Решения уравнения нестационарной теплопроводности
1. Для пластины толщиной 2
Таблица
2. Корни уравнения
для неограниченной
пластины
|
Bi |
μ1 |
μ2 |
μ3 |
μ4 |
μ5 |
μ6 |
|
0,00 |
0,0000 |
3,1416 |
6,2832 |
9,4248 |
12,5664 |
15,7080 |
|
0,001 |
0,0316 |
3,1419 |
6,2833 |
9,4249 |
12,5665 |
15,7080 |
|
0,002 |
0,0447 |
3,1422 |
6,2835 |
9,4250 |
12,5665 |
15,7081 |
|
0,004 |
0,0632 |
3,1429 |
6,2838 |
9,4252 |
12,5667 |
15,7082 |
|
0,006 |
0,0774 |
3,1435 |
6,2841 |
9,4254 |
12,5668 |
15,7083 |
|
0,008 |
0,0893 |
3,1441 |
6,2845 |
9,4256 |
12,5670 |
15,7085 |
|
0,01 |
0,0998 |
3,1448 |
6,2848 |
9,4258 |
12,5672 |
15,7086 |
|
0,02 |
0,1410 |
3,1479 |
6,2864 |
9,4269 |
12,5680 |
15,7092 |
|
0,04 |
0,1987 |
3,1543 |
6,2895 |
9,4290 |
12,5696 |
15,7105 |
|
0,06 |
0,2425 |
3,1606 |
6,2927 |
9,4311 |
12,5711 |
15,7118 |
|
0,08 |
0,2791 |
3,1668 |
6,2959 |
9,4333 |
12,5727 |
15,7131 |
|
0,1 |
0,3111 |
3,1731 |
6,2991 |
9,4354 |
12,5743 |
15,7143 |
|
0,2 |
0,4328 |
3,2039 |
6,3148 |
9,4459 |
12,5823 |
15,7207 |
|
0,3 |
0,5218 |
3,2341 |
6,3305 |
9,4565 |
12,5902 |
15,7270 |
|
0,4 |
0,5932 |
3,2636 |
6,3461 |
9,4670 |
12,5981 |
15,7334 |
|
0,5 |
0,6533 |
3,2923 |
6,3616 |
9,4775 |
12,6060 |
15,7397 |
|
0,6 |
0,7051 |
3,3204 |
6,3770 |
9,4879 |
12,6139 |
15,7460 |
|
0,7 |
0,7506 |
3,3477 |
6,3923 |
9,4983 |
12,6218 |
15,7524 |
|
0,8 |
0,7910 |
3,3744 |
6,4074 |
9,5087 |
12,6296 |
15,7587 |
|
0,9 |
0,8274 |
3,4003 |
6,4224 |
9,5190 |
12,6375 |
15,7650 |
|
1,0 |
0,8603 |
3,4256 |
6,4373 |
9,5293 |
12,6453 |
15,7713 |
|
1,5 |
0,9882 |
3,5422 |
6,5097 |
9,5801 |
12,6841 |
15,8026 |
|
2,0 |
1,0769 |
3,6436 |
6,5783 |
9,6296 |
12,7223 |
15,8336 |
|
3,0 |
1,1925 |
3,8088 |
6,7040 |
9,7240 |
12,7966 |
15,8945 |
|
4,0 |
1,2646 |
3,9352 |
6,8140 |
9,8119 |
12,8678 |
15,9536 |
|
5,0 |
1,3138 |
4,0336 |
6,9096 |
9,8928 |
12,9352 |
16,0107 |
|
6,0 |
1,3496 |
4,1116 |
6,9924 |
9,9667 |
12,9988 |
16,0654 |
|
7,0 |
1,3766 |
4,1746 |
7,0640 |
10,0339 |
13,0584 |
16,1177 |
|
8,0 |
1,3978 |
4,2264 |
7,1263 |
10,0949 |
13,1141 |
16,1675 |
|
9,0 |
1,4149 |
4,2694 |
7,1806 |
10,1502 |
13,1660 |
16,2147 |
|
10 |
1,4289 |
4,3058 |
7,2281 |
10,2003 |
13,2142 |
16,2594 |
|
15 |
1,4729 |
4,4255 |
7,3959 |
10,3898 |
13,4078 |
16,4474 |
|
20 |
1,4961 |
4,4915 |
7,4954 |
10,5117 |
13,5420 |
16,5864 |
|
30 |
1,5202 |
4,5615 |
7,6057 |
10,6543 |
13,7085 |
16,7691 |
|
40 |
1,5325 |
4,5979 |
7,6647 |
10,7334 |
13,8048 |
16,8794 |
|
50 |
1,5400 |
4,6202 |
7,7012 |
10,7832 |
13,8666 |
16,9519 |
|
60 |
1,5451 |
4,6353 |
7,7259 |
10,8172 |
13,9094 |
17,0026 |
|
80 |
1,5514 |
4,6543 |
7,7573 |
10,8606 |
13,9644 |
17,0686 |
|
100 |
1,5552 |
4,6658 |
7,7764 |
10,8871 |
13,9981 |
17,1093 |
|
∞ |
1,5708 |
4,7124 |
7,8540 |
10,9956 |
14,1372 |
17,2788 |
Рисунок 2. Безразмерная температура в середине неограниченной пластины
Рисунок 3. Безразмерная температура на поверхности неограниченной пластины