difusividad resultados y discusiones
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DIFUSIVIDAD resultados y discusiones.docxTRANSCRIPT
RESULTADOS Y DISCUCIONES
a) Historial trmico del producto registrado por el DATA TRACE y la grfica.
Cuadro 1: registro de datos experimentales
Tiempo(min)
T (C)
2
21.40
3
21.50
4
21.50
5
21.80
6
21.60
7
21.60
8
21.60
9
21.60
10
21.70
11
21.90
12
22.10
13
22.60
14
23.20
15
23.90
16
24.80
17
25.80
18
27.00
19
28.30
20
29.60
21
31.00
22
32.40
23
33.90
24
35.40
25
36.90
26
38.30
27
39.80
28
41.20
29
42.60
30
43.90
31
45.30
32
46.60
33
47.80
34
49.00
35
50.20
36
51.40
37
52.40
38
53.50
39
54.50
40
55.50
41
56.40
42
57.30
43
58.10
44
58.90
45
59.70
46
60.40
47
61.10
48
61.80
49
62.50
50
63.10
51
63.70
52
64.20
53
64.80
54
65.30
55
65.80
56
66.20
57
66.70
58
67.10
59
67.50
60
67.90
61
68.30
62
68.70
63
69.00
64
69.30
65
69.70
66
70.00
67
70.30
68
70.60
69
70.80
70
71.10
71
71.30
72
71.60
73
71.80
74
72.00
75
72.20
76
72.50
77
72.70
78
72.80
79
73.00
80
73.20
81
73.40
82
73.50
83
73.70
84
73.90
85
74.00
86
74.10
87
74.30
88
74.40
89
74.50
90
74.60
91
74.80
92
74.90
93
75.00
94
75.10
95
75.20
96
75.30
97
75.40
98
75.50
99
75.50
100
75.60
101
75.70
102
75.80
103
75.90
104
75.90
105
76.00
106
76.10
107
76.20
108
76.20
109
76.30
110
76.30
111
76.40
112
76.50
113
76.50
114
76.60
115
76.60
116
76.70
117
76.70
118
76.70
119
76.80
120
76.80
121
76.90
122
76.90
123
76.90
124
77.00
125
77.00
126
72.80
127
40.50
128
25.60
Fuente: Propia
Figura 1: Grafica Temperatura vs. Tiempo
Fuente: Propia
Alimento: ARROZ
Cuadro 2: Condiciones de frontera para la determinacin de la difusividad trmica.
To
21.40 C
T1
80 C
r
0.024 m
Fuente: Propia
Donde:
To= temperatura inicial de la muestra
T1= temperatura de las paredes del cilindro
r= radio interno de la clula que contiene la muestra
Cuadro 3: Difusividad trmica con respecto a la temperatura del centro del cilindro.
Tiempo
(min)
T(C)
Ti
A
B
N Fourier
Difusividad trmica
(m2/s)
221.40 60.47 0.99830 0.99829 0.04245 0.40753
3 21.50 60.50 0.99659 0.99658 0.04414 0.14124
4 21.50 60.50 0.99659 0.99658 0.04414 0.10593
5 21.80 60.60 0.99148 0.99147 0.04858 0.09327
6 21.60 60.53 0.99489 0.99488 0.04572 0.07315
7 21.60 60.53 0.99489 0.99488 0.04572 0.06270
8 21.60 60.53 0.99489 0.99488 0.04572 0.05486
9 21.60 60.53 0.99489 0.99488 0.04572 0.04876
10 21.70 60.57 0.99319 0.99318 0.04720 0.04531
11 21.90 60.63 0.98978 0.98977 0.04988 0.04353
12 22.10 60.70 0.98637 0.98636 0.05227 0.04181
13 22.60 60.87 0.97785 0.97784 0.05735 0.04235
14 23.20 61.07 0.96763 0.96762 0.06240 0.04279
15 23.90 61.30 0.95571 0.95570 0.06746 0.04317
16 24.80 61.60 0.94037 0.94037 0.07319 0.04391
17 25.80 61.93 0.92334 0.92333 0.07892 0.04457
