4.8828
6054.8-1.169225524.9-3.594945022.8-4.8828
6551.7-1.268526024.8-3.630045522.8-4.8828
7049-1.363826524.7-3.666446022.8-4.8828
7546.2-1.473327024.6-3.704146522.8-4.8828
8044.6-1.541727524.5-3.743447022.8-4.8828
8542.7-1.629528024.4-3.784247522.7-5.0163
9041.1-1.710028524.3-3.826748022.7-5.0163
9540.2-1.758229024.2-3.871248522.7-5.0163
10038.4-1.862429524.1-3.917749022.7-5.0163
10537.2-1.938430024-3.966549522.7-5.0163
11036.3-1.999430524-3.966550022.7-5.0163
11535.2-2.079431023.9-4.017850522.7-5.0163
12034.3-2.150131523.8-4.071951022.7-5.0163
12533.7-2.200132023.8-4.071951522.6-5.1705
13032.8-2.280132523.7-4.129052022.6-5.1705
13532.1-2.347133023.7-4.129052522.6-5.1705
14031.5-2.408433523.6-4.189753022.6-5.1705
14531-2.462434023.5-4.254253522.6-5.1705
15030.6-2.507934523.5-4.254254022.5-5.3528
15530.1-2.567835023.4-4.323254522.5-5.3528
16029.6-2.631535523.4-4.323255022.5-5.3528
16529.1-2.699636023.4-4.323255522.5-5.3528
17028.7-2.757636523.3-4.397356022.5-5.3528
17528.4-2.803437023.3-4.397356522.4-5.5759
18028-2.867937523.2-4.477357022.4-5.5759
18527.7-2.919238023.2-4.477357522.4-5.5759
19027.4-2.973338523.2-4.477358022.4-5.5759
Tabla N8: Datos de la Barra de Aluminio (3ra Corrida)
t (s)T (C)Ln(T(o)-Too)/(To-Too))t (s)T (C)Ln(T(o)-Too)/(To-Too)t (s)T (C)Ln(T(o)-Too)/(To-Too)
0144.60.000019527.5-3.104239023.1-4.7136
5139.5-0.042520027.2-3.160339523.1-4.7136
10131.9-0.109420527-3.199540023-4.8089
15120.9-0.214821026.8-3.240340523-4.8089
20111.7-0.312521526.6-3.282941022.9-4.9143
25104-0.402222026.4-3.327341522.9-4.9143
3095.8-0.507622526.2-3.373842022.8-5.0321
3588.4-0.613223026-3.422642522.8-5.0321
4081.9-0.716323525.8-3.473943022.8-5.0321
4574.8-0.842424025.6-3.528043522.8-5.0321
5070.5-0.927424525.5-3.556244022.8-5.0321
5565.9-1.027025025.3-3.615044522.8-5.0321
6061-1.145425525.2-3.645845022.7-5.1656
6557.5-1.239426025.1-3.677545522.7-5.1656
7054.3-1.333926524.9-3.744246022.7-5.1656
7551.3-1.431327024.8-3.779346522.7-5.1656
8048.8-1.520527524.7-3.815747022.7-5.1656
8546.6-1.606228024.6-3.853447522.7-5.1656
9045-1.673428524.5-3.892648022.7-5.1656
9543.2-1.754929024.4-3.933548522.6-5.3198
10041.6-1.833429524.3-3.976049022.6-5.3198
10539.9-1.924130024.2-4.020549522.6-5.3198
11038.8-1.987530524.1-4.067050022.6-5.3198
11537.5-2.068131024.1-4.067050522.6-5.3198
12036.2-2.155731524-4.115851022.6-5.3198
12535.3-2.221232023.9-4.167151522.5-5.5021
13034.4-2.291232523.9-4.167152022.5-5.5021
13533.5-2.366633023.8-4.221152522.5-5.5021
14032.8-2.429433523.8-4.221153022.5-5.5021
14532.2-2.486534023.7-4.2783
15031.7-2.536834523.7-4.2783
15531.2-2.589735023.6-4.3389
16030.8-2.634235523.5-4.4035
16530.2-2.704836023.5-4.4035
17029.8-2.754836523.4-4.4725
17529.3-2.821137023.4-4.4725
18028.8-2.892037523.3-4.5466
18528.2-2.984438023.2-4.6266
19027.8-3.051138523.2-4.6266
Tabla N9: Datos para Calcular la Conductividad Trmica
CobreN IteracinPendiente (s-1)h (W/m2K)K asumido (W/mK)K calculado (W/mK)
1ra Corrida-0.0071261.68
1-1.0090401398.85
2-1.0024398.85393.68
3-0.9959396.25393.25
2da Corrida-0.0066243.35
1-1.0209401403.56
2-1.0275403.56406.17
3-1.0341406.17408.78
Aluminio
1ra Corrida-0.0097253.79
1-0.8460237237.34
2-0.8489237.34238.16
2da Corrida-0.0087227.63
1-0.8471237237.65
2-0.8495237.65238.32
3ra Corrida-0.0099259.01
1-0.8437237236.69
2-0.8426236.69236.39
DISCUSIN DE RESULTADOS
En las tablas 4 y 5 se presenta los datos del decaimiento del valor de la temperatura con respecto al tiempo de una barra de cobre, previamente calentada hasta una temperatura elevada para luego ser sumergida en un tanque con agua a la temperatura ambiente observndose que la temperatura desciende hasta alcanzar un valor constante. Para la primera corrida (Tabla 4) se observa que el tiempo en que demora la barra de cobre en alcanzar una temperatura constante fue de 680 segundos desde una temperatura de 111.3 C a 22.5C. Asimismo en la segunda corrida (Tabla 5) se aprecia que el tiempo en que demora la barra en alcanzar una temperatura constante es de 700 segundos desde una temperatura de 125.4C hasta 22.6C.
