App

0082-APP Page 351 Wednesday, August 23, 2000 9:54 AM

Appendix

© 2001 by CRC PRESS LLC

Temp. T

Density °C

kg/m3

32 41 50 59 68 77 86 95 104 113 122 131 140 149 158 167 176 185 194 203 212

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

1.293 1.269 1.242 1.222 1.202 1.183 1.164 1.147 1.129 1.111 1.093 1.079 1.061 1.047 1.030 1.013 1.001 0.986 0.972 0.959 0.947

3.664 3.598 3.533 3.470 3.412 3.354 3.298 3.244 3.193 3.142 3.094 3.048 3.003 2.957 2.914 2.875 2.834 2.795 2.755 2.718 2.683

Specific Heat cp J/kg K

Thermal Cond. k W/m K

Absolute Viscosity  106 N s/m2

Kinematic Viscosity v 106 m2/s

Prandtl Number Pr –

1003.9 1004.3 1004.6 1004.9 1005.2 1005.4 1005.7 1006.0 1006.3 1006.6 1006.9 1007.3 1007.7 1008.0 1008.4 1008.8 1009.3 1009.8 1010.3 1010.7 1011.2

0.02417 0.02445 0.02480 0.02512 0.02544 0.02577 0.02614 0.02650 0.02684 0.02726 0.02761 0.02801 0.02837 0.02876 0.02912 0.02945 0.02979 0.03012 0.03045 0.03073 0.03101

17.17 17.35 17.58 17.79 18.00 18.22 18.46 18.70 18.92 19.19 19.42 19.68 19.91 20.16 20.39 20.60 20.82 21.02 21.23 21.41 21.58

13.28 13.67 14.16 14.56 14.98 15.40 15.86 16.30 16.76 17.27 17.77 18.24 18.77 19.26 19.80 20.34 20.80 21.32 21.84 22.33 22.79

0.7131 0.7127 0.7122 0.7118 0.7113 0.7108 0.7103 0.7098 0.7093 0.7087 0.7082 0.7077 0.7072 0.7067 0.7062 0.7057 0.7053 0.7048 0.7044 0.7041 0.7038

Thermal Design of Electronic Equipment

°F

Coef. Exp.  103 1/K



0082-APP Page 353 Wednesday, August 23, 2000 9:54 AM

353

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TABLE A1 Air at Sea-Level Atmospheric Pressure

Temp. T °F

°C

32 41 50 59 68 77 86 95 104 113 122 131 140 149 158 167 176 185 194 203 212

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Density  kg/m3 999.9 1000 999.7 999.1 998.2 997.1 995.7 994.1 992.2 990.2 988.1 985.8 983.5 980.8 978 974.9 971.7 968.5 965 961.7 958.4

Coef. Exp.   103 1/K 0.068 0.018 0.095 0.16 0.22 0.26 0.31 0.35 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.60 0.63 0.66 0.69 0.72 0.75

Specific Heat cp J/kg K

Thermal Cond. k W/m K

Absolute Viscosity  106 N s/m2

Kinematic Viscosity v 106 m2/s

4217.5 4202.7 4192.4 4185.8 4181.7 4179.5 4178.6 4178.5 4179.0 4179.9 4181.1 4182.6 4184.5 4186.8 4189.5 4192.9 4196.6 4201.0 4205.7 4210.6 4215.5

0.5580 0.5677 0.5774 0.5870 0.5967 0.6064 0.6155 0.6243 0.6325 0.6401 0.6472 0.6536 0.6594 0.6643 0.6686 0.6724 0.6753 0.6778 0.6797 0.6811 0.6822

1794 1530 1296 1136 993 880.6 792.4 719.8 658.0 605.1 555.1 512.6 470.0 436.0 402.0 376.6 350.0 330.5 311.0 294.3 277.5

1.794 1.530 1.296 1.137 0.995 0.883 0.796 0.724 0.663 0.611 0.562 0.520 0.478 0.445 0.411 0.386 0.361 0.341 0.322 0.306 0.290

Prandtl Number Pr – 13.56 11.33 9.410 8.101 6.959 6.069 5.380 4.818 4.348 3.951 3.586 3.280 2.983 2.748 2.519 2.348 2.175 2.048 1.924 1.819 1.715

0082-APP Page 354 Wednesday, August 23, 2000 9:54 AM

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TABLE A2 Water at Sea-Level Atmospheric Pressure

