A P P E N D I X
A
Tables
Table A-1 The error function. x erf √ 2 ατ
x √ 2 ατ
x erf √ 2 ατ
x √ 2 ατ
x erf 2 ατ
0.00 0.02 0.04 0.06 0.08
0.00000 0.02256 0.04511 0.06762 0.09008
0.76 0.78 0.80 0.82 0.84
0.71754 0.73001 0.74210 0.75381 0.76514
1.52 1.54 1.56 1.58 1.60
0.96841 0.97059 0.97263 0.97455 0.97636
0.10 0.12 0.14 0.16 0.18
0.11246 0.13476 0.15695 0.17901 0.20094
0.86 0.88 0.90 0.92 0.94
0.77610 0.78669 0.79691 0.80677 0.81627
1.62 1.64 1.66 1.68 1.70
0.97804 0.97962 0.98110 0.98249 0.98379
0.20 0.22 0.24 0.26 0.28
0.22270 0.24430 0.26570 0.28690 0.30788
0.96 0.98 1.00 1.02 1.04
0.82542 0.83423 0.84270 0.85084 0.85865
1.72 1.74 1.76 1.78 1.80
0.98500 0.98613 0.98719 0.98817 0.98909
0.30 0.32 0.34 0.36 0.38
0.32863 0.34913 0.36936 0.38933 0.40901
1.06 1.08 1.10 1.12 1.14
0.86614 0.87333 0.88020 0.88079 0.89308
1.82 1.84 1.86 1.88 1.90
0.98994 0.99074 0.99147 0.99216 0.99279
0.40 0.42 0.44 0.46 0.48
0.42839 0.44749 0.46622 0.48466 0.50275
1.16 1.18 1.20 1.22 1.24
0.89910 0.90484 0.91031 0.91553 0.92050
1.92 1.94 1.96 1.98 2.00
0.99338 0.99392 0.99443 0.99489 0.995322
0.50 0.52 0.54 0.56 0.58
0.52050 0.53790 0.55494 0.57162 0.58792
1.26 1.28 1.30 1.32 1.34
0.92524 0.92973 0.93401 0.93806 0.94191
2.10 2.20 2.30 2.40 2.50
0.997020 0.998137 0.998857 0.999311 0.999593
0.60 0.62 0.64 0.66 0.68
0.60386 0.61941 0.63459 0.64938 0.66278
1.36 1.38 1.40 1.42 1.44
0.94556 0.94902 0.95228 0.95538 0.95830
2.60 2.70 2.80 2.90 3.00
0.999764 0.999866 0.999925 0.999959 0.999978
0.70 0.72 0.74
0.67780 0.69143 0.70468
1.46 1.48 1.50
0.96105 0.96365 0.96610
3.20 3.40 3.60
0.999994 0.999998 1.000000
x √ 2 ατ
649
6 5 0
Table A-2 Property values for metals.† ◦
◦
Thermal conductivity k , W/m · C
Properties at 20 C ρ
Metal luminum: Pure Al-Cu (Duralumin), 94 – 96% Al, 3 – 5% Cu, trace Mg Al-Si (Silumin, copper-bearing), 86.5% Al, 1% Cu Al-Si (Alusil), 78 – 80% Al, 20 – 22% Si Al-Mg-Si, 97% Al, 1% Mg, 1% Si, 1% Mn Lead Iron: Pure Wrought iron, 0.5% C Steel (C max ≈ 1.5%): Carbon steel C ≈ 0.5% 1.0% 1.5%
kg/m3
c p
α × 105
k
kJ/kg · C
W/m · C
m2 /s
2,707
0.896
204
2,787
0.883
2,659
◦
◦
◦
100 C
−
◦
◦
0 C ◦
◦
100 C ◦
◦
200 C ◦
◦
300 C ◦
◦
400 C ◦
◦
600 C ◦
◦
◦
◦
◦
◦
800 C 1000 C 1200 C ◦
148 F
32 F
212 F
392 F
572 F
752 F
8.418
215
202
206
215
228
249
164
6.676
126
159
182
194
0.867
137
5.933
119
137
144
152
161
2,627
0.854
161
7.172
144
157
168
175
178
2,707 11,373
0.892 0.130
177 35
7.311 2.343
175 35.1
189 33.4
204 31.5
7,897 7,849
0.452 0.46
73 59
2.034 1.626
73 59
67 57
62 52
55 48
48 45
40 36
36 33
35 33
36 33
7,833 7,801 7,753
0.465 0.473 0.486
54 43 36
1.474 1.172 0.970
55 43 36
52 43 36
48 42 36
45 40 35
42 36 33
35 33 31
31 29 28
29 28 28
31 29 29
−
36.9 87
1112 F
1472 F 1832 F 2192 F
29.8
Table A-2 Property values for metals† (Continued ). ◦
◦
Thermal conductivity k , W/m · C
Properties at 20 C
Metal Nickel steel Ni ≈ 0% 20% 40% 80% Invar 36% Ni Chrome steel Cr = 0% 1% 5% 20% Cr-Ni (chromeickel): 15% Cr, 10% Ni 18% Cr, 8% Ni (V2A) 20% Cr, 15% Ni 25% Cr, 20% Ni Tungsten steel W = 0% 1% 5% 10% Copper: Pure Aluminum bronze 95% Cu, 5% Al
6 5 1
α × 105
−
W/m · C
m2 /s
−
0.452 0.46 0.46 0.46 0.46
73 19 10 35 10.7
2.026 0.526 0.279 0.872 0.286
7,897 7,865 7,833 7,689
0.452 0.46 0.46 0.46
73 61 40 22
2.026 1.665 1.110 0.635
7,865
0.46
19
0.527