18 27.00 62.33 0.90290 0.90289 0.08525 0.04547
1928.30 62.77 0.88075 0.88074 0.09170 0.04633
20 29.60 63.20 0.85860 0.85859 0.09786 0.04697
21 31.00 63.67 0.83475 0.83474 0.10432 0.04769
22 32.40 64.13 0.81090 0.81091 0.11065 0.04828
23 33.90 64.63 0.78535 0.78536 0.11739 0.04900
24 35.40 65.13 0.75980 0.75980 0.12413 0.04965
25 36.90 65.63 0.73424 0.73425 0.13091 0.05027
26 38.30 66.10 0.71039 0.71040 0.13733 0.05070
27 39.80 66.60 0.68484 0.68485 0.14431 0.05131
28 41.20 67.07 0.66099 0.66100 0.15097 0.05176
29 42.60 67.53 0.63714 0.63715 0.15778 0.05223
30 43.90 67.97 0.61499 0.61500 0.16427 0.05257
31 45.30 68.43 0.59114 0.59115 0.17147 0.05310
32 46.60 68.87 0.56899 0.56900 0.17836 0.05351
33 47.80 69.27 0.54855 0.54856 0.18492 0.05380
34 49.00 69.67 0.52811 0.52812 0.19170 0.05413
35 50.20 70.07 0.50767 0.50767 0.19872 0.05451
36 51.40 70.47 0.48722 0.48723 0.20599 0.05493
37 52.40 70.80 0.47019 0.47020 0.21227 0.05508
38 53.50 71.17 0.45145 0.45146 0.21943 0.05544
39 54.50 71.50 0.43441 0.43442 0.22619 0.05568
40 55.50 71.83 0.41738 0.41739 0.23320 0.05597
41 56.40 72.13 0.40204 0.40205 0.23976 0.05614
42 57.30 72.43 0.38671 0.38672 0.24655 0.05636
43 58.10 72.70 0.37308 0.37309 0.25282 0.05644
44 58.90 72.97 0.35945 0.35946 0.25931 0.05658
45 59.70 73.23 0.34583 0.34583 0.26605 0.05676
46 60.40 73.47 0.33390 0.33391 0.27217 0.05680
47 61.10 73.70 0.32198 0.32199 0.27850 0.05689
48 61.80 73.93 0.31005 0.31006 0.28507 0.05701
49 62.50 74.17 0.29813 0.29813 0.29190 0.05719
50 63.10 74.37 0.28790 0.28791 0.29797 0.05721
51 63.70 74.57 0.27768 0.27769 0.30425 0.05727
52 64.20 74.73 0.26917 0.26917 0.30967 0.05717
53 64.80 74.93 0.25894 0.25895 0.31640 0.05731
54 65.30 75.10 0.25043 0.25044 0.32221 0.05728
55 65.80 75.27 0.24191 0.24192 0.32822 0.05729
56 66.20 75.40 0.23509 0.23510 0.33319 0.05712
57 66.70 75.57 0.22658 0.22658 0.33960 0.05720
58 67.10 75.70 0.21976 0.21977 0.34490 0.05709
59 67.50 75.83 0.21295 0.21296 0.35037 0.05701
60 67.90 75.97 0.20613 0.20614 0.35602 0.05696
61 68.30 76.10 0.19932 0.19933 0.36186 0.05695
62 68.70 76.23 0.19250 0.19251 0.36790 0.05697
63 69.00 76.33 0.18739 0.18740 0.37258 0.05677
64 69.30 76.43 0.18228 0.18229 0.37738 0.05661
65 69.70 76.57 0.17547 0.17548 0.38399 0.05671
66 70.00 76.67 0.17036 0.17037 0.38913 0.05660
67 70.30 76.77 0.16525 0.16526 0.39441 0.05651
68 70.60 76.87 0.16014 0.16015 0.39987 0.05645
69 70.80 76.93 0.15673 0.15674 0.40360 0.05615
70 71.10 77.03 0.15162 0.15163 0.40936 0.05614
71 71.30 77.10 0.14821 0.14822 0.41330 0.05588
72 71.60 77.20 0.14310 0.14311 0.41940 0.05592
73 71.80 77.27 0.13969 0.13970 0.42358 0.05570
74 72.00 77.33 0.13629 0.13630 0.42787 0.05551
