TRANSPORT PROPERTIES

APPENDIX B TRANSPORT PROPERTIES List of Properties Tables Table B.1 Air at 1 atm ....................................................................................... 957 Table B.2 Carbon dioxide (CO2) at 1 atm ......................................................... 958 Table B.3 Helium (He) at 1 atm ........................................................................ 958 Table B.4 Hydrogen (H2) at 1 atm .................................................................... 959 Table B.5 Nitrogen (N2) at 1 atm....................................................................... 959 Table B.6 Oxygen (O2) at 1 atm ....................................................................... 960 Table B.7 Water (H2O) vapor at 1 atm ............................................................. 960 Table B.8 Volume expansion coefficients for liquids........................................ 961 Table B.9 Density and volume expansion coefficients of water........................ 961 Table B.10 Aluminum ....................................................................................... 962 Table B.11 Aluminum alloy, 2024-T6............................................................... 962 Table B.12 Cartridge brass ................................................................................ 962 Table B.13 Copper ............................................................................................. 962 Table B.14 Fused silica...................................................................................... 963 Table B.15 Inconel® X-750 .............................................................................. 963 Table B.16 Iron .................................................................................................. 963 Table B.17 Molybdenum ................................................................................... 964 Table B.18 Nickel .............................................................................................. 964 Table B.19 Niobium........................................................................................... 964 Table B.20 Plain carbon steel ............................................................................ 965 Table B.21 Stainless steel 304 ........................................................................... 965 Table B.22 Tantalum ......................................................................................... 965 Table B.23 Titanium .......................................................................................... 966 Table B.24 Tungsten.......................................................................................... 966 Table B.25 Phase Change Materials (PCMs)..................................................... 967 Table B.26 Thermophysical properties at saturation for acetone ...................... 968 Table B.27 Thermophysical properties at saturation for ammonia.................... 969 Table B.28 Thermophysical properties at saturation for cesium ....................... 970 Table B.30 Thermophysical properties at saturation for ethane ........................ 971 Table B.31 Thermophysical properties at saturation for ethanol....................... 971

954

Transport Phenomena in Multiphase Systems

Table B.32 Thermophysical properties at saturation for Freon®-113 ............... 972 Table B.33 Thermophysical properties at saturation for Freon®-123 ............... 972 Table B.34 Thermophysical properties at saturation for Freon®-134a ............. 973 Table B.35 Thermophysical properties at saturation for Freon®-21 ................. 973 Table B.36 Thermophysical properties at saturation for Freon®-22 ................. 974 Table B.37 Thermophysical properties at saturation for helium........................ 974 Table B.38 Thermophysical properties at saturation for heptane ...................... 975 Table B.39 Thermophysical properties at saturation for lead ............................ 975 Table B.40 Thermophysical properties at saturation for lithium ....................... 976 Table B.41 Thermophysical properties at saturation for mercury ..................... 976 Table B.42 Thermophysical properties at saturation for methanol.................... 977 Table B.43 Thermophysical properties at saturation for nitrogen ..................... 977 Table B.44 Thermophysical properties at saturation for potassium .................. 978 Table B.45 Thermophysical properties at saturation for rubidium .................... 978 Table B.46 Thermophysical properties at saturation for silver.......................... 979 Table B.47 Thermophysical properties at saturation for sodium....................... 980 Table B.48 Thermophysical properties at saturation for water.......................... 980 Polynomial Temperature-Property Relation ...................................................... 981 Table B.49 Coefficients of temperature-property relations for acetone............. 982 Table B.50 Coefficients of temperature-property relations for ammonia.......... 982 Table B.51 Coefficients of temperature-property relations for cesium ............. 983 Table B.52 Coefficients of temperature-property relations for Dowtherm®..... 983 Table B.53 Coefficients of temperature-property relations for ethane .............. 984 Table B.54 Coefficients of temperature-property relations for ethanol ............. 984 Table B.55 Coefficients of temperature-property relations for Freon®-113 ..... 985 Table B.56 Coefficients of temperature-property relations for Freon®-123 ..... 985 Table B.57 Coefficients of temperature-property relations for Freon®-134a ... 986 Table B.58 Coefficients of temperature-property relations for Freon®-21 ....... 986 Table B.59 Coefficients of temperature-property relations for Freon®-22 ....... 987 Table B.60 Coefficients of temperature-property relations for heptane ............ 987 Table B.61 Coefficients of temperature-property relations for lead .................. 988 Table B.62 Coefficients of temperature-property relations for lithium ............. 988 Table B.63 Coefficients of temperature-property relations for mercury ........... 989 Table B.64 Coefficients of temperature-property relations for methanol.......... 989 Table B.65 Coefficients of temperature-property relations for nitrogen ........... 990 Table B.66 Coefficients of temperature-property relations for potassium......... 990 Table B.67 Coefficients of temperature-property relations for rubidium .......... 991 Table B.68 Coefficients of temperature-property relations for silver................ 991 Table B.69 Coefficients of temperature-property relations for sodium ............. 992 Table B.70 Coefficients of temperature-property relations for water................ 992 Table B.71 Binary diffusion coefficients at 1 atm ............................................. 993 Table B.72 Diffusion coefficients in air at 1 atm (1.013 x 105 Pa).................... 994 Table B.73 Diffusion coefficients in solids ...................................................... 995 Table B.74 Schmidt number for vapors in dilute mixture in air at normal temperature, enthalpy of vaporization, and boiling point at 1 atm .................... 996