7,817 7,833 7,865
0.46 0.46 0.46
16.3 15.1 12.8
0.444 0.415 0.361
7,897 7,913 8,073 8,314
0.452 0.448 0.435 0.419
73 66 54 48
2.026 1.858 1.525 1.391
8,954
0.3831
386
11.234
8,666
0.410
83
2.330
ρ
c p
kg/m 3
kJ/kg · C
7,897 7,933 8,169 8,618 8,137
k ◦
◦
◦
0 C
148 F
◦
32 F
87
100 C
407
◦
◦
200 C
212 F
◦
73 62 40 22
16.3
◦
386
◦
300 C
◦
400 C
392 F
◦
572 F
◦
67 55 38 22
62 52 36 22
17
379
100 C
◦
600 C
◦
752 F
◦
1112 F
55 47 36 22
48 42 33 24
40 36 29 24
36 33 29 26
35 33 29 29
17
19
19
22
27
31
374
369
363
353
◦
◦
800 C ◦
◦
◦
◦
◦
1000 C 1200 C
1472 F 1832 F 2192 F
36
6 5 2
Table A-2 Property values for metals† (Continued ). ◦
◦
Thermal conductivity k , W/m · C
Properties at 20 C
ρ , Metal Bronze 75% Cu, 25% Sn Red brass 85% Cu, 9% Sn, 6% Zn Brass 70% Cu, 30% Zn German silver 62% Cu, 15% Ni, 22% Zn Constantan 60% Cu, 40% Ni Magnesium: Pure Mg-Al (electrolytic) 6 – 8% Al, 1 – 2% Zn Molybdenum Nickel: Pure (99.9%) Ni-Cr 90% Ni, 10% Cr 80% Ni, 20% Cr Silver: Purest Pure (99.9%) Tin, pure Tungsten Zinc, pure
kg/m 3
c p
α × 105
k ◦
◦
m2
◦
100 C
−
◦
kJ/kg · C
W/m · C
8,666
0.343
26
0.859
8,714
0.385
61
1.804
8,522
0.385
111
3.412
88
8,618
0.394
24.9
0.733
8,922
0.410
22.7
1,746
1.013
1,810 10,220
148 F
◦
0 C ◦
◦
100 C ◦
◦
400 C ◦
128
144
147
147
19.2
31
40
45
48
0.612
21
22.2
26
171
9.708
178
171
168
163
157
1.00 0.251
66 123
3.605 4.790
138
52 125
62 118
74 114
83 111
109
8,906
0.4459
90
2.266
104
93
83
73
64
59
8,666 8,314
0.444 0.444
17 12.6
0.444 0.343
17.1 12.3
18.9 13.8
20.9 15.6
22.8 17.1
24.6 18.0
10,524 10,525 7,304 19,350 7,144
0.2340 0.2340 0.2265 0.1344 0.3843
419 407 64 163 112.2
17.004 16.563 3.884 6.271 4.106
114
71
◦
752 F
419 419 74
59
◦
300 C 572 F
−
212 F
◦
392 F
/s
32 F
◦
200 C
417 410 65.9 166 112
415 415 59 151 109
†Adapted to SI units from E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer, 2nd ed. New York: McGraw-Hill, 1959.
412 374 57 142 106
362
360
133 100
126 93
◦
600 C ◦
1112 F
106
◦
◦
◦
◦
◦
1472 F 1832 F 2192 F
102
22.5
112
◦
800 C 1000 C 1200 C
76
99
92
654
APPENDIX A
Table A-3
Properties of nonmetals † (Continued ).
coustic tile luminum oxide, sapphire luminum oxide, polycrystalline sphalt Bakelite Brick: Building brick, common Face Carborundum brick Chrome brick
Diatomaceous earth, molded and fired Fireclay brick Burnt 2426 F ◦
◦
Burnt 2642 F
Missouri
Magnesite
Cement, portland Mortar Coal, anthracite Concrete, cinder Stone, 1-2-4 mix Glass, window Corosilicate Graphite, pyrolytic parallel to layers perpendicular to layers Gypsum board Lexan Nylon Particle board, low density high density Phenolic Plaster, gypsum Metal lath Wood lath
α × 107 m2 /s
Temperature C
k W/m · C
kg/m3
30
0.06
290
1.3
46
3970
0.76
150
36 0.74 – 0.76 0.23
3970
0.76
120
1200
1.6
1.2
0.69 1.32 18.5 11.1 2.32 2.47 1.99
1600 2000
0.84
5.2
3000
0.84
9.2 9.8 7.9
2000
0.96
5.4
2300
0.96
5.8
2600
0.96
4.0
◦
Substance
Tables
30 30 20 – 55 30
20 600 1400 200 550 900 200 870 500 800 1100 500 800 1100 200 600 1400 200 650 1200 23 30 23 20 20 30 – 75 30
◦
0.24 0.31 1.04 1.07 1.09 1.28 1.37 1.40 1.00 1.47 1.77 3.81 2.77 1.90 0.29 1.16 0.26 0.76 1.37 0.78 (avg) 1.09 1900
ρ
c kJ/kg · C ◦
1.6
1.13
1500
1300
1.25
1.6
1900 – 2300 2700 2200
0.88 0.84
8.2 – 6.8 3.4
2200
0.71
12 ,200 36
30 30 30 30
5.6 0.16 0.2 0.16
2200
0.71
