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
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
|
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Introduction to Convection"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2 Page 356 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Napthalene Sublimation rate per unit length\n",
"import math\n",
"#Operating Conditions\n",
"\n",
"h = .05; \t\t\t#[W/m^2.K] Heat Convection coefficient\n",
"D = .02; \t\t\t#[m] Diameter of cylinder\n",
"Cas = 5*math.pow(10,-6); #[kmol/m^3] Surface molar Conc\n",
"Casurr = 0; \t\t\t#[kmol/m^3] Surrounding molar Conc\n",
"Ma = 128; \t\t\t#[Kg/kmol] Molecular weight\n",
"#calculations\n",
"#From Eqn 6.15\n",
"Na = h*(math.pi*D)*(Cas-Casurr);\n",
"na = Ma*Na;\n",
"#results\n",
"print '%s %.2e %s' %(\"\\n\\n Mass sublimation Rate is =\",na,\" kg/s.m \");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Mass sublimation Rate is = 2.01e-06 kg/s.m \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3 Page 357"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Convection Mass Transfer coefficient \n",
"import math\n",
"#Operating Conditions\n",
"\n",
"Dab = .288*math.pow(10,-4); \t#[m^2/s] Table A.8 water vapor-air (319K)\n",
"pas = .1; \t\t\t\t#[atm] Partial pressure at surface\n",
"pasurr = .02; \t\t\t#[atm] Partial pressure at infinity\n",
"y0 = .003; \t\t\t\t#[m] Tangent at y = 0 intercepts y axis at 3 mm\n",
"#calculations\n",
"#From Measured Vapor Pressure Distribution\n",
"delp = (0 - pas)/(y0 - 0); #[atm/m]\n",
"hmx = -Dab*delp/(pas - pasurr); #[m/s] \n",
"#results\n",
"print '%s %.4f %s' %(\"\\n\\n Convection Mass Transfer coefficient at prescribed location =\",hmx,\" m/s\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Convection Mass Transfer coefficient at prescribed location = 0.0120 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4 Page 362 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Convection Mass Transfer coefficient \n",
"import math\n",
"#Operating Conditions\n",
"v = 1; \t\t\t\t#[m/s] Velocity of water\n",
"L = 0.6; \t\t\t\t#[m] Plate length\n",
"Tw1 = 300.; \t\t\t\t#[K]\n",
"Tw2 = 350.; \t\t\t\t#[K]\n",
"#Coefficients [W/m^1.5 . K]\n",
"Clam1 = 395;\n",
"Cturb1 = 2330;\n",
"Clam2 = 477;\n",
"Cturb2 = 3600;\n",
"\n",
"#Water Properties at T = 300K\n",
"p1 = 997; \t\t\t\t#[kg/m^3] Density\n",
"u1 = 855*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"#Water Properties at T = 350K\n",
"p2 = 974; \t\t\t\t#[kg/m^3] Density\n",
"u2 = 365*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"\n",
"\n",
"Rec = 5*math.pow(10,5); #Transititon Reynolds Number\n",
"xc1 = Rec*u1/(p1*v); \t\t#[m]Transition length at 300K\n",
"xc2 = Rec*u2/(p2*v); \t\t#[m]Transition length at 350K\n",
"#calculations\n",
"#Integrating eqn 6.14\n",
"#At 300 K\n",
"h1 = (Clam1*math.pow(xc1,.5) /.5 + Cturb1*(math.pow(L,.8)-math.pow(xc1,.8))/.8)/L;\n",
"\n",
"#At 350 K\n",
"h2 = (Clam2*math.pow(xc2,.5) /.5 + Cturb2*(math.pow(L,.8)-math.pow(xc2,.8))/.8)/L;\n",
"#results\n",
"print '%s %.2f %s %.2f %s' %(\"\\n\\n Average Convection Coefficient over the entire plate for the two temperatures at 300K =\",h1,\" W/m^2.K and at 350K =\",h2,\" W/m^2.K\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Average Convection Coefficient over the entire plate for the two temperatures at 300K = 1622.45 W/m^2.K and at 350K = 3707.93 W/m^2.K\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5 Page 372"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Heat Flux to blade when surface temp is reduced\n",
"# Heat flux to a larger turbine blade\n",
"\n",
"#Operating Conditions\n",
"v = 160; \t\t\t\t#[m/s] Velocity of air\n",
"L = 0.04; \t\t\t\t\t#[m] Blade length\n",