Temp. T °F 32 41 50 59 68 77 86 95 104 113 122 131

°C 0 5 10 15 20 25 30 35 40 45 50 55

Density  kg/m3

Coef. Exp.   103 1/K

1740 1727 1714 1701 1688 1675 1662 1649 1636 1623 1610 1597

1.601 1.611 1.619 1.626 1.633 1.640 1.647 1.654 1.662 1.670 1.680 1.689

Specific Heat cp J/kg K 1005.0 1016.2 1025.6 1033.2 1039.8 1046.6 1053.5 1060.8 1068.7 1077.5 1087.0 1096.5

Thermal Cond. k W/m K 0.0600 0.0595 0.0590 0.0585 0.0580 0.0575 0.0570 0.0565 0.0560 0.0555 0.0550 0.0545

Absolute Viscosity  106 N s/m2 1009.5 932.4 861.6 799.5 743.0 693.8 648.2 610.1 574.3 543.9 514.8 486.0

Kinematic Viscosity v  106 m2/s 0.5802 0.5399 0.5027 0.4700 0.4402 0.4142 0.3900 0.3700 0.3510 0.3351 0.3198 0.3043

Prandtl Number Pr – 16.91 15.93 14.98 14.12 13.32 12.63 11.98 11.46 10.96 10.56 10.17 9.778

0082-APP Page 355 Wednesday, August 23, 2000 3:58 PM

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TABLE A3 Perflurocarbon FC-72 at Atmospheric Pressure (Boils at 56°C)

Temp. T

Density

°F

°C

kg/m3

Coef. Exp.  103 1/K

32 41 50 59 68 77 86 95 104 113 122 131 140 149 158 167 176 185 194 203

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

1838 1826 1814 1802 1789 1777 1765 1753 1740 1728 1716 1704 1691 1679 1667 1655 1642 1630 1618 1605

1.399 1.407 1.414 1.421 1.429 1.436 1.443 1.451 1.458 1.466 1.473 1.481 1.489 1.497 1.504 1.512 1.520 1.527 1.534 1.541



Specific Heat cp J/kg K

Thermal Cond. k W/m K

Absolute Viscosity  106 N s/m2

Kinematic Viscosity v 106 m2/s

Prandtl Number Pr –

1005 1016 1025 1033 1041 1048 1056 1063 1071 1079 1087 1096 1105 1114 1123 1131 1140 1147 1154 1159

0.0649 0.0646 0.0643 0.0640 0.0637 0.0634 0.0631 0.0628 0.0625 0.0621 0.0617 0.0613 0.0609 0.0604 0.0600 0.0595 0.0590 0.0585 0.0580 0.0575

2356 2117 1905 1719 1554 1413 1288 1178 1083 1001 927.0 862.4 805.0 753.2 706.1 662.3 622.1 584.0 548.0 513.2

1.282 1.159 1.052 0.9539 0.8686 0.7592 0.7298 0.6720 0.6224 0.5793 0.5402 0.5061 0.4761 0.4486 0.4236 0.4002 0.3789 0.3583 0.3387 0.3198

36.48 33.30 30.37 27.75 25.40 23.36 21.56 19.94 18.56 17.39 16.33 15.42 14.61 13.89 13.22 12.59 12.02 11.45 10.90 10.34

Source: Data from FluorinertTM Liquids Product Manual, 3M, St. Paul, MN. With permission.

0082-APP Page 356 Wednesday, August 23, 2000 9:54 AM

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TABLE A4 Perflurocarbon FC-77 at Atmospheric Pressure (Boils at 97°C)

0082-APP Page 357 Wednesday, August 23, 2000 9:54 AM

TABLE A5 Thermophysical Properties of Nonferrous Metals at 20°C

Materials

Density  kg/m3

Aluminum (1100) Aluminum (2014) Aluminum (2024) Aluminum (5052) Aluminum (6061) Aluminum (7075) Aluminum (356) Beryllium Brass (C36000) Bronze (C22000) Copper (C11000) Copper (C12200) Copper (C22000) Copper (alloy MF 202) Glass seal (alloy Ni 50) Gold Inconel (625) Kovar Lead

2713 2796 2768 2685 2713 2796 2685 1855 8498 8802 8913 8941 8802 8862 8332 19,321 8442 8343 11,349

© 2001 by CRC PRESS LLC

Coef. Exp.   106 1/K 23.6 23.0 23.2 23.8 23.4 23.6 21.4 11.5 20.5 18.4 17.6 17.6 18.4 17.0 8.46 14.2 12.8 4.30 29.3