1200 1100
1.3 1.6
1.3 0.9
30 30 30 20 20 20
0.079 0.17 0.03 0.48 0.47 0.28
590 1000 1400 1440
1.3 1.3 1.6 0.84
1.0 1.3 0.13 4.0
654
APPENDIX A
Table A-3
Tables
Properties of nonmetals † (Continued ). Temperature
Substance
◦
C
k
c kJ/kg · C
α × 107 m2 /s
1200 960 1150 1000 1700 1200 3150
1.5 2.1 1.9 1.3 1.1 2.0 0.68
1.1 1.64 0.73 1.1 0.48 0.62 2290
2640 2500 2500 – 2700 2160 – 2300
0.82 0.90 0.80 0.71
8 – 18 5.6 – 5.9 10 – 13.6 11.2 – 11.9
1.05 0.7
ρ ◦
W/m · C
3
kg/m
◦
Structural and heat-resistant materials
Plexiglass Polyethylene Polypropylene Polystrene Polyvinylchloride Rubber, hard Silicon carbide Stone: Granite Limestone Marble Sandstone Structural concrete low density light weight medium weight normal weight Teflon Titanium dioxide Wood (across the grain): Balsa, 8.8 lb/ft 3 Cypress Fir Maple or oak Yellow pine White pine
30 30 30 30 30 30 30
100 – 300 40
0.2 0.33 0.16 0.14 0.09 0.15 490 1.73 – 3.98 1.26 – 1.33 2.07 – 2.94 1.83
30 30 30 30 30 30
0.21 0.65 0.75 2.32 0.35 8.4
670 1570 1840 2260 2200 4150
30 30 23 30 23 30
0.055 0.097 0.11 0.166 0.147 0.112
140 460 420 540 640 430
2.72 2.4 2.8
1.5 29
0.96 1.28 0.82
Insulating materials
Asbestos: Loosely packed
Asbestos-cement boards Sheets Felt, 40 laminations/in
20 laminations/in
Corrugated, 4 plies/in
Asbestos cement Balsam wood, 2.2 lb/ft 3 Cardboard, corrugated Celotex Cork, regranulated Ground Corkboard, 10 lb/ft 3
45 0 100 20
0.149 0.154 0.161 0.74
51 38 150 260 38 150 260 38 93 150 — 32 — 32 32 32 30
0.166 0.057 0.069 0.083 0.078 0.095 0.112 0.087 0.100 0.119 2.08 0.04 0.064 0.048 0.045 0.043 0.043
−
470 – 570
0.816
3.3 – 4
1.88
2 – 5.3
35
45 – 120 150 160
656
APPENDIX A
Tables
Properties of saturated liquids. †
Table A-4
k
Temperature ◦
Substance
Diamond, Type IIa, insulator Diatomaceous earth (Sil-o-cel) Felt, hair Wool Fiber, insulating board Glass fiber, duct liner Glass fiber, loose blown Glass wool, 1.5 lb/ft 3 Ice Insulex, dry
C
30
ρ ◦
W/m · C
2300
◦
0.509
α × 107 m2 /s
12 ,900
0.061 0.036 0.052 0.048
320 130 – 200 330 240
30
0.038
32
0.84
14.1
30 23 0 32
16 24 910
0.84 0.7 1.93
32 22.6 12.6
900
1.2
1.1
Kapok Magnesia, 85%
30 38 93 150 204
Paper (avg.) Polyisocyanurate sheet Polystyrene, extruded Polyurethane foam
30 30 30 30 32 150 260 23 32 32 30 23
0.12 0.023 0.028 0.017 0.040 0.067 0.087 0.059 0.024 0.033 0.025 0.059
Sawdust Silica aerogel Styrofoam rethane, cerllular ood shavings
3500
c kJ/kg · C
0 30 30 20
0.043 0.038 2.22 0.064 0.144 0.035 0.067 0.071 0.074 0.080
Rock wool, 10 lb/ft 3 Loosely packed
kg/m
3
270
160 64
140
†Adapted to SI units from A. I. Brown and S. M. Marco, Introduction to Heat Transfer, 3rd ed. New York: McGraw-Hill, 1958.
Other properties from various sources.
656
APPENDIX A
Table A-4
Properties of saturated liquids. † ρ
T
◦ ,
C
Tables
3
kg/m
c p kJ/kg · C ◦
k
ν,
2 m / s
◦
W/m · C
2 s α , m /
Pr
β , K 1 −
Ammonia, NH3
50 40 30 20 10
703.69 691.68 679.34 666.69 653.55
4.463 4.467 4.476 4.509 4.564
0.435×10 6 0.406 0.387 0.381 0.378
0.547 0.547 0.549 0.547 0.543
1.742×10 7 1.775 1.801 1.819 1.825
2.60 2.28 2.15 2.09 2.07
0 10 20 30 40 50
640.10 626.16 611.75 596.37 580.99 564.33
4.635 4.714 4.798 4.890 4.999 5.116
0.373 0.368 0.359 0.349 0.340 0.330
0.540 0.531 0.521 0.507 0.493 0.476
1.819 1.801 1.775 1.742 1.701 1.654