"Tsurr = 1150+273.; \t\t\t#[K]\n",
"Ts = 800+273.; \t\t\t\t#[K] Surface Temp\n",
"q = 95000; \t\t\t\t#[W/m^2] Original heat flux\n",
"#calculations\n",
"#Case 1\n",
"Ts1 = 700+273.; \t \t\t\t#[K] Surface Temp\n",
"q1 = q*(Tsurr-Ts1)/(Tsurr-Ts);\n",
"\n",
"#Case 2\n",
"L2 = .08; \t\t\t#[m] Length\n",
"q2 = q*L/L2; \t\t\t#[W/m^2] Heat flux\n",
"#results\n",
"\n",
"print '%s %d %s' %(\"\\n\\n (a) Heat Flux to blade when surface temp is reduced =\",q1/1000. ,\" KW/m^2\") \n",
"print '%s %.2f %s' %(\"\\n (b) Heat flux to a larger turbine blade = \",q2/1000. ,\"KW/m^2\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" (a) Heat Flux to blade when surface temp is reduced = 122 KW/m^2\n",
"\n",
" (b) Heat flux to a larger turbine blade = 47.50 KW/m^2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6 Page 379"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Water vapor conc and flux associated with the same location on larger surface of the same shape\n",
"import math\n",
"#Operating Conditions\n",
"v = 100; \t\t\t#[m/s] Velocity of air\n",
"Tsurr = 20+273.; \t\t#[K] Surrounding Air Temperature\n",
"L1 = 1; \t\t\t\t#[m] solid length\n",
"Ts = 80+273.; \t\t\t#[K] Surface Temp\n",
"qx = 10000; \t\t\t#[W/m^2] heat flux at a point x\n",
"Txy = 60+273.; \t\t#[K] Temp in boundary layer above the point\n",
"\n",
"#Table A.4 Air Properties at T = 323K\n",
"v = 18.2*math.pow(10,-6); #[m^2/s] Viscosity\n",
"k = 28*math.pow(10,-3); \t#[W/m.K] Conductivity\n",
"Pr = 0.7; \t\t\t#Prandttl Number\n",
"#Table A.6 Saturated Water Vapor at T = 323K\n",
"pasat = 0.082; \t\t\t#[kg/m^3]\n",
"Ma = 18; \t\t\t#[kg/kmol] Molecular mass of water vapor\n",
"#Table A.8 Water Vapor-air at T = 323K\n",
"Dab = .26*math.pow(10,-4);\t#[m^2/s]\n",
"#calculations\n",
"#Case 1\n",
"Casurr = 0;\n",
"Cas = pasat/Ma; \t\t#[kmol/m^3] Molar conc of saturated water vapor at surface\n",
"Caxy = Cas + (Casurr - Cas)*(Txy - Ts)/(Tsurr - Ts);\n",
"\n",
"#Case 2\n",
"L2 = 2.;\n",
"hm = L1/L2 * Dab/k * qx/(Ts-Tsurr);\n",
"Na = hm*(Cas - Casurr);\n",
"#results\n",
"\n",
"print '%s %.4f %s' %(\"\\n (a) Water vapor Concentration above the point =\",Caxy,\"Kmol/m^3 \\n\") \n",
"print '%s %.2e %s' %(\"(b) Molar flux to a larger surface = \",Na,\"Kmol/s.m^2\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (a) Water vapor Concentration above the point = 0.0030 Kmol/m^3 \n",
"\n",
"(b) Molar flux to a larger surface = 3.53e-04 Kmol/s.m^2\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7 Page 383 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable initialization\n",
"# Steady State Temperature of Beverage\n",
"import math\n",
"#Operating Conditions\n",
"Tsurr = 40+273.; \t\t#[K] Surrounding Air Temperature\n",
"#Volatile Wetting Agent A\n",
"hfg = 100; \t\t\t#[kJ/kg]\n",
"Ma = 200; \t\t\t#[kg/kmol] Molecular mass\n",
"pasat = 5000; \t\t\t#[N/m^2] Saturate pressure\n",
"Dab = .2*math.pow(10,-4); #[m^2/s] Diffusion coefficient\n",
"\n",
"#Table A.4 Air Properties at T = 300K\n",
"p = 1.16; \t#[kg/m^3] Density\n",
"cp = 1.007; \t#[kJ/kg.K] Specific Heat\n",
"alpha = 22.5*math.pow(10,-6)#[m^2/s] \n",
"R = 8.314; \t#[kJ/kmol] Universal Gas Constt\n",
"#calculations\n",
"#Applying Eqn 6.65 and setting pasurr = 0\n",
"# Ts^2 - Tsurr*Ts + B = 0 , where the coefficient B is\n",
"B = Ma*hfg*pasat*math.pow(10,-3) /(R*p*cp*math.pow((alpha/Dab),(2./3.)));\n",
"Ts = (Tsurr + math.sqrt(Tsurr*Tsurr - 4*B))/2. ;\n",
"#results\n",
"print '%s %.1f %s' %(\"\\n Steady State Surface Temperature of Beverage =\",Ts-273.,\"degC\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Steady State Surface Temperature of Beverage = 5.9 degC\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
|