Appendix B. Transport Properties

955

Table B.75 Schmidt numbers for dilute solution in water at 300K ................... 997 Table B.76 Solubility and permeability of gases in solids................................. 998 Table B.77 Henry’s constant for selected gases in water at moderate pressure1000 Table B.78 The solubility of selected gases and solids.................................... 1000 Table B.79 Solubility of inorganic compounds in water ................................. 1001 Table B.80 Equilibrium compositions for the NH3-water system ................... 1002 Table B.81 Equilibrium compositions for the SO2-water system .................... 1002 Table B.82 Thermodynamic properties of water vapor-air mixtures at 1 atm. 1003 References........................................................................................................ 1004

956

Transport Phenomena in Multiphase Systems

Table B.1 Air at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)G

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

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 3000

3.5562 2.3364 1.7458 1.3947 1.1614 0.995 0.8711 0.7740 0.6964 0.6329 0.5804 0.5356 0.4975 0.4643 0.4354 0.4097 0.3868 0.3666 0.3482 0.3166 0.2902 0.2679 0.2488 0.2322 0.2177 0.2049 0.1935 0.1833 0.1741 0.1658 0.1582 0.1513 0.1448 0.1389 0.1135

1.032 1.012 1.007 1.006 1.007 1.009 1.014 1.021 1.030 1.040 1.051 1.063 1.075 1.087 1.099 1.110 1.121 1.131 1.141 1.159 1.175 1.189 1.207 1.23 1.248 1.267 1.286 1.307 1.337 1.372 1.417 1.478 1.558 1.665 2.726

71.1 103.4 132.5 159.6 184.6 208.2 230.1 250.7 270.1 288.4 305.8 322.5 338.8 354.6 369.8 384.3 398.1 411.3 424.4 449 473 496 530 557 584 611 637 663 689 715 740 766 792 818 955

2.00 4.426 7.59 11.44 15.89 20.92 26.41 32.39 38.79 45.57 52.69 60.21 68.10 76.37 84.93 93.80 102.9 112.2 121.9 141.8 162.9 185.1 213 240 268 298 329 362 396 431 468 506 547 589 841

9.34 13.8 18.1 22.3 26.3 30.0 33.8 37.3 40.7 43.9 46.9 49.7 52.4 54.9 57.3 59.6 62.0 64.3 66.7 71.5 76.3 82 91 100 106 113 120 128 137 147 160 175 196 222 486