En las tablas 6, 7 y 8 se presentan los resultados de la variacin de la temperatura con respecto al tiempo de una barra de aluminio, previamente calentada hasta una temperatura determinada, para luego ser sumergido en un tanque con agua a la temperatura ambiental. Los resultados de la tabla 6 corresponden a la primera corrida y puede verse que el tiempo que demora la barra de aluminio en alcanzar una temperatura constante es de 490 segundos desde una temperatura de 135.5C hasta 22.2C. en la Tala 7 corresponden los resultados correspondiente a la segunda corrida y se observa que el tiempo que requiri la barra para alcanzar una temperatura constante fue de 580 segundos desde 127.6C hasta 22.4C. finalmente en la tabla 8 que corresponden a la tercera corrida se observa que el tiempo que demora en alcanzar una temperatura constante fue de 530 segundos desde una temperatura de 144.6C hasta 22.5C.
En las grficas 1,5,9,12 y 15 en las cuales se grfica el Ln[(T(-T()/(To-T()] vs. Tiempo, se aprecia que se obtiene un curva, pero se aproxima a una lnea recta, en la cual el valor de la pendiente se utiliza para poder despejar el valor del coeficiente de pelcula h. Obtenindose para el cobre: h=261.68w/m2K (primera corrida), h=243.35w/m2k (segunda corrida) y para el aluminio: h=253.79w/m2K (primera corrida), h=227.63 w/m2K(segunda corrida) y h=259.01 w/m2K (tercera corrida).
En las grficas 2,3,4,5,6,7,8,10,11,13, 14,16 y 17 en donde se grafica Ln[(T(-T()/(To-T()]/a Vs. tiempo, en la cual a es el nmero de Biot. La grfica que se obtiene es una curva pero se aproxima a una recta de cuya pendiente se obtiene el valor de la conductividad trmica K. Este es un mtodos iterativo, se realiza hasta que el valor de K asumido, sea aproximadamente igual al valor de k calculado grficamente. Finalmente se obtuvieron las siguientes para la barra de cobre; k = 393.68 w/mk (primera corrida), k = 408.78w/mk (segunda corrida), y para la barra de aluminio k = 238.17 w/mk (primera corrida), k = 238.32 w/mk (segunda corrida), y k = 236.39 w/mk (tercera corrida).
CONCLUSIONES
El valor de la conductividad trmica viene dado por el promedio de los valores obtenidos en cada corrida (Kcobre = 401.22 w/mk, Kalumnio =237.63 w/mk)
El valor de la conductividad trmica no presenta demasiada variacin dentro de un amplio rango de temperatura para el cobre y el aluminio.
RECOMENDACIONES
Medir exactamente las dimensiones de las barras, porque esto influir en la determinacin del nmero de Biot.
Calentar las barras hasta una temperatura adecuada que nos permita obtener una buena grfica Ln[(T(-T()/(To-T()] versus t. con aproximacin lineal.
Medir exactamente la temperatura a medida que esta desciende ya que esto influir en las grfica a realizar tanto para la determinacin de k como de h.
Tomar las propiedades de las barras ((, Cp y K) al promedio de las temperaturas mxima y mnima alcanzada.
REFERENCIAS BIBLIOGRAFICAS
Kern D, Procesos de Transferencia de Calor, Ed CECSA, Pg 30-35
Foust A, Principios de las Operaciones Unitarias, Ed Continental, Pg 291-296
Incropera, Procesos de Transferencia de Calor, Ed Prentice may, Pg 212-217
APNDICE
EJEMPLO DE CLCULO
* Para la barra de Cobre (1ra. corrida)
1) Determinacin del coeficiente de transferencia de calor h
Se determinaL
Donde:
T = Temperatura en el tiempo
T0 = Temperatura Inicial
T = Temperatura del medio
Para el primer dato ( = 0) : T = To = 11,3C , T = 22C
L = -0,0588
Los resultados para los dems datos se encuentran en la Tabla 4.
Luego se grafica L vs
Deduccin de la curva obtenida:
Se parte de = e-(hs/(cpv))
Tomando L :
L =
Esta ecuacin indica que al efectuar la grfica
L vs , la pendiente ser
La curva que se obtiene para este caso se muestra en la grfica N 1
Pendiente: m = -0,0071
Luego
S = Superficie de la barra
V = Volumen de la barra
C = calor especfico
P = densidad
S = 0,0276 m2
C = 385 .
Reemplazando en (B)
2) Determinacin de la conductividad termina K de ()
,
BioTLuego:
Reemplazando en :
L =
L = ... ()
La ecuacin indica que al graficar:
L vs , la pendiente es
Este es un mtodo iterativo:
Se asume un K: K asumido = 401 W/mK
Luego
a = 6,9959 x 10-3 ( (1/a) = 142,94.
Luego se multiplica por (Ha) los datos de la Tabla 4 y se grafica versus el tiempo . La curva obtenido se muestra en la grfica 2.
M =
Segn iteracin : (K asumido) = 398.85 W/mK
a = 7,0084 x 10-3 ( (1/a) = 142,68
La curva obtenida para la segunda iteracin se muestra en la grfica 3.