2.05 2.04 2.02 2.01 2.00 1.99
− − − − −
−
−
2.45 × 10 3 −
Carbon dioxide, CO2
50 40 30 20 10
1 ,156.34 1 ,117.77 1 ,076.76 1 ,032.39 983.38
1.84 1.88 1.97 2.05 2.18
0 10 20 30
926.99 860.03 772.57 597.81
2.47 3.14 5.0 36.4
− − − − −
0.119×10 6 0.118 0.117 0.115 0.113
0.0855 0.1011 0.1116 0.1151 0.1099
0.4021×10 7 0.4810 0.5272 0.5445 0.5133
0.108 0.101 0.091 0.080
0.1045 0.0971 0.0872 0.0703
0.4578 0.3608 0.2219 0.0279
−
−
2.96 2.46 2.22 2.12 2.20 2.38 2.80 4.10 28.7
14.00 × 10 3 −
Sulfur dioxide, SO2
50 40 30 20 10
1 ,560.84 1 ,536.81 1 ,520.64 1 ,488.60 1 ,463.61
1.3595 1.3607 1.3616 1.3624 1.3628
0.484×10 6 0.424 0.371 0.324 0.288
0.242 0.235 0.230 0.225 0.218
1.141×10 7 1.130 1.117 1.107 1.097
4.24 3.74 3.31 2.93 2.62
0 10 20 30 40 50
1 ,438.46 1 ,412.51 1 ,386.40 1 ,359.33 1 ,329.22 1 ,299.10
1.3636 1.3645 1.3653 1.3662 1.3674 1.3683
0.257 0.232 0.210 0.190 0.173 0.162
0.211 0.204 0.199 0.192 0.185 0.177
1.081 1.066 1.050 1.035 1.019 0.999
2.38 2.18 2.00 1.83 1.70 1.61
− − − − −
−
−
1.94 × 10 3 −
Dichlorodifluoromethane (Freon-12), CCl2 F2
50 40 30 20 10
1 ,546.75 1 ,518.71 1 ,489.56 1 ,460.57 1 ,429.49
0.8750 0.8847 0.8956 0.9073 0.9203
0.310×10 6 0.279 0.253 0.235 0.221
0.067 0.069 0.069 0.071 0.073
0.501×10 7 0.514 0.526 0.539 0.550
6.2 5.4 4.8 4.4 4.0
0 10 20 30 40 50
1 ,397.45 1 ,364.30 1 ,330.18 1 ,295.10 1 ,257.13 1 ,215.96
0.9345 0.9496 0.9659 0.9835 1.0019 1.0216
0.214×10 6 0.203 0.198 0.194 0.191 0.190
0.073 0.073 0.073 0.071 0.069 0.067
0.557×10 7 0.560 0.560 0.560 0.555 0.545
3.8 3.6 3.5 3.5 3.5 3.5
− − − − −
−
−
−
−
2.63 × 10 3 −
658
APPENDIX A
Table A-5 ρ
T
◦ ,
C
3
kg/m
c p kJ/kg · C ◦
Tables
Properties of air at atmospheric pressure. † k
ν,
2 m / s
2 s α , m /
◦
W/m · C
Pr
β , K 1 −
Glycerin, C3 H5 ( OH )3
0 10 20 30 40 50
1 ,276.03 1 ,270.11 1 ,264.02 1 ,258.09 1 ,252.01 1 ,244.96
2.261 2.319 2.386 2.445 2.512 2.583
0.00831 0.00300 0.00118 0.00050 0.00022 0.00015
0.983×10 7 0.965 0.947 0.929 0.914 0.893 −
0.282 0.284 0.286 0.286 0.286 0.287
84.7×103 31.0 12.5 0.50 × 10 3 5.38 2.45 1.63 −
Ethylene glycol, C2 H4 ( OH )2
0 20 40 60 80 100
1 ,130.75 1 ,116.65 1 ,101.43 1 ,087.66 1 ,077.56 1 ,058.50
2.294 2.382 2.474 2.562 2.650 2.742
7.53×10 6 19.18 8.69 4.75 2.98 2.03 −
0.242 0.249 0.256 0.260 0.261 0.263
0.934×10 7 0.939 0.939 0.932 0.921 0.908 −
615 204 93 51 32.4 22.4
0.65 × 10 3 −
Engine oil (unused)
0 20 40 60 80
899.12 888.23 876.05 864.04 852.02
1.796 1.880 1.964 2.047 2.131
0.00428 0.00090 0.00024 0.839×10 4 0.375
0.147 0.145 0.144 0.140 0.138
0.911×10 7 0.872 0.834 0.800 0.769
100 120 140 160
840.01 828.96 816.94 805.89
2.219 2.307 2.395 2.483
0.203 0.124 0.080 0.056
0.137 0.135 0.133 0.132
0.738 0.710 0.686 0.663
−
−
47,100 10,400 2,870 1,050 490
0.70 × 10 3 −
276 175 116 84
Mercury, Hg
0 20 50 100 150
13 ,628.22 13 ,579.04 13 ,505.84 13 ,384.58 13 ,264.28
0.1403 0.1394 0.1386 0.1373 0.1365
0.124×10 6 0.114 0.104 0.0928 0.0853
8.20 8.69 9.40 10.51 11.49
42.99×10 7 46.06 50.22 57.16 63.54
0.0288 0.0249 0.0207 0.0162 0.0134
200 250 315.5
13 ,144.94 13 ,025.60 12 ,847
0.1570 0.1357 0.134
0.0802 0.0765 0.0673
12.34 13.07 14.02
69.08 74.06 81.5
0.0116 0.0103 0.0083
−
−
1.82 × 10 4
†Adapted to SI un its from E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer, 2nd ed. New York: McGraw-Hill, 1959.