75 72.20 77.40 0.13288 0.13289 0.43226 0.05533
76 72.50 77.50 0.12777 0.12778 0.43907 0.05546
77 72.70 77.57 0.12436 0.12437 0.44376 0.05533
78 72.80 77.60 0.12266 0.12267 0.44616 0.05491
79 73.00 77.67 0.11925 0.11926 0.45105 0.05481
80 73.20 77.73 0.11584 0.11585 0.45608 0.05473
81 73.40 77.80 0.11244 0.11245 0.46126 0.05467
82 73.50 77.83 0.11073 0.11074 0.46391 0.05431
83 73.70 77.90 0.10733 0.10733 0.46934 0.05429
84 73.90 77.97 0.10392 0.10393 0.47494 0.05428
85 74.00 78.00 0.10221 0.10222 0.47781 0.05396
86 74.10 78.03 0.10051 0.10052 0.48073 0.05366
87 74.30 78.10 0.09710 0.09711 0.48671 0.05371
88 74.40 78.13 0.09540 0.09541 0.48979 0.05343
89 74.50 78.17 0.09370 0.09371 0.49291 0.05317
90 74.60 78.20 0.09199 0.09200 0.49610 0.05292
91 74.80 78.27 0.08859 0.08860 0.50265 0.05303
92 74.90 78.30 0.08688 0.08689 0.50602 0.05280
93 75.00 78.33 0.08518 0.08519 0.50946 0.05259
94 75.10 78.37 0.08348 0.08348 0.51297 0.05239
95 75.20 78.40 0.08177 0.08178 0.51655 0.05220
96 75.30 78.43 0.08007 0.08008 0.52020 0.05202
97 75.40 78.47 0.07836 0.07837 0.52393 0.05185
98 75.50 78.50 0.07666 0.07667 0.52775 0.05170
99 75.50 78.50 0.07666 0.07667 0.52775 0.05118
100 75.60 78.53 0.07496 0.07497 0.53165 0.05104
101 75.70 78.57 0.07325 0.07326 0.53564 0.05091
102 75.80 78.60 0.07155 0.07156 0.53973 0.05080
103 75.90 78.63 0.06985 0.06986 0.54391 0.05069
104 75.90 78.63 0.06985 0.06986 0.54391 0.05021
105 76.00 78.67 0.06814 0.06815 0.54820 0.05012
106 76.10 78.70 0.06644 0.06645 0.55259 0.05005
107 76.20 78.73 0.06474 0.06475 0.55710 0.04998
108 76.20 78.73 0.06474 0.06475 0.55710 0.04952
109 76.30 78.77 0.06303 0.06304 0.56173 0.04947
110 76.30 78.77 0.06303 0.06304 0.56173 0.04902
111 76.40 78.80 0.06133 0.06134 0.56648 0.04899
112 76.50 78.83 0.05963 0.05963 0.57137 0.04897
113 76.50 78.83 0.05963 0.05963 0.57137 0.04854
114 76.60 78.87 0.05792 0.05793 0.57641 0.04854
115 76.60 78.87 0.05792 0.05793 0.57641 0.04812
116 76.70 78.90 0.05622 0.05623 0.58159 0.04813
117 76.70 78.90 0.05622 0.05623 0.58159 0.04772
118 76.70 78.90 0.05622 0.05623 0.58159 0.04732
119 76.80 78.93 0.05451 0.05452 0.58693 0.04735
120 76.80 78.93 0.05451 0.05452 0.58693 0.04695
121 76.90 78.97 0.05281 0.05282 0.59244 0.04700
122 76.90 78.97 0.05281 0.05282 0.59244 0.04662
123 76.90 78.97 0.05281 0.05282 0.59244 0.04624
124 77.00 79.00 0.05111 0.05112 0.59813 0.04631
125 77.00 79.00 0.05111 0.05112 0.59813 0.04594
126 72.80 77.60 0.12266 0.12267 0.44616 0.03399
127 40.50 66.83 0.67291 0.67292 0.14762 0.01116
128 25.60 61.87 0.92675 0.92674 0.07781 0.00584
* Todos los datos de difusividad deben de multiplicarse por 10-6
* Resultados para la difusividad del arroz procesados con el software de URE~A.
