1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
|
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 10 : Unsteady State And Multidimensional Heat Conduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 10.8 Page No : 444"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The bottom surface temperature of given slab is 10.3 C\n",
"The top surface temperature of given slab is 19.4 C\n",
"The mid plane temperature of given slab is 12.6 C\n"
]
}
],
"source": [
"# Variables\n",
"l = 0.05 \t\t\t#m,thickness of margarine slab\n",
"ro = 990. \t\t\t#Kg/m**3, density of margarine slab \n",
"cp = 0.55 \t\t\t#Kcal/kg C, ddpecific heat of slab\n",
"k = 0.143 \t\t\t#kcal/h mC, thermal conductivity of slab\n",
"Ti = 4. \t\t\t#C, initial temp\n",
"To = 25. \t\t\t#C, ambient temp.\n",
"t = 4. \t\t\t#hours, time\n",
"h = 8. \t\t\t#kcal/h m**2 C\n",
"\n",
"#calculation\n",
"Fo = k*t/(ro*cp*l**2) \t\t\t#, fourier no.\n",
"Bi = h*l/k \t\t\t#Biot no.\n",
"#from fig. 10.6 a\n",
"Tcbar = 0.7 \t\t\t#Tcbar = (Tc-To)/(Ti-To)\n",
"Tc = To+Tcbar*(Ti-To) \t\t\t#C, centre temp.\n",
"#from fig 10.6 b\n",
"#(T-To)/(Tc-To) = 0.382\n",
"T = 0.382*(Tc-To)+To \t\t\t#c,top surface temp.\n",
"#again from fig. 10.6 b\n",
"Tm = 0.842*(Tc-To)+To \t\t\t#, mid plane temp.\n",
"\n",
"# Results\n",
"print \"The bottom surface temperature of given slab is %.1f C\"%(Tc);\n",
"print \"The top surface temperature of given slab is %.1f C\"%(T);\n",
"print \"The mid plane temperature of given slab is %.1f C\"%(Tm);\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 10.9 Page No : 449"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"i) time required for the cantre-line temp.to drop down to 200 C is 229 s\n",
"ii)the temp. at half radius at that moment is 161 C \n",
"iii)the amount of heat that has been transfered to the liquid is 19647 Kj\n"
]
}
],
"source": [
"import math \n",
"# Variables\n",
"Ti = 870. \t\t\t#C, initial temp.\n",
"To = 30. \t\t\t#C, ambient temp.\n",
"Tc = 200. \t\t\t#C, centre line temp.\n",
"h = 2000. \t\t\t#W/m**2 C, surface heat transfer coefficient\n",
"a = 0.05 \t\t\t#m, radius of cylinder \n",
"k = 20. \t\t\t#W/m C, thermal conductivity\n",
"ro = 7800. \t\t\t#kg/m**3, density\n",
"cp = 0.46*10**3 \t\t\t#j/kg C, specific heat\n",
"\n",
"#calculation\n",
"#i\n",
"Bi = h*a/k \t\t\t#Biot no.\n",
"alpha = k/(ro*cp) \t\t\t#m**2/C, thermal diffusivity\n",
"Tcbar = (Tc-To)/(Ti-To) \t\t\t# dimensionless centre line temp.\n",
"#from fig 10.7 a\n",
"fo = 0.51 \t\t\t#fourier no. fo = alpha*t/a**2\n",
"t = fo*a**2/alpha \t\t\t#s, time\n",
"\n",
"#ii\n",
"#at the half radius, r/a = 0.5 & Bi = 5\n",
"T = To+0.77*(Tc-To) \t\t\t#from fig. 10.7 b\n",
"\n",
"#iii\n",
"x = Bi**2*fo\n",
"#for x = 12.75 & Bi = 5.0. fig.10.9 b gives\n",
"#q/qi = 0.83\n",
"qi = math.pi*a**2*(1)*ro*cp*(Ti-To) \t\t\t#kj, initial amount of heat energy \n",
" #present in 1 m length of shaft\n",
"q = 0.83*qi \t\t\t#j, amount of heat transfered \n",
"\n",
"# Results\n",
"print \"i) time required for the cantre-line temp.to drop down to 200 C is %.0f s\"%(t);\n",
"print \"ii)the temp. at half radius at that moment is %.0f C \"%(T);\n",
"print \"iii)the amount of heat that has been transfered to the liquid is %d Kj\"%(q*10**-3)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