Kcalculado = 396,25 W / mK
Tercera iteracin: Kasumido = 396.25 W/mK
a = 7,0289 x 10-3 ( (1/a ) = 142,27
La curva obtenida para la tercera iteracin se muestra en la grfica 4
K = 393,68 W/mK
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Tiempo(s)
ln(T8o)-Too)/(To-Too))/a
Grafico N8: Barra de Cobre 3ra Iteracion
Hoja1
0122.700000000
5120.35-0.02412177265-3.70750554425-3.73124807755-3.7553551245
10114.910-0.080622153910-12.391588623910-12.470943247210-12.551516184
15105.315-0.189697250615-29.1563816915-29.343096546215-29.5326779929
2097.220-0.291994568820-44.879433274220-45.16683714420-45.4586534599
2589.825-0.395583604825-60.801021299425-61.190385592525-61.5857277067
3083.230-0.497998610230-76.542161354730-77.032330498430-77.5300250971
3577.235-0.601182846435-92.401531837535-92.993262968935-93.5940788133
4072.740-0.686219889140-105.471686872140-106.147118105340-106.8329190801
4567.745-0.790047501845-121.429944026445-122.207570508745-122.9971357129
506450-0.874476181450-134.406593932150-135.267321717850-136.1412640607
5561.255-0.943469052955-145.010767103455-145.93940306455-146.8822961606
6057.660-1.039800161960-159.816815017460-160.840267582460-161.8794329809
6554.965-1.11867314265-171.939556415965-173.040641930665-174.15863216
705270-1.210948418170-186.122224656870-187.314134708370-188.5243438828
7550.275-1.272823821875-195.632446248375-196.885258906875-198.1573057121
8048.480-1.338781789680-205.77015609380-207.087889737180-208.4258542451
8546.785-1.405342556185-216.000515829685-217.383763780985-218.7882484222
9045.190-1.472313182290-226.293870799790-227.743036473990-229.2144508581
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Hoja1
Tiempo(s)
ln(T(o)-Too)/To-Too))
Grafico N5: Barra de Cobre Determinacion de h
Hoja2
Tiempo (s)
ln(T(o)-Too)/(To-Too))
Grafico N6: Barra de Cobre 1ra Iteracion
Hoja3
Tiempo(s)
ln(T(o)-Too)/(To-Too))
Grafico N7: Barra de Cobre 2da Iteracion
Tiempo(s)
ln(T8o)-Too)/(To-Too))/a
Grafico N8: Barra de Cobre 3ra Iteracion
_1074979391.xlsGrfico3
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Tiempo (s)
ln(T(o)-Too)/(To-Too))/a
Grafico N14: Barra de Aluminio 2da Iteracion
Hoja1
aluminio 2
0127.610000
5125.30.978219697-0.02202099515-2.1380906607-2.144020779
10118.20.9109848485-0.093229013610-9.0519107769-9.0770167757
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47522.70.0066287879-5.0163333152475-487.0522581194-488.4031257681
48022.70.0066287879-5.0163333152480-487.0522581194-488.4031257681
48522.70.0066287879-5.0163333152485-487.0522581194-488.4031257681
49022.70.0066287879-5.0163333152490-487.0522581194-488.4031257681
49522.70.0066287879-5.0163333152495-487.0522581194-488.4031257681
50022.70.0066287879-5.0163333152500-487.0522581194-488.4031257681
50522.70.0066287879-5.0163333152505-487.0522581194-488.4031257681
51022.70.0066287879-5.0163333152510-487.0522581194-488.4031257681
51522.60.0056818182-5.170483995515-502.0192533294-503.4116328062
52022.60.0056818182-5.170483995520-502.0192533294-503.4116328062
52522.60.0056818182-5.170483995525-502.0192533294-503.4116328062
53022.60.0056818182-5.170483995530-502.0192533294-503.4116328062
53522.60.0056818182-5.170483995535-502.0192533294-503.4116328062
54022.50.0047348485-5.3528055518540-519.7214514012-521.1629289498
54522.50.0047348485-5.3528055518545-519.7214514012-521.1629289498
55022.50.0047348485-5.3528055518550-519.7214514012-521.1629289498
55522.50.0047348485-5.3528055518555-519.7214514012-521.1629289498
56022.50.0047348485-5.3528055518560-519.7214514012-521.1629289498
56522.40.0037878788-5.5759491031565-541.3871908414-542.8887595732
57022.40.0037878788-5.5759491031570-541.3871908414-542.8887595732
57522.40.0037878788-5.5759491031575-541.3871908414-542.8887595732
58022.40.0037878788-5.5759491031580-541.3871908414-542.8887595732
58522.40.0037878788-5.5759491031585-541.3871908414-542.8887595732
Hoja1
0
0
0
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0
Tiempo (s)
ln(T(o)-Too)/(To-Too))
Grafico N12: Barra de Aluminio Determinacion del h
Hoja2
0
0
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0
0
0
0
0
0
0
0
Tiempo (s)
ln(T(o)-Too)/(To-Too))/a
Grafico N13: Barra de Aluminio 1ra Iteracion
Hoja3
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
Tiempo (s)
ln(T(o)-Too)/(To-Too))/a
Grafico N14: Barra de Aluminio 2da Iteracion
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_1148538484.unknown
_1244193119.unknown
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_1244188725.unknown
_1148538466.unknown
_1148538454.unknown
_1148538458.unknown
_1148538448.unknown
_1075744606.unknown
_1148538428.unknown
_1148538432.unknown
_1076227926.unknown
_1148538423.unknown