2.54 5.84 10.3 15.9 22.5 29.9 38.3 47.2 56.7 66.7 76.9 87.3 98 109 120 131 143 155 168 195 224 238 303 350 390 435 482 534 589 646 714 783 869 960 1570

0.786 0.758 0.737 0.72 0.707 0.700 0.690 0.686 0.684 0.683 0.685 0.690 0.695 0.702 0.709 0.716 0.720 0.723 0.726 0.728 0.728 0.719 0.703 0.685 0.688 0.685 0.683 0.677 0.672 0.667 0.655 0.647 0.63 0.613 0.536

Appendix B. Transport Properties

957

Table B.2 Carbon dioxide (CO2) at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

280 300 320 340 360 380 400 450 500 550 600 650 700 750 800

1.9022 1.7730 1.6609 1.5618 1.4743 1.3961 1.3257 1.1782 1.0594 0.9625 0.8826 0.8143 0.7564 0.7057 0.6614

0.830 0.851 0.872 0.891 0.908 0.926 0.942 0.981 1.020 1.050 1.080 1.100 1.130 1.150 1.170

140 149 156 165 173 181 190 210 231 251 270 288 305 321 337

7.36 8.40 9.39 10.60 11.70 13.00 14.30 17.80 21.80 26.10 30.60 35.40 40.30 45.50 51.00

15.20 16.55 18.05 19.70 21.20 22.75 24.30 28.30 32.50 36.60 40.70 44.50 48.10 51.70 55.10

9.63 11.00 12.50 14.20 15.80 17.60 19.50 24.50 30.10 36.20 42.70 49.70 56.30 63.70 71.20

0.765 0.766 0.754 0.746 0.741 0.737 0.737 0.728 0.725 0.721 0.717 0.712 0.717 0.714 0.716

Table B.3 Helium (He) at 1 atm (Bejan, 1994) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-6N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

4.22 7 10 20 30 60 100 200 300 600 1000

16.900 7.530 5.020 2.440 1.620 0.811 0.487 0.244 0.162 0.0818 0.0487

9.78 5.71 5.41 5.25 5.22 5.20 5.20 5.19 5.19 5.19 5.19

1.25 1.76 2.26 3.58 4.63 7.12 9.78 15.1 19.9 32.2 46.3

0.0739 0.234 0.449 1.470 2.860 8.800 20.10 62.20 122.0 396.0 946.0

0.011 0.014 0.018 0.027 0.034 0.053 0.074 0.118 0.155 0.251 0.360

0.00064 0.00321 0.00642 0.0209 0.0403 0.125 0.291 0.932 1.830 5.940 14.20

1.15 0.73 0.70 0.70 0.71 0.70 0.69 0.67 0.67 0.67 0.67

958

Transport Phenomena in Multiphase Systems

Table B.4 Hydrogen (H2) at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

100 150 200 250 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

0.24255 0.16156 0.12115 0.09693 0.08078 0.06924 0.06059 0.05386 0.04848 0.04407 0.04040 0.03463 0.03030 0.02694 0.02424 0.02204 0.02020 0.01865 0.01732 0.01616 0.01520 0.01430 0.01350 0.01280 0.01210

11.230 12.600 13.540 14.060 14.310 14.430 14.480 14.500 14.520 14.530 14.550 14.610 14.700 14.830 14.990 15.170 15.370 15.590 15.810 16.020 16.280 16.580 16.960 17.490 18.250

42.1 56.0 68.1 78.9 89.6 98.8 108.2 117.2 126.4 134.3 142.4 157.8 172.4 186.5 201.3 213.0 226.2 238.5 250.7 262.7 273.7 284.9 296.1 307.2 318.2

17.4 34.7 56.2 81.4 111 143 179 218 261 305 352 456 569 692 830 966 1120 1279 1447 1626 1801 1992 2193 2400 2630