Fuente: Propia
Ti = temperatura media de toda la muestra
T =temperatura en el centro geomtrico (punto mas frio) de la muestra
A = T1 - T
T1 - To
To= temperatura inicial de la muestra
T1= temperatura media de calentamiento
X = NFourier =
= difusividad trmica (m2 /s)
= tiempo (s)
r= radio interno (m)
Figura 2: Variacin de la difusividad trmica durante el calentamiento de la muestra
Fuente: Propia
b) De la Figura 2, se pudo calcular grficamente que la difusividad trmica a 70 C de la muestra de arroz fue de 0.05660E-06
c) Comparacin del dato experimental de difusividad con el hallado mediante el programa COSTHERM y fuente bibliogrfica.
Cuadro 4: Cuadro comparativo de Difusividad trmica a 70C
Difusividad (m2/s)
Experimental
0.04897E-06 0.04854E-06
Costherm 1
Literatura
1Calculado a partir de la siguiente composicin: humedad 13.1 %, protena 8.2%, lpidos 0.5%, carbohidratos 77.8% y minerales 0.4%.
Fuente: Propia
El valor de la difusividad es el que se encuentra sombreado en el Cuadro 3 ya que coinciden A y B, pudiendo ser cualquiera de los dos.
Este valor de difusividad encontrado es para todo el rango de temperatura en la cual se ha trabajado.
La difusividad experimental fue: 0.04897E-06 0.04854E-06
Debido a que la A y B coinciden a 78.83C la temperatura media para hallar la difusividad con el COSTHERM fue la misma.
En la Figura 3 se aprecia el valor de la difusividad con el programa COSTHERM, este fue de:
Figura 3: COSTHERM
Fuente: COSTHERM, 2010
Arroz2345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697989910010110210310410510610710810911011111211311411511611711811912012112212312412512612712821.421.521.521.821.621.621.621.621.721.922.122.623.223.924.825.82728.329.63132.433.935.436.938.29999999999999739.79999999999999741.242.643.945.346.647.84950.251.452.453.554.555.556.457.358.158.959.760.461.161.862.563.163.764.264.865.365.866.266.767.09999999999999467.567.90000000000000668.368.76969.369.77070.370.59999999999999470.871.09999999999999471.371.59999999999999471.87272.272.572.772.87373.273.40000000000000673.573.773.9000000000000067474.09999999999999474.374.40000000000000674.574.59999999999999474.874.9000000000000067575.09999999999999475.275.375.40000000000000675.575.575.59999999999999475.775.875.90000000000000675.9000000000000067676.09999999999999476.276.276.376.376.40000000000000676.576.576.59999999999999476.59999999999999476.776.776.776.876.876.90000000000000676.90000000000000676.900000000000006777772.840.525.6Columna223456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128Columna123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128
Tiempo (min)
Temperatura (C)
Serie 121.421.521.521.821.621.621.621.621.721.922.122.623.223.924.825.82728.329.63132.433.935.436.938.29999999999999739.79999999999999741.242.643.945.346.647.84950.251.452.453.554.555.556.457.358.158.959.760.461.161.862.563.163.764.264.865.365.866.266.767.09999999999999467.567.90000000000000668.368.76969.369.77070.370.59999999999999470.871.09999999999999471.371.59999999999999471.87272.272.572.772.87373.273.40000000000000673.573.773.9000000000000067474.09999999999999474.374.40000000000000674.574.59999999999999474.874.9000000000000067575.09999999999999475.275.375.40000000000000675.575.575.59999999999999475.775.875.90000000000000675.9000000000000067676.09999999999999476.276.276.376.376.40000000000000676.576.576.59999999999999476.59999999999999476.776.776.776.876.876.90000000000000676.90000000000000676.900000000000006777772.840.525.64.0753E-71.4124000000000001E-71.0593E-79.3270000000000001E-87.3150000000000003E-86.2699999999999999E-85.4860000000000003E-84.8760000000000001E-84.531E-84.353E-84.1810000000000002E-84.2349999999999999E-84.2790000000000001E-84.3170000000000002E-84.3910000000000001E-84.4570000000000001E-84.5470000000000003E-84.6329999999999999E-84.6970