_1076227980.unknown
_1076227826.unknown
_1075584134.unknown
_1075584503.unknown
_1075586768.unknown
_1075586769.unknown
_1075584411.unknown
_1075583209.unknown
_1075583523.unknown
_1075583137.unknown
_1075582877.unknown
_1074979393.xlsGrfico3
0
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Tiempo (s)
ln(T(o)-To)/(To-Too))/a
Grafico N17: Barra de Aluminio 2da Iteracion
Hoja1
Aluminio
To=135.5CToo=22CTo=127.6CToo=22CTo=144.6CToo=22C
Tiempo (s)T (C)Tiempo (s)T (C)Tiempo (s)T (C)
0135.50.000010127.60.000010144.60.0000100
590.2-0.50940.60088105735125.3-0.02200.9782196975139.5-0.04250.9584013051-3.6258150905-3.6209326458
1081.1-0.65260.520704845810118.2-0.09320.910984848510131.9-0.10940.896411093-9.3320180858-9.3194517908
1573.2-0.79610.451101321615110.2-0.18010.835227272715120.9-0.21480.8066884176-18.3316917422-18.3070066801
2066.8-0.92960.394713656420101.1-0.28890.749053030320111.7-0.31250.7316476346-26.6637687501-26.6278638921
2561.7-1.05050.34977973572592.7-0.40120.669507575825104-0.40220.6688417618-34.3228051377-34.2765867859
3057.4-1.16510.31189427313084.9-0.51810.59564393943095.8-0.50760.6019575856-43.3138507161-43.2555252155
3553.5-1.28180.27753303963577.8-0.63790.52840909093588.4-0.61320.5415986949-52.3305960404-52.2601287844
4049.6-1.41400.24317180624071.8-0.75160.47159090914081.9-0.71630.4885807504-61.1219584119-61.0396528962
4547.5-1.49310.22466960354565.6-0.88460.41287878794574.8-0.84240.4306688418-71.8884024178-71.79159904
5045.1-1.59200.20352422915062.1-0.96830.37973484855070.5-0.92740.3955954323-79.1374736223-79.030908801
5543-1.68730.18502202645558.2-1.07060.34280303035565.9-1.02700.3580750408-87.6411620461-87.5231463407
6041.2-1.77690.16916299566054.8-1.16920.31060606066061-1.14540.3181076672-97.7409065203-97.6092907161
6539.6-1.86390.15506607936551.7-1.26850.281256557.5-1.23940.2895595432-105.7649615157-105.6225406914
7035.7-2.11440.12070484587049-1.36380.25568181827054.3-1.33390.2634584013-113.8262670945-113.6729910894
7534.7-2.19020.11189427317546.2-1.47330.22916666677551.3-1.43130.2389885808-122.1447965542-121.9803189961
8033.9-2.25530.1048458158044.6-1.54170.21401515158048.8-1.52050.2185970636-129.7555418683-129.5808158441
8533.1-2.32490.09779735688542.7-1.62950.19602272738546.6-1.60620.2006525285-137.0650353862-136.8804665551
9032.3-2.39970.09074889879041.1-1.71000.18087121219045-1.67340.1876019576-142.8040718223-142.6117749281
9531.6-2.47000.08458149789540.2-1.75820.17234848489543.2-1.75490.1729200653-149.7583618682-149.5567004765
10031-2.53460.079295154210038.4-1.86240.155303030310041.6-1.83340.1598694943-156.454816101-156.2441374079
10530.5-2.59170.074889867810537.2-1.93840.143939393910539.9-1.92410.1460032626-164.1972540627-163.9761495691
11029.9-2.66490.069603524211036.3-1.99940.135416666711038.8-1.98750.1370309951-169.6094194133-169.3810270141
11529.4-2.73030.065198237911535.2-2.07940.12511537.5-2.06810.1264274062-176.4822842518-176.2446370005
12028.9-2.80030.060792951512034.3-2.15010.116477272712036.2-2.15570.1158238173-183.9575527524-183.7098394652
12528.5-2.86000.057268722512533.7-2.20010.110795454512535.3-2.22120.1084828711-189.5451777156-189.2899402527
13028.1-2.92350.053744493413032.8-2.28010.102272727313034.4-2.29120.101141925-195.5244636475-195.2611746067
13527.8-2.97390.051101321613532.1-2.34710.095643939413533.5-2.36660.0938009788-201.9544836632-201.6825360956
14027.5-3.02710.048458149814031.5-2.40840.089962121214032.8-2.42940.088091354-207.3136617375-207.0344976158
14527.1-3.10260.044933920714531-2.46240.085227272714532.2-2.48650.0831973899-212.1913324741-211.9056001859
15026.9-3.14260.043171806215030.6-2.50790.081439393915031.7-2.53680.0791190865-216.4804767-216.1889687423
15526.6-3.20570.040528634415530.1-2.56780.076704545515531.2-2.58970.075040783-220.996663059-220.6990737019
16026.4-3.25020.038766519816029.6-2.63150.07196969716030.8-2.63420.0717781403-224.7899989289-224.4873015472
16526.1-3.32080.03612334816529.1-2.69960.067234848516530.2-2.70480.0668841762-230.8162200563-230.5054078947
17025.9-3.37080.034361233517028.7-2.75760.063446969717029.8-2.75480.0636215334-235.083909598-234.7673506574
17525.7-3.42350.032599118917528.4-2.80340.060606060617529.3-2.82110.05954323-240.7373675487-240.4131957832
18025.5-3.47900.030837004418028-2.86790.056818181818028.8-2.89200.0554649266-246.7921053033-246.459780358
18525.4-3.50800.029955947118527.7-2.91920.053977272718528.2-2.98440.0505709625-254.6748754885-254.3319357742
19025.2-3.56870.028193832619027.4-2.97330.051136363619027.8-3.05110.0473083197-260.3660510115-260.0154476826
19525-3.63320.026431718119527.1-3.03040.048295454519527.5-3.10420.0448613377-264.898231374-264.5415251085