Specific Heat cp J/kg K 921 921 921 921 963 963 935 1884 380 377 383 385 377 382 482 129 410 439 130

Thermal Cond. k W/m K 222 192 189 139 180 121 159 151 116 189 391 339 189 150 10.4 313 9.82 16.0 33.9

0082-APP Page 358 Wednesday, August 23, 2000 9:54 AM

TABLE A6 Thermophysical Properties of Ferrous Metals at 20°C

Materials Carbon steel (AISI 1010) Carbon steel (AISI 1042) Cast iron (ASTM A-48) Cast iron (ASTM A-220) Cast steels (carbon and alloy) Stainless steel (4130) Stainless steel (17-4 PH) Stainless steel (304) Stainless steel (316) Stainless steel (440)

Density  kg/m3 7830 7840 7197 7363 7834 7833 7778 8027 2685 7750

Coef. Exp.   106 1/K 6.60 6.50 10.8 13.5 14.7 13.5 10.8 17.3 16.0 10.1

Specific Heat cp J/kg K 434 460 544 544 440 456 461 477 468 461

Thermal Cond. k W/m K 64.0 50.0 50.2 51.1 46.7 43.3 18.0 16.3 16.3 24.2

TABLE A7 Thermophysical Properties of Plastics at 20°C

Materials ABS (acrylonitrile butadiene styrene) Acetal Acrylic Alkyd Cellulose acetate Epoxy (cast) Epoxy (IC molding) Fluorocarbon (PTFE) Polyamide (nylon type 6) Phenolic Polycarbonate Polybutylene Terephthalate (PBT) Polyester Polyimide Polyamide-imide Polyetherimide Polyesteretherketone Polyetherketone Polystyrene Polyethylene Polypropylene Polyvinyl chloride (PVC)

© 2001 by CRC PRESS LLC

Density  kg/m3

Coef. Exp.   106 1/K

Specific Heat cp J/kg K

Thermal Cond. k W/m K

1058

72.0

1466

2.70

1415 1178 2206 1257 1148 1820 2196 1247 1387 1203 1307

82.8 81.0 36.0 121 59.4 17.0 90.9 89.1 37.4 67.5 72.0

1465 1466 1256 1508 1884 984 1047 1675 1570 1256 1905

3.01 2.49 9.87 3.01 4.15 4.00 2.91 2.08 1.74 2.39 1.90

1287 1427 1397 1277 1317 – 1039 933 903 1447

85.5 47.7 36.0 54.0 40.5 103 72.9 225 86.4 54.0

1780 1214 – 1090 – – 1361 2261 1884 1050

2.29 8.05 2.94 2.2 2.95 – 1.54 3.95 2.22 1.77

0082-APP Page 359 Wednesday, August 23, 2000 9:54 AM

TABLE A8 Thermophysical Properties of Ceramics at 20°C

Materials

Density  kg/m3

Coef. Exp.   106 1/K

Specific Heat cp J/kg K

3982 3200 2900 2200 3500 2200 2900 2300 3300

5.67 4.40 7.00 3.80 2.00 0.50 50.0 4.20 2.00

879 711 1030 709 510 745

30.0 200 300 1300 1200 1.60

664 624

83.7 21.0

Aluminum oxide Aluminum nitride Beryllium oxide Boron nitride (cubic) Diamond (film) Fused quartz Glass (die attach) Silicon Silicon nitride

Thermal Cond. k W/m K

TABLE A9 Properties of Common Gases MW

 cp/cv

pc  106 atm

C2H2 (a) NH3 Ar C4H10 CO2

26.038 28.966 17.031 39.948 58.124 44.010

1.260 1.400 1.310 1.660 1.090 1.285

6.1404 3.6883 11.2777 4.8738 3.7998 7.3766

CO

28.010

1.399

Cl2 C2H6 C2H4 F2 CC12F2 He H2 CH4 CH4O Ne N2 N2O

70.096 30.070 28.054 37.997 120.914 4.003 2.016 16.043 32.042 20.183 28.013 44.013

C8H18 O2 C5H12 C3H8

114.232 32.00 72.151 44.097

Gas Acetylene Air Ammonia Argon Butane Carbon dioxide Carbon monoxide Chlorine Ethane Ethylene Fluorine Freon-12 Helium Hydrogen Methane Methanol Neon Nitrogen Nitrous oxide Octane Oxygen Pentane Propane