67 101 131 157 183 204 226 247 266 285 305 342 378 412 448 488 528 568 610 655 697 742 786 835 878

24.6 49.6 79.9 115 158 204 258 316 378 445 519 676 849 1030 1230 1460 1700 1955 2230 2530 2815 3130 3435 3730 3975

0.707 0.699 0.704 0.707 0.701 0.700 0.695 0.689 0.691 0.685 0.678 0.675 0.670 0.671 0.673 0.662 0.659 0.655 0.650 0.643 0.639 0.637 0.639 0.643 0.661

Table B.5 Nitrogen (N2) at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

100 150 200 250 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300

3.4388 2.2594 1.6883 1.3488 1.1233 0.9625 0.8425 0.7485 0.6739 0.6124 0.5615 0.4812 0.4211 0.3743 0.3368 0.3062 0.2807 0.2591

1.070 1.050 1.043 1.042 1.041 1.042 1.045 1.050 1.056 1.065 1.075 1.098 1.220 1.146 1.167 1.187 1.204 1.219

68.8 100.6 129.2 154.9 178.2 200.0 220.4 239.6 257.7 274.7 290.8 321.0 349.1 375.3 399.9 423.2 445.3 466.2

2.00 4.45 7.65 11.48 15.86 20.78 26.16 32.01 38.24 44.86 51.79 66.71 82.9 100.3 118.7 138.2 158.6 179.9

9.58 13.9 18.3 22.2 25.9 29.3 32.7 35.8 38.9 41.7 44.6 49.9 54.8 59.7 64.7 70.0 75.8 81.0

2.6 5.86 10.4 15.8 22.1 29.2 37.1 45.6 54.7 63.9 73.9 94.4 116 139 165 193 224 256

0.768 0.759 0.736 0.727 0.716 0.711 0.704 0.703 0.700 0.702 0.701 0.706 0.715 0.721 0.721 0.718 0.707 0.701

Appendix B. Transport Properties

959

Table B.6 Oxygen (O2) at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

100 150 200 250 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300

3.9450 2.5850 1.9300 1.5420 1.2840 1.1000 0.9620 0.8554 0.7698 0.6998 0.6414 0.5498 0.4810 0.4275 0.3848 0.3498 0.3206 0.2960

0.9620 0.9210 0.9150 0.9150 0.9200 0.9290 0.9420 0.9560 0.9720 0.9880 1.0030 1.0310 1.0540 1.0740 1.0900 1.1030 1.1150 1.1250

76.4 114.8 147.5 178.6 207.2 233.5 258.2 281.4 303.3 324.0 343.7 380.8 415.2 447.2 477.0 505.5 532.5 588.4

1.94 4.44 7.64 11.58 16.14 21.23 26.84 32.90 39.40 46.30 53.59 69.26 86.32 104.6 124.0 144.5 166.1 188.6

9.25 13.8 18.3 22.6 26.8 29.6 33.0 36.3 41.2 44.1 47.3 52.8 58.9 64.9 71.0 75.8 81.9 87.1

2.44 5.80 10.4 16.0 22.7 29.0 36.4 44.4 55.1 63.8 73.5 93.1 116 141 169 196 229 262

0.796 0.766 0.737 0.723 0.711 0.733 0.737 0.741 0.716 0.726 0.729 0.744 0.743 0.740 0.733 0.736 0.725 0.721

Table B.7 Water (H2O) vapor at 1 atm (Incropera and DeWitt, 2001) T Temp. (K)

ȡ density (kg/m3)

cp specific heat (kJ/Kg-K)

ȝ viscosity (10-7N-s/m²)

Ȟ kinematic viscosity (10-6m2/s)

k thermal conductivity (10-3W/m-K)

Į thermal diffusivity (10-6m2/s)