20024.9-3.66710.025550660820026.8-3.09100.045454545520027.2-3.16030.0424143556-269.6846824272-269.3215308295
20524.8-3.70220.024669603520526.6-3.13360.043560606120527-3.19950.0407830343-273.0316214334-272.6639629196
21024.7-3.73860.023788546321026.4-3.17810.041666666721026.8-3.24030.0391517129-276.5152073958-276.14285796
21524.5-3.81550.022026431721526.1-3.24870.038825757621526.6-3.28290.0375203915-280.1470748999-279.7698348694
22024.4-3.85630.021145374422026-3.27340.037878787922026.4-3.32730.0358890701-283.9404107698-283.5580627147
22524.3-3.89890.020264317222525.8-3.32470.035984848522526.2-3.37380.0342577488-287.9102430952-287.5225493492
23024.2-3.94330.019383259923025.6-3.37870.034090909123026-3.42260.0326264274-292.0738008292-291.6805005258
23524.1-3.98990.018502202623525.4-3.43590.032196969723525.8-3.47390.030995106-296.4509656981-296.0517711986
24024-4.03870.017621145424025.3-3.46570.0312524025.6-3.52800.0293637847-301.0648464076-300.6594389555
24523.9-4.08990.016740088124525.2-3.49650.030303030324525.5-3.55620.028548124-303.4688365286-303.0601919151
25023.8-4.14400.015859030825025-3.56100.028409090925025.3-3.61500.0269168026-308.4900497816-308.0746437102
25523.7-4.20120.014977973625524.9-3.59490.027462121225525.2-3.64580.0261011419-311.115980225-310.697038132
26023.7-4.20120.014977973626024.8-3.63000.026515151526025.1-3.67750.0252854812-313.8252873294-313.4026969418
26523.6-4.26180.014096916326524.7-3.66640.025568181826524.9-3.74420.0236541599-319.5164628524-319.0862088501
27023.5-4.32630.01321585927024.6-3.70410.024621212127024.8-3.77930.0228384992-322.5110159244-322.0767295213
27523.5-4.32630.01321585927524.5-3.74340.023674242427524.7-3.81570.0220228385-325.6144854193-325.1760199509
28023.4-4.39530.012334801828024.4-3.78420.022727272728024.6-3.85340.0212071778-328.8350942681-328.392291997
28523.4-4.39530.012334801828524.3-3.82670.02178030328524.5-3.89260.0203915171-332.1820332744-331.7347240872
29023.3-4.46940.011453744529024.2-3.87120.020833333329024.4-3.93350.0195758564-335.6656192367-335.2136191275
29523.3-4.46940.011453744529524.1-3.91770.019886363629524.3-3.97600.0187601958-339.2974867409-338.8405960369
30023.2-4.54950.010572687230024-3.96650.018939393930024.2-4.02050.0179445351-343.0908226108-342.6288238822
30523.2-4.54950.010572687230524-3.96650.018939393930524.1-4.06700.0171288744-347.0606549362-346.5933105168
31023.1-4.63650.0096916331023.9-4.01780.017992424231024.1-4.06700.0171288744-347.0606549362-346.5933105168
31523.1-4.63650.0096916331523.8-4.07190.017045454531524-4.11580.0163132137-351.2242126701-350.7512616934
32023.1-4.63650.0096916332023.8-4.07190.017045454532023.9-4.16710.015497553-355.601377539-355.1225323661
32523-4.73180.008810572732523.7-4.12900.016098484832523.9-4.16710.015497553-355.601377539-355.1225323661
33023-4.73180.008810572733023.7-4.12900.016098484833023.8-4.22110.0146818923-360.2152582485-359.730200123
33522.9-4.83720.007929515433523.6-4.18970.015151515233523.8-4.22110.0146818923-360.2152582485-359.730200123
34022.9-4.83720.007929515434023.5-4.25420.014204545534023.7-4.27830.0138662316-365.0929289852-364.601302693
34522.9-4.83720.007929515434523.5-4.25420.014204545534523.7-4.27830.0138662316-365.0929289852-364.601302693
35022.8-4.95490.007048458135023.4-4.32320.013257575835023.6-4.33890.013050571-370.2663920659-369.7677992996
35522.8-4.95490.007048458135523.4-4.32320.013257575835523.5-4.40350.0122349103-375.7738516819-375.2678426888
36022.8-4.95490.007048458136023.4-4.32320.013257575836023.5-4.40350.0122349103-375.7738516819-375.2678426888
36522.8-4.95490.007048458136523.3-4.39730.012310606136523.4-4.47250.0114192496-381.6614277653-381.1474906888
37022.8-4.95490.007048458137023.3-4.39730.012310606137023.4-4.47250.0114192496-381.6614277653-381.1474906888
37522.7-5.08850.006167400937523.2-4.47730.011363636437523.3-4.54660.0106035889-387.985506109-387.4630531646
38022.7-5.08850.006167400938023.2-4.47730.011363636438023.2-4.62660.0097879282-394.8160310777-394.2843802951
38522.7-5.08850.006167400938523.2-4.47730.011363636438523.2-4.62660.0097879282-394.8160310777-394.2843802951
39022.7-5.08850.006167400939023.1-4.56430.010416666739023.1-4.71360.0089722675-402.2412344517-401.6995850498
39522.7-5.08850.006167400939523.1-4.56430.010416666739523.1-4.71360.0089722675-402.2412344517-401.6995850498
40022.6-5.24260.005286343640023.1-4.56430.010416666740023-4.80890.0081566069-410.3746245111-409.8220228609
40522.6-5.24260.005286343640523-4.65970.00946969740523-4.80890.0081566069-410.3746245111-409.8220228609
41022.6-5.24260.005286343641023-4.65970.00946969741022.9-4.91430.0073409462-419.3656700895-418.8009612905