© 2001 by CRC PRESS LLC

  106 N s/m2

Å

T

K

308.3 132.0 405.6 150.8 425.2 304.2

– 19.3 32.7 26.4 25.0 34.3

4.033 3.711 2.900 3.542 4.687 3.941

231.8 78.60 558.3 93.30 531.4 195.2

3.4958

132.9

19.0

3.690

91.70

1.355 1.183 1.208 – 1.139 1.667 1.404 1.320 1.203 1.667 1.400 1.303

7.7009 4.8840 5.0360 5.2183 4.1240 0.2270 1.2970 4.6003 8.0960 2.7561 3.3945 7.2449

417.0 305.4 282.4 144.3 385.0 5.190 33.20 190.6 512.6 44.40 126.2 309.6

42.0 21.7 21.7 27.5 – 2.54 3.47 15.9 39.3 16.3 18.0 33.2

4.217 4.443 4.163 3.357 – 2.551 2.827 3.758 3.626 2.820 3.798 3.828

316.0 215.7 224.7 112.6 – 10.22 59.70 148.6 481.8 32.80 71.40 232.4

1.044 1.395 1.086 1.124

4.2845 5.0461 3.3742 4.2456

563.4 154.6 469.6 369.8

24.1 25.0 25.0 23.3

– 3.467 5.784 5.118

– 106.7 34.10 237.1

Tc (K) K

0082-APP Page 360 Wednesday, August 23, 2000 9:54 AM

TABLE A9 (continued) Properties of Common Gases MW

 cp/cv

pc  106 atm

Tc (K) K

  106 N s/m2

Å

T

K

18.015 92.140 131.30

1.329 – 1.660

22.049 4.1139 5.8364

647.3 591.7 289.7

54.1 127.0 53.7

2.641 – 4.047

809.1 – 231.0

Gas Steam Toluene Xenon

H2O C7H8 Xe

Note: Pc  critical pressure (Pa) MW  molecular weight Tc  critical temperature (K) T  effective temperature characteristic force potential (K)



 ratio of specfic heat at constant pressure to specific heat at constant volume at 15°C to 25°C



 molecular collision diameter (Å)

c  viscosity at critical pressure and critical temperature (N s/m2) a

Properties 78.084% 20.946% 0.934% 0.033% 1.0%

of air based on: N2 O2 Ar CO2 other, by volume.

TABLE A10 U.S. Standard Atmosphere Altitude H (m) 100 0 100 200 400 600 800 1000 1500 2000 2500 3000 3500

© 2001 by CRC PRESS LLC

Temperaure T (K)

Density  (kg/m3)

Pressure P (N/m2)

Viscosity   106 (N/m2)

288.80 288.15 287.50 286.85 285.55 284.25 282.95 281.65 278.40 275.15 271.90 268.65 265.40

1.237 1.225 1.213 1.202 1.179 1.156 1.134 1.112 1.058 1.007 0.9567 0.9091 0.8632

102,534 101,327 100,131 98,948 96,613 94,324 92,079 89,877 84,558 79,497 74,684 70,110 65,766

17.92 17.89 17.86 17.83 17.76 17.70 17.64 17.57 17.41 17.25 17.09 16.93 16.77

0082-APP Page 361 Wednesday, August 23, 2000 9:54 AM

TABLE A10 (continued) U.S. Standard Atmosphere Altitude H (m) 4000 4500 5000 6000 7000 8000 9000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 19,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 60,000 70,000

© 2001 by CRC PRESS LLC

Temperaure T (K) 262.15 258.90 255.65 249.15 242.65 236.15 229.65 223.15 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 216.65 221.65 226.65 237.05 251.05 265.05 270.65 245.45 217.45

Density  (kg/m3)

Pressure P (N/m2)

Viscosity   106 (N/m2)

0.8191 0.7768 0.7361 0.6597 0.5895 0.5252 0.4664 0.4127 0.3639 0.3108 0.2655 0.2268 0.1937 0.1654 0.1413 0.1207 0.1031 0.08803 0.03946 0.01801 0.00821 0.00385 0.00188 0.00097 0.00028 0.00007

61,642 57,730 54,022 47,183 41,062 35,601 30,380 26,437 22,633 19,331 16,511 14,102 12,045 10,288 8,787.1 7,505.2 6,410.4 5,475.2 2,511.2 1,172.0 558.97 277.55 143.15 75.954 20.317 4.6348

16.61 16.44 16.28 15.95 15.60 15.26 14.92 14.57 14.21 14.21 14.21 14.21 14.21 14.21 14.21 14.21 14.21 14.21 14.48 14.76 15.31 16.04 16.75 17.03 15.75 14.26