Pr Prandtl number

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

127.1 134.4 152.5 170.4 188.4 206.7 224.7 242.6 260.4 278.6 296.9

21.68 24.25 31.11 38.68 47.04 56.60 66.48 77.26 88.84 101.7 115.1

24.6 26.1 29.9 33.9 37.9 42.2 46.4 50.5 54.9 59.2 63.7

20.4 23.4 30.8 38.8 47.4 57.0 66.8 77.1 88.4 100.0 113.0

1.060 1.040 1.010 0.998 0.993 0.993 0.996 1.000 1.000 1.010 1.020

960

Transport Phenomena in Multiphase Systems

Table B.8 Volume expansion coefficients for liquids (Mills, 1999) Liquid Ammonia Engine oil (SAE 50) Ethylene glycol C2H4(OH)2 Refrigerant-22

Refrigerant-134a

Glycerin C3H5(OH)3

T (K) 293 273 430 273 373 250 260 270 280 290 300 310 320 330 340 350 230 240 250 260 270 280 290 300 310 320 330 340 350 280 300 320

ȕ × 103 (1/K) 2.45 0.70 0.70 0.65 0.65 2.27 2.41 2.58 2.78 3.03 3.35 3.75 4.30 5.09 6.34 8.64 2.00 2.09 2.20 2.32 2.47 2.65 2.86 3.13 3.48 3.95 4.61 5.60 7.32 0.47 0.48 0.50

Liquid Hydrogen Mercury Nitrogen

Oxygen Sodium Therminol® 60

T (K) 20.3 273 550 70 77.4 80 90 100 110 120 89 366 230 250 300 350 400 450 500 550

ȕ × 103 (1/K) 15.1 0.18 0.18 4.9 5.7 5.9 7.2 9.0 12 24 2.0 0.27 0.79 0.75 0.70 0.70 0.76 0.84 0.96 1.1

Table B.9 Density and volume expansion coefficients of water (Mills, 1999) T (K)

ȡ (kg/m3)

ȕ ×106 (1/K)

T (K)

ȡ (kg/m3)

ȕ ×106 (1/K)

273.15 274.00 275.00 276.00 277.00 278.00 279.00 280.00 285.00 290.00 295.00 300.00 310.00

999.8679 999.9190 999.9628 999.9896 999.9999 999.9941 999.9727 999.9362 999.5417 998.8281 997.8332 996.5833 993.4103

-68.05 -51.30 -32.74 -15.30 1.16 16.78 31.69 46.04 114.1 174.0 227.5 276.1 361.9

320.00 330.00 340.00 350.00 360.00 370.00 373.15 380.00 390.00 400.00 450.00 500.00

989.12 984.25 979.43 973.71 967.12 960.61 957.85 953.29 945.17 937.21 890.47 831.26

436.7 504.0 566.0 624.4 697.9 728.7 750.1 788 841 896 1129 1432

Appendix B. Transport Properties

961

Table B.10 Aluminum T Temp. K

ȡ density (kg/m³)

100 150 200 250 300 400 600 800

2732 2726 2719 2710 2701 2681 2639 2591

Aluminum, Al, Tm = 933 K (Rohsenow et al., 1985) k c thermal conductivity specific heat (W/m-K) (kJ/kg-K) 0.481 0.683 0.797 0.859 0.902 0.949 1.042 1.134

300 250 237 235 237 240 231 218

Table B.11 Aluminum alloy, 2024-T6

T Temp. K

Aluminum Alloy, 2024-T6, Tm = 775 K (Incropera and DeWitt, 2001) (4.5% Cu, 1.5% Mg, 0.6% Mn) k c ȡ thermal conductivity specific heat density (W/m-K) (kJ/kg-K) (kg/m³)

100 200 300 400 600

0.473 0.787 0.875 0.925 1.042

2770

65 163 177 186 186

Table B.12 Cartridge brass Cartridge brass, Tm = 1188 K (Incropera and DeWitt, 2001) c ȡ specific heat density (kJ/kg-K) (kg/m³)