−
658
APPENDIX A
Table A-5
Tables
Properties of air at atmospheric pressure. † The values of µ, k , c p , and Pr are not strongly pressure-dependent and may be used over a fairly wide range of pressures
kg/m
c p kJ/kg · C
µ × 105 kg/m· s
ν × 106 m2 /s
k W/m · C
α × 104 m2 /s
Pr
3.6010 2.3675 1.7684 1.4128 1.1774 0.9980 0.8826 0.7833 0.7048 0.6423 0.5879 0.5430 0.5030 0.4709 0.4405 0.4149 0.3925 0.3716 0.3524 0.3204 0.2947 0.2707 0.2515 0.2355 0.2211 0.2082 0.1970 0.1858 0.1762 0.1682 0.1602 0.1538 0.1458 0.1394
1.0266 1.0099 1.0061 1.0053 1.0057 1.0090 1.0140 1.0207 1.0295 1.0392 1.0551 1.0635 1.0752 1.0856 1.0978 1.1095 1.1212 1.1321 1.1417 1.160 1.179 1.197 1.214 1.230 1.248 1.267 1.287 1.309 1.338 1.372 1.419 1.482 1.574 1.688
0.6924 1.0283 1.3289 1.5990 1.8462 2.075 2.286 2.484 2.671 2.848 3.018 3.177 3.332 3.481 3.625 3.765 3.899 4.023 4.152 4.44 4.69 4.93 5.17 5.40 5.63 5.85 6.07 6.29 6.50 6.72 6.93 7.14 7.35 7.57
1.923 4.343 7.490 11.31 15.69 20.76 25.90 31.71 37.90 44.34 51.34 58.51 66.25 73.91 82.29 90.75 99.3 108.2 117.8 138.6 159.1 182.1 205.5 229.1 254.5 280.5 308.1 338.5 369.0 399.6 432.6 464.0 504.0 543.5
0.009246 0.013735 0.01809 0.02227 0.02624 0.03003 0.03365 0.03707 0.04038 0.04360 0.04659 0.04953 0.05230 0.05509 0.05779 0.06028 0.06279 0.06525 0.06752 0.0732 0.0782 0.0837 0.0891 0.0946 0.100 0.105 0.111 0.117 0.124 0.131 0.139 0.149 0.161 0.175
0.02501 0.05745 0.10165 0.15675 0.22160 0.2983 0.3760 0.4222 0.5564 0.6532 0.7512 0.8578 0.9672 1.0774 1.1951 1.3097 1.4271 1.5510 1.6779 1.969 2.251 2.583 2.920 3.262 3.609 3.977 4.379 4.811 5.260 5.715 6.120 6.540 7.020 7.441
0.770 0.753 0.739 0.722 0.708 0.697 0.689 0.683 0.680 0.680 0.680 0.682 0.684 0.686 0.689 0.692 0.696 0.699 0.702 0.704 0.707 0.705 0.705 0.705 0.705 0.705 0.704 0.704 0.702 0.700 0.707 0.710 0.718 0.730
ρ
T K ,
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
3
◦
† From Natl. Bur. Stand. (U.S.) Circ. 564, 1955.
◦
660
APPENDIX A
Table A-6
Tables
Properties of gases at atmospheric pressure † (Continued ).
Values of µ, k , c p , and Pr are not strongly pressure-dependent for He,H2 , O2 , and N2 and may be used over a fairly wide range of pressures ρ
T , K
kg/m3
c p kJ/kg · C ◦
k 2 s v , m /
µ, kg/m · s
◦
W/m · C
2 s α , m /
Pr
Helium
144 200 255 366 477 589 700 800
0.3379 0.2435 0.1906 0.13280 0.10204 0.08282 0.07032 0.06023
5.200 5.200 5.200 5.200 5.200 5.200 5.200 5.200
125.5×10 7 156.6 181.7 230.5 275.0 311.3 347.5 381.7
37.11×10 6 64.38 95.50 173.6 269.3 375.8 494.2 634.1
−
−
0.0928 0.1177 0.1357 0.1691 0.197 0.225 0.251 0.275
0.5275×10 4 0.9288 1.3675 2.449 3.716 5.215 6.661 8.774 −
0.70 0.694 0.70 0.71 0.72 0.72 0.72 0.72
Hydrogen
150 200 250 300 350 400 450 500 550 600 700 800 900
0.16371 0.12270 0.09819 0.08185 0.07016 0.06135 0.05462 0.04918 0.04469 0.04085 0.03492 0.03060 0.02723
12.602 13.540 14.059 14.314 14.436 14.491 14.499 14.507 14.532 14.537 14.574 14.675 14.821
5.595×10 6 6.813 7.919 8.963 9.954 10.864 11.779 12.636 13.475 14.285 15.89 17.40 18.78 −
34.18×10 6 55.53 80.64 109.5 141.9 177.1 215.6 257.0 301.6 349.7 455.1 569 690 −
0.0981 0.1282 0.1561 0.182 0.206 0.228 0.251 0.272 0.292 0.315 0.351 0.384 0.412
0.475×10 4 0.772 1.130 1.554 2.031 2.568 3.164 3.817 4.516 5.306 6.903 8.563 10.217 −
0.718 0.719 0.713 0.706 0.697 0.690 0.682 0.675 0.668 0.664 0.659 0.664 0.676
Oxygen
150 200 250 300 350 400 450 500 550
2.6190 1.9559 1.5618 1.3007 1.1133 0.9755 0.8682 0.7801 0.7096
0.9178 0.9131 0.9157 0.9203 0.9291 0.9420 0.9567 0.9722 0.9881
11.490×10 6 14.850 17.87 20.63 23.16 25.54 27.77 29.91 31.97 −
4.387×10 6 7.593 11.45 15.86 20.80 26.18 31.99 38.34 45.05 −
0.01367 0.01824 0.02259 0.02676 0.03070 0.03461 0.03828 0.04173 0.04517
0.05688×10 4 0.10214 0.15794 0.22353 0.2968 0.3768 0.4609 0.5502 0.641
0.773 0.745 0.725 0.709 0.702 0.695 0.694 0.697 0.700
0.01824 0.02620 0.03335 0.03984 0.04580 0.05123 0.05609 0.06070 0.06475 0.06850 0.07184
0.10224×10 4 0.22044 0.3734 0.5530 0.7486 0.9466 1.1685 1.3946 1.6250 1.8571 2.0932
0.747 0.713 0.691 0.684 0.686 0.691 0.700 0.711 0.724 0.736 0.748
−
Nitrogen
200 300 400 500 600 700 800 900 1000 1100 1200
1.7108 1.1421 0.8538 0.6824 0.5687 0.4934 0.4277 0.3796 0.3412 0.3108 0.2851
1.0429 1.0408 1.0459 1.0555 1.0756 1.0969 1.1225 1.1464 1.1677 1.1857 1.2037
12.947×10 6 17.84 21.98 25.70 29.11 32.13 34.84 37.49 40.00 42.28 44.50 −
7.568×10 6 15.63 25.74 37.66 51.19 65.13 81.46 91.06 117.2 136.0 156.1 −
−
660
APPENDIX A
Table A-6
Tables
Properties of gases at atmospheric pressure † (Continued ).