41522.5-5.42500.004405286341523-4.65970.00946969741522.9-4.91430.0073409462-419.3656700895-418.8009612905
42022.5-5.42500.004405286342022.9-4.76500.008522727342022.8-5.03210.0065252855-429.4168039068-428.8385604671
42522.5-5.42500.004405286342522.9-4.76500.008522727342522.8-5.03210.0065252855-429.4168039068-428.8385604671
43022.5-5.42500.004405286343022.9-4.76500.008522727343022.8-5.03210.0065252855-429.4168039068-428.8385604671
43522.5-5.42500.004405286343522.9-4.76500.008522727343522.8-5.03210.0065252855-429.4168039068-428.8385604671
44022.4-5.64810.003524229144022.8-4.88280.007575757644022.8-5.03210.0065252855-429.4168039068-428.8385604671
44522.4-5.64810.003524229144522.8-4.88280.007575757644522.8-5.03210.0065252855-429.4168039068-428.8385604671
45022.4-5.64810.003524229145022.8-4.88280.007575757645022.7-5.16560.0057096248-440.8118396063-440.2182518564
45522.4-5.64810.003524229145522.8-4.88280.007575757645522.7-5.16560.0057096248-440.8118396063-440.2182518564
46022.4-5.64810.003524229146022.8-4.88280.007575757646022.7-5.16560.0057096248-440.8118396063-440.2182518564
46522.3-5.93580.002643171846522.8-4.88280.007575757646522.7-5.16560.0057096248-440.8118396063-440.2182518564
47022.3-5.93580.002643171847022.8-4.88280.007575757647022.7-5.16560.0057096248-440.8118396063-440.2182518564
47522.3-5.93580.002643171847522.7-5.01630.006628787947522.7-5.16560.0057096248-440.8118396063-440.2182518564
48022.3-5.93580.002643171848022.7-5.01630.006628787948022.7-5.16560.0057096248-440.8118396063-440.2182518564
48522.3-5.93580.002643171848522.7-5.01630.006628787948522.6-5.31980.0048939641-453.9664429186-453.3551414626
49022.2-6.34120.001762114549022.7-5.01630.006628787949022.6-5.31980.0048939641-453.9664429186-453.3551414626
49522.7-5.01630.006628787949522.6-5.31980.0048939641-453.9664429186-453.3551414626
50022.7-5.01630.006628787950022.6-5.31980.0048939641-453.9664429186-453.3551414626
50522.7-5.01630.006628787950522.6-5.31980.0048939641-453.9664429186-453.3551414626
51022.7-5.01630.006628787951022.6-5.31980.0048939641-453.9664429186-453.3551414626
51522.6-5.17050.005681818251522.5-5.50210.0040783034-469.525036352-468.8927840284
52022.6-5.17050.005681818252022.5-5.50210.0040783034-469.525036352-468.8927840284
52522.6-5.17050.005681818252522.5-5.50210.0040783034-469.525036352-468.8927840284
53022.6-5.17050.005681818253022.5-5.50210.0040783034-469.525036352-468.8927840284
53522.6-5.17050.0056818182
54022.5-5.35280.0047348485
54522.5-5.35280.0047348485
55022.5-5.35280.0047348485
55522.5-5.35280.0047348485
56022.5-5.35280.0047348485
56522.4-5.57590.0037878788
57022.4-5.57590.0037878788
57522.4-5.57590.0037878788
58022.4-5.57590.0037878788
Hoja1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Tiempo(s)
ln(T(o)-To)/(To-Too))
Grafico N15: Barra de Aluminio Determinacion del h
Hoja2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Tiempo (s)
ln(T(o)-Too)/(To-Too))/a
Grafico N16: Barra de Aluminio 1ra Iteracion
Hoja4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Tiempo (s)
ln(T(o)-To)/(To-Too))/a
Grafico N17: Barra de Aluminio 2da Iteracion
Hoja3
Cobre
To=111.3CToo=22CTo=125.4CToo=22C
Tiempo (s)T (C)Tiempo (s)T (C)
0111.310.00000125.40.00001
5106.20.9428891377-0.05885122.7-0.02650.9738878143
1097.20.8421052632-0.171910120.3-0.05060.9506769826
1589.10.751399776-0.285815114.9-0.10710.8984526112
2082.20.6741321389-0.394320105.3-0.21620.8056092843
2576.10.6058230683-0.50122597.2-0.31850.7272727273
3070.90.5475923852-0.60223089.8-0.42200.6557059961
3566.50.4983202688-0.69653583.2-0.52450.5918762089
4062.80.4568868981-0.78334077.2-0.62760.5338491296
4559.40.4188129899-0.87034572.2-0.72260.4854932302
5056.40.3852183651-0.95395067.7-0.81650.4419729207
5553.80.3561030235-1.03255564-0.90090.4061895551
6051.40.3292273236-1.11106061.2-0.96990.3791102515
6549.40.3068309071-1.18156557.6-1.06630.3442940039
7047.60.2866741321-1.24947054.9-1.14510.3181818182
75460.2687569989-1.31397552-1.23740.2901353965
8044.50.2519596865-1.37858050.2-1.29930.2727272727
8543.20.2374020157-1.43808548.4-1.36520.2553191489
90420.2239641657-1.49639046.7-1.43180.2388781431
9540.90.2116461366-1.55289545.1-1.49880.2234042553
10039.90.2004479283-1.607210043.8-1.55670.2108317215
10538.90.18924972-1.664710542.5-1.61820.1982591876
110380.1791713326-1.719411041.4-1.67330.1876208897
11537.20.170212766-1.770711540.3-1.73170.1769825919
12036.50.1623740202-1.817912039.4-1.78210.16827853
12535.70.1534154535-1.874612538.5-1.83520.1595744681
13035.10.1466965286-1.919413037.7-1.88490.1518375242
13534.40.1388577828-1.974313536.9-1.93720.1441005803
14033.90.1332586786-2.015514036.3-1.97830.1382978723
14533.40.1276595745-2.058414535.5-2.03590.1305609284
15032.80.1209406495-2.112515034.9-2.08140.1247582205