T Temp. K 100 200 300 400 600

75 95 110 137 149

0.360 0.380 0.395 0.425

8530

k thermal conductivity (W/m-K)

Table B.13 Copper T Temp. K 100 150 200 250 300 400 600 800 1000 1200

962

Copper, Cu, Tm = 1358 K (Rohsenow et al., 1985) c ȡ specific heat density (kJ/kg-K) (kg/m³) 9009 8992 8973 8951 8930 8884 8787 8642 8568 8458

Transport Phenomena in Multiphase Systems

0.254 0.323 0.357 0.377 0.386 0.396 0.431 0.448 0.446 0.480

k thermal conductivity (W/m-K) 480 429 413 406 401 393 379 366 352 339

Table B.14 Fused silica T Temp. K

Silicon dioxide, SiO, Tm = 1883 K (Incropera and DeWitt, 2001) k c ȡ thermal conductivity specific heat density (W/m-K) (kJ/kg-K) (kg/m³)

100 200 300 400 600 800 1000 1200

2220

0.745 0.905 1.040 1.105 1.155 1.195

0.69 1.14 1.38 1.51 1.75 2.17 2.87 4.00

Table B.15 Inconel® X-750

T Temp. K 100 200 300 400 600 800 1000 1200 1500

Inconel X-750, Tm = 1665 K (Incropera and DeWitt, 2001) (73% Ni, 15% Cr, 6.7% Fe) c ȡ specific heat density (kJ/kg-K) (kg/m³) 8510

0.372 0.439 0.473 0.510 0.546 0.626

k thermal conductivity (W/m-K) 8.7 10.3 11.7 13.5 17.0 20.5 24.0 27.6 33.0

Table B.16 Iron T Temp. K 100 150 200 250 300 400 600 800 1000 1200 1400 1600 1800

Iron, Fe, Tm = 1810 K (Rohsenow et al., 1985) c ȡ specific heat density (kJ/kg-K) (kg/m³) 7900 7890 7880 7870 7860 7830 7760 7690 7650 7620 7520 7420 7420

0.216 0.324 0.384 0.422 0.450 0.491 0.555 0.692 1.034

k thermal conductivity (W/m-K) 134 104 94 87 80 70 55 43 32 28 31

Appendix B. Transport Properties

963

Table B.17 Molybdenum T Temp. K 100 150 200 250 300 400 500 600 800 1000 1200 1400

Molybdenum, Mo, Tm = 2892 K (Rohsenow et al., 1985) c ȡ specific heat density (kJ/kg-K) (kg/m³) 10260 10250 10250 10250 10240 10220 10210 10190 10160 10120 10080 10040

0.140 0.196 0.223 0.241 0.248 0.261 0.268 0.274 0.280 0.292

k thermal conductivity (W/m-K) 180 149 143 140 138 134 130 126 118 112 105 100

Table B.18 Nickel T Temp. K 100 150 200 250 300 400 600 800 1000 1200 1400 1600

Nickel, Ni, Tm = 1728 K (Rohsenow et al., 1985) ȡ c density specific heat (kg/m³) 8960 8940 8930 8910 8900 8860 8780 8690 8610 8510 8410 8320

(kJ/kg-K) 0.323 0.329 0.383 0.416 0.444 0.490 0.590 0.530 0.556 0.582

k thermal conductivity (W/m-K) 165 120 105 98 91 80 66 68 72 76 80

Table B.19 Niobium T Temp. K 100 150 200 250 300 400 500 600 800 1000 1200 1400

964

Niobium, Nb, Tm = 2740 K (Rohsenow et al., 1985) ȡ c density specific heat (kg/m³) (kJ/kg-K) 8600 0.202 8590 0.238 8580 0.254 8570 0.263 8570 0.268 8550 0.272 8530 0.277 8510 0.281 8470 0.290 8430 0.298 8380 0.307 8340