000000000003E-84.7689999999999999E-84.828E-84.9000000000000002E-84.9649999999999998E-85.0269999999999999E-85.0699999999999997E-85.1310000000000001E-85.1760000000000002E-85.2229999999999999E-85.257E-85.3099999999999999E-85.3510000000000001E-85.3799999999999999E-85.4130000000000002E-85.4510000000000003E-85.4930000000000003E-85.5080000000000001E-85.5439999999999999E-85.568E-85.5969999999999998E-85.6139999999999998E-85.6360000000000003E-85.6440000000000001E-85.6580000000000001E-85.676E-85.6799999999999999E-85.6890000000000002E-85.7009999999999999E-85.7189999999999998E-85.7210000000000001E-85.7270000000000003E-85.7170000000000002E-85.7310000000000002E-85.7280000000000001E-85.7289999999999999E-85.7119999999999998E-85.7200000000000003E-85.7089999999999997E-85.7009999999999999E-85.6960000000000002E-85.6949999999999997E-85.697E-85.6769999999999998E-85.6610000000000002E-85.6710000000000003E-85.6599999999999997E-85.6510000000000001E-85.6449999999999999E-85.6150000000000003E-85.6139999999999998E-85.5880000000000001E-85.592E-85.5700000000000002E-85.5509999999999999E-85.533E-85.5460000000000002E-85.533E-85.491E-85.4809999999999999E-85.4730000000000001E-85.4669999999999999E-85.4310000000000001E-85.4289999999999998E-85.428E-85.3960000000000001E-85.3659999999999999E-85.3710000000000003E-85.3430000000000003E-85.3169999999999999E-85.292E-85.3029999999999999E-85.2800000000000003E-85.2590000000000003E-85.2390000000000001E-85.2199999999999998E-85.2019999999999999E-85.1849999999999998E-85.17E-85.1179999999999999E-85.1039999999999999E-85.0909999999999997E-85.0799999999999998E-85.0689999999999999E-85.0209999999999998E-85.0120000000000001E-85.0050000000000001E-84.9980000000000002E-84.9520000000000003E-84.9469999999999999E-84.9019999999999998E-84.8989999999999997E-84.8970000000000001E-84.8540000000000003E-84.8540000000000003E-84.8119999999999997E-84.8130000000000002E-84.772E-84.7320000000000003E-84.7349999999999997E-84.695E-84.6999999999999997E-84.6620000000000003E-84.6240000000000002E-84.6310000000000002E-84.594E-83.3990000000000002E-81.116E-85.8399999999999997E-9Serie 221.421.521.521.821.621.621.621.621.721.922.122.623.223.924.825.82728.329.63132.433.935.436.938.29999999999999739.79999999999999741.242.643.945.346.647.84950.251.452.453.554.555.556.457.358.158.959.760.461.161.862.563.163.764.264.865.365.866.266.767.09999999999999467.567.90000000000000668.368.76969.369.77070.370.59999999999999470.871.09999999999999471.371.59999999999999471.87272.272.572.772.87373.273.40000000000000673.573.773.9000000000000067474.09999999999999474.374.40000000000000674.574.59999999999999474.874.9000000000000067575.09999999999999475.275.375.40000000000000675.575.575.59999999999999475.775.875.90000000000000675.9000000000000067676.09999999999999476.276.276.376.376.40000000000000676.576.576.59999999999999476.59999999999999476.776.776.776.876.876.90000000000000676.90000000000000676.900000000000006777772.840.525.6Serie 321.421.521.521.821.621.621.621.621.721.922.122.623.223.924.825.82728.329.63132.433.935.436.938.29999999999999739.79999999999999741.242.643.945.346.647.84950.251.452.453.554.555.556.457.358.158.959.760.461.161.862.563.163.764.264.865.365.866.266.767.09999999999999467.567.90000000000000668.368.76969.369.77070.370.59999999999999470.871.09999999999999471.371.59999999999999471.87272.272.572.772.87373.273.40000000000000673.573.773.9000000000000067474.09999999999999474.374.40000000000000674.574.59999999999999474.874.9000000000000067575.09999999999999475.275.375.40000000000000675.575.575.59999999999999475.775.875.90000000000000675.9000000000000067676.09999999999999476.276.276.376.376.40000000000000676.576.576.59999999999999476.59999999999999476.776.776.776.876.876.90000000000000676.90000000000000676.900000000000006777772.840.525.6
TEMPERATURA (C)
Difusividad trmica ()