15532.40.1164613662-2.150215534.3-2.12900.1189555126
16031.90.110862262-2.199516033.8-2.17050.1141199226
16531.50.1063829787-2.240716533.2-2.22270.1083172147
17031.10.1019036954-2.283717032.7-2.26840.1034816248
17530.80.0985442329-2.317217532.3-2.30650.0996131528
18030.50.0951847704-2.351918031.9-2.34610.0957446809
18530.10.0907054871-2.400118531.5-2.38730.0918762089
19029.70.0862262038-2.450819031.1-2.43030.0880077369
19529.50.0839865622-2.477119530.8-2.46390.085106383
20029.10.0795072788-2.531920030.5-2.49850.082205029
20528.80.0761478163-2.575120530.1-2.54670.0783365571
21028.50.0727883539-2.620221029.8-2.58450.0754352031
21528.30.0705487122-2.651521529.5-2.62370.0725338491
220280.0671892497-2.700222029.2-2.66450.0696324952
22527.80.0649496081-2.734122528.8-2.72170.0657640232
23027.60.0627099664-2.769223028.6-2.75150.0638297872
23527.40.0604703247-2.805623528.4-2.78230.0618955513
24027.10.0571108623-2.862824028.1-2.83030.0589941973
24526.90.0548712206-2.902824527.9-2.86370.0570599613
25026.80.0537513998-2.923425027.7-2.89810.0551257253
25526.60.0515117581-2.965925527.5-2.93390.0531914894
26026.40.0492721165-3.010426027.3-2.97090.0512572534
26526.20.0470324748-3.056926527.1-3.00940.0493230174
27026.10.045912654-3.081027026.9-3.04940.0473887814
27525.90.0436730123-3.131027526.8-3.07000.0464216634
28025.70.0414333707-3.183728026.6-3.11250.0444874275
28525.50.039193729-3.239228526.4-3.15700.0425531915
29025.30.0369540873-3.298129026.3-3.18000.0415860735
29525.10.0347144457-3.360629526.2-3.20350.0406189555
300250.0335946249-3.393430026-3.25230.0386847195
30524.90.032474804-3.427330525.9-3.27760.0377176015
31024.70.0302351624-3.498731025.8-3.30360.0367504836
31524.70.0302351624-3.498731525.7-3.33030.0357833656
32024.50.0279955207-3.575732025.6-3.35770.0348162476
32524.50.0279955207-3.575732525.5-3.38580.0338491296
33024.40.0268756999-3.616533025.4-3.41480.0328820116
33524.30.0257558791-3.659133525.2-3.47550.0309477756
34024.20.0246360582-3.703534025.2-3.47550.0309477756
34524.10.0235162374-3.750134525.1-3.50720.0299806576
35024.10.0235162374-3.750135025-3.54000.0290135397
355240.0223964166-3.798935524.9-3.57390.0280464217
36023.90.0212765957-3.850136024.8-3.60900.0270793037
36523.90.0212765957-3.850136524.8-3.60900.0270793037
37023.90.0212765957-3.850137024.7-3.64540.0261121857
37523.80.0201567749-3.904237524.6-3.68310.0251450677
38023.80.0201567749-3.904238024.5-3.72230.0241779497
38523.70.0190369541-3.961438524.5-3.72230.0241779497
39023.70.0190369541-3.961439024.4-3.76310.0232108317
39523.60.0179171333-4.022039524.4-3.76310.0232108317
40023.60.0179171333-4.022040024.3-3.80570.0222437137
40523.50.0167973124-4.086540524.2-3.85010.0212765957
41023.50.0167973124-4.086541024.2-3.85010.0212765957
41523.50.0167973124-4.086541524.1-3.89670.0203094778
42023.40.0156774916-4.155542024.1-3.89670.0203094778
42523.40.0156774916-4.155542524-3.94550.0193423598
43023.40.0156774916-4.155543024-3.94550.0193423598
43523.30.0145576708-4.229643523.9-3.99680.0183752418
44023.30.0145576708-4.229644023.9-3.99680.0183752418
44523.20.0134378499-4.309744523.8-4.05080.0174081238
45023.20.0134378499-4.309745023.8-4.05080.0174081238
45523.20.0134378499-4.309745523.7-4.10800.0164410058
46023.20.0134378499-4.309746023.7-4.10800.0164410058
46523.10.0123180291-4.396746523.7-4.10800.0164410058
47023.10.0123180291-4.396747023.6-4.16860.0154738878
47523.10.0123180291-4.396747523.6-4.16860.0154738878
48023.10.0123180291-4.396748023.5-4.23310.0145067698
485230.0111982083-4.492048523.5-4.23310.0145067698
490230.0111982083-4.492049023.5-4.23310.0145067698
495230.0111982083-4.492049523.5-4.23310.0145067698
50022.90.0100783875-4.597450023.4-4.30210.0135396518
50522.90.0100783875-4.597450523.4-4.30210.0135396518
51022.90.0100783875-4.597451023.4-4.30210.0135396518
51522.90.0100783875-4.597451523.4-4.30210.0135396518
52022.90.0100783875-4.597452023.3-4.37620.0125725338
52522.90.0100783875-4.597452523.3-4.37620.0125725338
53022.80.0089585666-4.715153023.3-4.37620.0125725338
53522.80.0089585666-4.715153523.2-4.45630.0116054159
54022.80.0089585666-4.715154023.2-4.45630.0116054159
54522.80.0089585666-4.715154523.2-4.45630.0116054159
55022.80.0089585666-4.715155023.2-4.45630.0116054159
55522.80.0089585666-4.715155523.2-4.45630.0116054159
56022.70.0078387458-4.848756023.1-4.54330.0106382979
56522.70.0078387458-4.848756523.1-4.54330.0106382979
57022.70.0078387458-4.848757023.1-4.54330.0106382979
57522.70.0078387458-4.848757523.1-4.54330.0106382979
58022.70.0078387458-4.848758023.1-4.54330.0106382979
58522.70.0078387458-4.848758523.1-4.54330.0106382979
59022.70.0078387458-4.848759023-4.63860.0096711799