Values of µ, k , c p , and Pr are not strongly pressure-dependent for He,H2 , O2 , and N2 and may be used over a fairly wide range of pressures ρ
T , K
3
kg/m
c p kJ/kg · C ◦
µ, kg/m · s
v,
k W/m · C
2 m / s
◦
2 s α , m /
Pr
Carbon dioxide
220 250 300 350 400 450 500 550 600
2.4733 2.1657 1.7973 1.5362 1.3424 1.1918 1.0732 0.9739 0.8938
0.783 0.804 0.871 0.900 0.942 0.980 1.013 1.047 1.076
11.105×10 6 12.590 14.958 17.205 19.32 21.34 23.26 25.08 26.83 −
4.490×10 6 5.813 8.321 11.19 14.39 17.90 21.67 25.74 30.02 −
0.010805 0.012884 0.016572 0.02047 0.02461 0.02897 0.03352 0.03821 0.04311
0.05920×10 4 0.07401 0.10588 0.14808 0.19463 0.24813 0.3084 0.3750 0.4483
0.818 0.793 0.770 0.755 0.738 0.721 0.702 0.685 0.668
0.0220 0.0270 0.0327 0.0391 0.0467
0.1308×10 4 0.1920 0.2619 0.3432 0.4421
0.90 0.88 0.87 0.87 0.84
0.0246 0.0261 0.0299 0.0339 0.0379 0.0422 0.0464 0.0505 0.0549 0.0592 0.0637
0.2036×10 4 0.2338 0.307 0.387 0.475 0.573 0.666 0.772 0.883 1.001 1.130
1.060 1.040 1.010 0.996 0.991 0.986 0.995 1.000 1.005 1.010 1.019
−
Ammonia, NH3
273 323 373 423 473
0.7929 0.6487 0.5590 0.4934 0.4405
2.177 2.177 2.236 2.315 2.395
9.353×10 6 11.035 12.886 14.672 16.49 −
1.18×10 5 1.70 2.30 2.97 3.74 −
−
Water vapor
380 400 450 500 550 600 650 700 750 800 850
0.5863 0.5542 0.4902 0.4405 0.4005 0.3652 0.3380 0.3140 0.2931 0.2739 0.2579
2.060 2.014 1.980 1.985 1.997 2.026 2.056 2.085 2.119 2.152 2.186
12.71×10 6 13.44 15.25 17.04 18.84 20.67 22.47 24.26 26.04 27.86 29.69 −
2.16×10 5 2.42 3.11 3.86 4.70 5.66 6.64 7.72 8.88 10.20 11.52 −
−
†Adapted to SI un its from E. R. G. Eckert and R. M. Drake, Heat and Mass Transfer, 2nd ed. New York: McGraw-Hill, 1959.
662
APPENDIX A
Table A-9 Melting point C ◦
Metal
Properties of water (saturated liquid). †
Normal boiling point C ◦
Bismuth
271
1477
Lead
327
1737
Lithium
179
1317
39
357
Potassium
63.8
760
Sodium
97.8
883
Sodium potassium: 22% Na
19
826
11
784
125
1670
Mercury
−
56% Na
−
Lead-bismuth, 44.5% Pb
Tables
Temperature C ◦
316 760 371 704 204 982 10 316 149 704 204 704
93.3 760 93.3 760 288 649
Density, 3 × 10 3 kg/m
ρ
−
Viscosity µ × 103 kg/m · s
kJ/kg · C
W/m · C
1.62 0.79 2.40 1.37 0.60 0.42 1.59 0.86 0.37 0.14 0.43 0.18
0.144 0.165 0.159 0.155 4.19 4.19 0.138 0.134 0.796 0.754 1.34 1.26
16.4 15.6 16.1 14.9 38.1
0.014 0.0084 0.024 0.016 0.065
8.1 14.0 45.0 33.1 80.3 59.7
0.027 0.0084 0.0066 0.0031 0.0072 0.0038
0.49 0.146 0.58 0.16
0.946 0.883 1.13 1.04
24.4
0.019
25.6 28.9
0.026 0.058
1.76 1.15
0.147
10.7
0.024
10.01 9.47 10.5 10.1 0.51 0.44 13.6 12.8 0.81 0.67 0.90 0.78
0.848 0.69 0.89 0.74 10.3 9.84
Heat capacity ◦
Thermal conductivity ◦
†Adapted to SI un its from J. G. Knudsen and D. L. Katz, Fluid Dynamics and Heat Transfer, New York: McGraw-Hill, 1958.
Table A-8
Diffusion coefficients of gases and vapors in air at 25 C and 1 atm. † ◦
Substance
D , cm2 /s
Ammonia Carbon dioxide Hydrogen Oxygen Water Ethyl ether Methanol Ethyl alcohol
0.28 0.164 0.410 0.206 0.256 0.093 0.159 0.119
Sc
ν =
D
0.78 0.94 0.22 0.75 0.60 1.66 0.97 1.30
Substance
D , cm2 /s
Formic Acid Acetic acid Aniline Benzene Toluene Ethyl benzene Propyl benzene
† From J. H. Perry (ed.), Chemical En gineer s’ Handbook, 4th ed. New York: McGraw-Hill, 1963.