59522.70.0078387458-4.848759523-4.63860.0096711799
60022.70.0078387458-4.848760022.9-4.74400.0087040619
60522.60.006718925-5.002860522.9-4.74400.0087040619
61022.60.006718925-5.002861022.9-4.74400.0087040619
61522.60.006718925-5.002861522.8-4.86170.0077369439
62022.60.006718925-5.002862022.8-4.86170.0077369439
62522.60.006718925-5.002862522.8-4.86170.0077369439
63022.60.006718925-5.002863022.8-4.86170.0077369439
63522.60.006718925-5.002863522.8-4.86170.0077369439
64022.60.006718925-5.002864022.8-4.86170.0077369439
64522.50.0055991041-5.185164522.8-4.86170.0077369439
65022.50.0055991041-5.185165022.7-4.99530.0067698259
65522.50.0055991041-5.185165522.7-4.99530.0067698259
66022.50.0055991041-5.185166022.7-4.99530.0067698259
66522.50.0055991041-5.185166522.7-4.99530.0067698259
67022.50.0055991041-5.185167022.7-4.99530.0067698259
67522.50.0055991041-5.185167522.7-4.99530.0067698259
68022.50.0055991041-5.185168022.7-4.99530.0067698259
68522.7-4.99530.0067698259
69022.7-4.99530.0067698259
69522.7-4.99530.0067698259
70022.6-5.14940.0058027079
0
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-0.501167302
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-0.7833194065
-0.8703307835
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-1.0325351981
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-1.607200775
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-1.77070606
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-2.0583881325
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-2.7341435703
-2.7692348901
-2.8056025343
-2.8627609482
-2.9027662828
-2.92338557
-2.9659451844
-3.010396947
-3.0569169626
-3.0810145142
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-3.1836686682
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-3.3605993764
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-3.4987497149
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-3.6590923649
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-3.7500641432
-3.7988543073
-3.8501476017
-3.8501476017
-3.8501476017
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-3.904214823
-3.9613732368
-3.9613732368
-4.0219978586
-4.0219978586
-4.0865363798
-4.0865363798
-4.0865363798
-4.1555292513
-4.1555292513
-4.1555292513
-4.2296372234
-4.2296372234
-4.3096799311
-4.3096799311
-4.3096799311
-4.3096799311
-4.3966913081
-4.3966913081
-4.3966913081
-4.3966913081
-4.4920014879
-4.4920014879
-4.4920014879
-4.5973620035
-4.5973620035
-4.5973620035
-4.5973620035
-4.5973620035
-4.5973620035
-4.7151450392
-4.7151450392
-4.7151450392
-4.7151450392
-4.7151450392
-4.7151450392
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-4.8486764318
-5.0028271116
-5.0028271116
-5.0028271116
-5.0028271116
-5.0028271116
-5.0028271116
-5.0028271116
-5.0028271116
-5.1851486684
-5.1851486684
-5.1851486684
-5.1851486684
-5.1851486684
-5.1851486684
-5.1851486684
-5.1851486684
Corrida N1
Tiempo (s)
ln(T(o)-Too/To-Too)
Grafico N1: Barra de Cobre
_1074979386.xlsGrfico2
0
-44.5068952082
-57.0206695725
-69.5587134475
-81.2264687867
-91.7867521485
-101.803753144
-112.002929892
-123.551883895
-130.466773917
-139.1037617606
-147.4318098505
-155.2619741472
-162.8648863799
-170.6485191928
-177.4166780815
-184.7534360746
-191.3761781625
-197.0613288506
-203.1422772029
-209.6782852245
-215.8280444763
-221.4673152109
-226.4617242046
-232.8581182761
-238.5711571615
-244.6840245532
-249.9021938978
-255.4518917192
-259.858457472
-264.4991074023
-271.096834211
-274.5924351132
-280.1129045117
-283.9970270381
-290.1674749059
-294.5373039042
-299.1372274906
-303.9928304673
-306.5257141696
-311.8229947639
-317.4622654986
-320.4245278011
-323.4907501031
-326.6684955464
-333.3932258213
-336.9601851345
-340.6789748408
-344.5630973672
-348.6279404737
-352.8911454572
-357.3730698773
-362.097375505
-362.097375505
-367.0917844987
-367.0917844987
-372.389065093
-378.0283358277
-378.0283358277
-384.0568204322
-384.0568204322
-390.5322541919
-390.5322541919
-397.5262554636
-397.5262554636
-405.1291676963
-405.1291676963
-405.1291676963
-413.4572157863
-413.4572157863
-422.6634458341
-422.6634458341
-422.6634458341
-432.9551354221
-432.9551354221
-432.9551354221
-432.9551354221
-432.9551354221
-444.6228907613
-444.6228907613
-444.6228907613
-444.6228907613
-444.6228907613
-458.0923257926
-458.0923257926
-458.0923257926
-474.0232861154
-474.0232861154
-474.0232861154
-474.0232861154
-474.0232861154
-493.5212057512
-493.5212057512
-493.5212057512
-493.5212057512
-493.5212057512
-518.6583961217
-518.6583961217
-518.6583961217
-518.6583961217
-518.6583961217
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
-554.0872760803
Tiempo(s)
ln(T(o)-Too)/