0.159 0.133 0.073 0.088 0.084 0.077 0.059
Sc
=
ν D
0.97 1.16 2.14 1.76 1.84 2.01 2.62
Prandtl number
662
APPENDIX A
Table A-9
Tables
Properties of water (saturated liquid). †
Note: Gr x Pr =
g βρ2 c p µk
c p ◦
F
32 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 350 400 450 500 550 600
◦
C
0 4.44 10 15.56 21.11 26.67 32.22 37.78 43.33 48.89 54.44 60 65.55 71.11 76.67 82.22 87.78 93.33 104.4 115.6 126.7 137.8 148.9 176.7 204.4 232.2 260 287.7 315.6
x 3
T
µ
ρ ◦
3
kJ/kg · C
kg/m
4.225 4.208 4.195 4.186 4.179 4.179 4.174 4.174 4.174 4.174 4.179 4.179 4.183 4.186 4.191 4.195 4.199 4.204 4.216 4.229 4.250 4.271 4.296 4.371 4.467 4.585 4.731 5.024 5.703
999.8 999.8 999.2 998.6 997.4 995.8 994.9 993.0 990.6 988.8 985.7 983.3 980.3 977.3 973.7 970.2 966.7 963.2 955.1 946.7 937.2 928.1 918.0 890.4 859.4 825.7 785.2 735.5 678.7
g βρ 2 c p
k
kg/m · s
1.79×10 3 1.55 1.31 1.12 9.8×10 4 8.6 7.65 6.82 6.16 5.62 5.13 4.71 4.3 4.01 3.72 3.47 3.27 3.06 2.67 2.44 2.19 1.98 1.86 1.57 1.36 1.20 1.07 9.51×10 5 8.68 −
−
µk ◦
Pr
0.566 0.575 0.585 0.595 0.604 0.614 0.623 0.630 0.637 0.644 0.649 0.654 0.659 0.665 0.668 0.673 0.675 0.678 0.684 0.685 0.685 0.685 0.684 0.677 0.665 0.646 0.616
13.25 11.35 9.40 7.88 6.78 5.85 5.12 4.53 4.04 3.64 3.30 3.01 2.73 2.53 2.33 2.16 2.03 1.90 1.66 1.51 1.36 1.24 1.17 1.02 1.00 0.85 0.83
W/m · C
1/m3 · C ◦
1.91 × 109 6.34 × 109 1.08 × 1010 1.46 × 1010 1.91 × 1010 2.48 × 1010 3.3 × 1010 4.19 × 1010 4.89 × 1010 5.66 × 1010 6.48 × 1010 7.62 × 1010 8.84 × 1010 9.85 × 1010 1.09 × 1011
−
† Adapted to SI units from A. I. Brown and S. M. Marco, Introduction to Heat Transfer,3rd ed. New York: McGraw-Hill, 1958.
664
APPENDIX A
Tables
Table A-10 Normal totalA-10 emissivity of various surfaces. †of various surfaces † (Continued ). Table Normal total emissivity ◦
T , F
Surface
Emissivity
Metals and their oxides
Aluminum: Highly polished plate, 98.3% pure Commercial sheet Heavily oxidized Al-surfaced roofing Brass: Highly polished: 73.2% Cu, 26.7% Zn 62.4% Cu, 36.8% Zn, 0.4% Pb, 0.3% Al 82.9% Cu, 17.0% Zn Hard-rolled, polished, but direction of polishing visible Dull plate Chromium (see nickel alloys for Ni-Cr steels), polished Copper: Polished Plate, heated long time, covered with thick oxide layer Gold, pure, highly polished Iron and steel (not including stainless): Steel, polished Iron, polished Cast iron, newly turned turned and heated Mild steel Iron and steel (oxidized surfaces): Iron plate, pickled, then rusted red Iron, dark-gray surface Rough ingot iron Sheet steel with strong, rough oxide layer Lead: Unoxidized, 99.96% pure Gray oxidized Oxidized at 300 F Magnesium, magnesium oxide Molybdenum: Filament Massive, polished Monel metal, oxidized at 1110 F Nickel: Polished Nickel oxide Nickel alloys: Copper nickel, polished Nichrome wire, bright Nichrome wire, oxidized Platinum, polished plate, pure Silver: Polished, pure Polished ◦
◦
440 – 1070 212 299 – 940 100
0.039 – 0.057 0.09 0.20 – 0.31 0.216
476 – 674 494 – 710 530 70 120 – 660 100 – 2000
0.028 – 0.031 0.033 – 0.037 0.030 0.038 0.22 0.08 – 0.36
242 212 77 440 – 1160
0.023 0.052 0.78 0.018 – 0.035
212 800 – 1880 72 1620 – 1810 450 – 1950
0.066 0.14 – 0.38 0.44 0.60 – 0.70 0.20 – 0.32
68 212 1700 – 2040 75
0.61 0.31 0.87 – 0.95 0.80
240 – 440 75 390 530 – 1520
0.057 – 0.075 0.28 0.63 0.55 – 0.20
1340 – 4700 212 390 – 1110
0.096 – 0.202 0.071 0.41 – 0.46
212 1200 – 2290
0.072 0.59 – 0.86
212 120 – 1830 120 – 930 440 – 1160
0.059 0.65 – 0.79 0.95 – 0.98 0.054 – 0.104
440 – 1160 100 – 700
0.020 – 0.032 0.022 – 0.031
664
APPENDIX A
Tables
Table A-10 Normal total emissivity of various surfaces † (Continued ). ◦
T, F
Surface
Emissivity
Metals and their oxides
Stainless steels: Polished Type 301; B Tin, bright tinned iron
212 450 – 1725 76
Tungsten, filament Zinc, galvanized sheet iron, fairly bright
6000 82
0.074 0.54 – 0.63 0.043 and 0.064 0.39 0.23
Refractories, building materials, paints, and miscellaneous
Alumina (85 – 99.5%, Al2 O3 , 0 – 12% SiO2 , 0 – 1% Ge2 O3 ); effect of mean grain size, microns ( µm): 10 µm 50 µm 100 µm Asbestos, board Brick: Red, rough, but no gross irregularities Fireclay Carbon: T-carbon (Gebrüder Siemens) 0.9% ash, started with emissivity of 0.72 at 260 F but on heating changed to values given Filament Rough plate Lampblack, rough deposit Concrete tiles Enamel, white fused, on iron Glass: Smooth Pyrex, lead, and soda Paints, lacquers, varnishes: Snow-white enamel varnish on rough iron plate Black shiny lacquer, sprayed on iron Black shiny shellac on tinned iron sheet Black matte shellac Black or white lacquer Flat black lacquer Aluminum paints and lacquers: 10% Al, 22% lacquer body, on rough or smooth surface Other Al paints, varying age and Al content Porcelain, glazed Quartz, rough, fused Roofing paper Rubber, hard, glossy plate Water
74
0.30 – 0.18 0.39 – 0.28 0.50 – 0.40 0.96
70 1832
0.93 0.75
260 – 1160
0.81 – 0.79
1900 – 2560 212 – 608 212 – 932 1832 66
0.526 0.77 0.84 – 0.78 0.63 0.90
72 500 – 1000
0.94 0.95 – 0.85
73 76 70 170 – 295 100 – 200 100 – 200
0.906 0.875 0.821 0.91 0.80 – 0.95 0.96 – 0.98
212
0.52
◦
212 72 70 69 74 32 – 212
† Courtesy of H. C. Hottel, from W. H. McAdams, Heat Transmissions, 3rd ed. New York: McGraw-Hill, 1954.
0.27 – 0.67 0.92 0.93 0.91 0.94 9.95 – 0.963
664
APPENDIX A
Table A-11 Nominal pipe size, in
Steel-pipe Tabledimensions. A-10 Normal total emissivity of various surfaces † (Continued ).
OD, in
1 8
0.405
1 4
0.540
3 8
0.675
1 2
0.840
3 4
1.050
1
1.315
1 21
1.900
2
2.375
3
3.500
4
4.500
5
5.563
6
6.625
10
Tables
10.75
Schedule no.
40 80 40 80 40 80 40 80 40 80 40 80 40 80 160 40 80 40 80 40 80 40 80 120 160 40 80 40 80
Wall Thickness, in
0.068 0.095 0.088 0.119 0.091 0.126 0.109 0.147 0.113 0.154 0.133 0.179 0.145 0.200 0.281 0.154 0.218 0.216 0.300 0.237 0.337 0.258 0.375 0.500 0.625 0.280 0.432 0.365 0.500
Metal sectional
Inside crosssectional
ID, in
area, in2
area, ft2
0.269 0.215 0.364 0.302 0.493 0.423 0.622 0.546 0.824 0.742 1.049 0.957 1.610 1.500 1.338 2.067 1.939 3.068 2.900 4.026 3.826 5.047 4.813 4.563 4.313 6.065 5.761 10.020 9.750
0.072 0.093 0.125 0.157 0.167 0.217 0.250 0.320 0.333 0.433 0.494 0.639 0.799 1.068 1.429 1.075 1.477 2.228 3.016 3.173 4.407 4.304 6.122 7.953 9.696 5.584 8.405 11.90 16.10
0.00040 0.00025 0.00072 0.00050 0.00133 0.00098 0.00211 0.00163 0.00371 0.00300 0.00600 0.00499 0.01414 0.01225 0.00976 0.02330 0.02050 0.05130 0.04587 0.08840 0.7986 0.1390 0.1263 0.1136 0.1015 0.2006 0.1810 0.5475 0.5185
666
Tables
APPENDIX A
Conversion factors. (See also inside cover .)
Table A-12
Length: 12 in = 1 ft 2.54 cm = 1 in 1 µm = 10 6 m = 10 4 cm Mass: 1 kg = 2.205 lbm 1 slug = 32.16 lbm 454 g = 1 lbm Force: 1 dyn = 2.248 × 10 6 lb f 1 lb f = 4.448 N 105 dyn = 1 N −
Energy: 1 ft · lb f = 1.356 J 1 kWh = 3413 Btu 1 hp · h = 2545 Btu 1 Btu = 252 cal 1 Btu = 778 ft · lb f Pressure: 1 atm = 14.696 lb f /in2 = 2116 lb f /ft 2 1 atm = 1.01325 × 105 Pa 1 in Hg = 70.73 lb f /ft2 Viscosity: 1 centipoise = 2.42 lbm /h · ft 1 lb f · s/ft2 = 32.16 lbm /s · ft Thermal conductivity: 1 cal/s · cm · C = 242 Btu/h · ft · F 1 W/cm · C = 57.79 Btu/h · ft · F
−
−
◦
◦
◦
◦
Useful conversion to SI units
Length: 1 in = 0.0254 m 1 ft = 0.3048 m 1 mi = 1.60934 km rea: 1 in2 = 645.16 mm2 1 ft2 = 0.092903 m2 1 mi2 = 2.58999 km2 Pressure: 1 N/m2 = 1 Pa 1 atm = 1.01325 × 105 Pa 1 lb f /in2 = 6894.76 Pa Energy: 1 erg = 10 7 J 1 Btu = 1055.04 J 1 ft · lb f = 1.35582 J 1 cal (15 C) = 4.1855 J Power: 1 hp = 745.7 W 1 Btu/h = 0.293 W Heat flux: 1 Btu/h · ft2 = 3.15372 W/m2 1 Btu/h · ft = 0.96128 W/m Thermal conductivity: 1 Btu/h · ft · F = 1.7307 W/m · C Heat-transfer c oefficient: 1 Btu/h · ft2 · F = 5.6782 W/m2 · C −
◦
◦
◦
◦
◦
Volume: 1 in3 = 1.63871 × 10 5 m3 1 ft3 = 0.0283168 m3 1 gal = 231 in3 = 0.0037854 m3 Mass: 1 lbm = 0.45359237 kg Density: 1 lbm /in3 = 2.76799 × 104 kg/m3 1 lbm /ft3 = 16.0185 × 104 kg/m3 Force: 1 dyn = 10 5 N 1 lb f = 4.44822 N −
−