Transport Phenomena in Multiphase Systems

k thermal conductivity (W/m-K) 55 53 53 53 54 55 57 58 61 64 68 71

Table B.20 Plain carbon steel Plain Carbon Steel, Tm=1480 °C (Incropera and DeWitt, 2001)

T Temp. K

ȡ density (kg/m³)

c specific heat (kJ/kg-K)

k thermal conductivity (W/m-K)

300 400 600 800 1000

7854

0.434 0.487 0.559 0.685 1.169

60.5 56.7 48.0 39.2 30.0

Table B.21 Stainless steel 304 Stainless Steel 304, Tm = 1670 K (Incropera and DeWitt, 2001)

T Temp. K 100 200 300 400 600 800 1000 1200 1500

ȡ density (kg/m³) 7900

c specific heat (kJ/kg-K)

k thermal conductivity (W/m-K)

0.272 0.402 0.477 0.515 0.557 0.582 0.611 0.640 0.682

9.2 12.6 14.9 16.6 19.8 22.6 25.4 28.0 31.7

Table B.22 Tantalum T Temp. K 100 150 200 250 300 400 500 600 800 1000 1200 1400

Tantalum, Ta, Tm = 3252 K (Rohsenow et al., 1985) ȡ c density specific heat (kg/m³) (kJ/kg-K) 16490 0.108 16480 0.125 16460 0.132 16450 0.137 16440 0.141 16410 0.145 16370 0.148 16340 0.149 16270 0.152 16200 0.160 16130 16060

k thermal conductivity (W/m-K) 59 58 58 57 58 58 59 59 59 60 61 62

Appendix B. Transport Properties

965

Table B.23 Titanium T Temp. K 100 150 200 250 300 400 600 800 1000 1200 1400 1600

Titanium, Ti, Tm = 1953 K (Rohsenow et al., 1985) ȡ c density specific heat (kg/m³) (kJ/kg-K) 4510 0.295 4515 0.406 4520 0.464 4515 0.501 4510 0.525 4490 0.555 4470 0.597 4440 0.627 4410 0.652 4380 4350 4320

k thermal conductivity (W/m-K) 31 27 25 23 21 20 19 19 21 22 24

Table B.24 Tungsten T Temp. K 100 150 200 250 300 400 500 600 800 1000 1200 1400

966

Tungsten, W, Tm = 3660 K (Rohsenow et al., 1985) ȡ c density specific heat (kg/m³) (kJ/kg-K) 19310 0.089 19300 0.113 19290 0.125 19280 0.131 19270 0.135 19240 0.137 19220 0.139 19190 0.140 19130 0.144 19080 0.148 19020 18950

Transport Phenomena in Multiphase Systems

k thermal conductivity (W/m-K) 208 192 185 180 174 159 146 137 125 118 112 108

967 Transport Phenomena in Multiphase Systems

Table B.25 Phase Change Materials (PCMs)

PCMs

n-Tetradecane a n-Hexadecane b n-Octadecane c n-Eicosane b Gallium d Aluminum c Water f Acetic Acid a Sodium Hydrogen Phosphate Dodecahydrate a a

hsA

latent heat (kJ/kg)

ȡs solid density (kg/m³)

ȡƐ liquid density (kg/m³)

5.5 18.2 27.5 36.40 29.78 660.4 0 16.7

226 228.9 244 247.3 80.16 395 333.7 g 187

825 833 814 a 815 6095 2702 920 1214

771 774 774 a 780 6093 2380 e 1000 1050

36

280

1520

1446

chemical formula

Tm melting point (°C)

C14H30 C16H34 C18H38 C20H42 Ga Al H2O CH3COOH Na2HPO4· 12H2O

ȝƐ liquid viscosity G (10-3 N-s/m²)

ks solid thermal conductivityG (W/mK)

3.9

0.358

1.81 1.3 1.75 1.31

33.5 238 1.88

0.514

kƐ liquid thermal conductivityG (W/mK)

cp,s solid specific heat (kJ/kg-K)

cp,Ɛ liquid specific heatG (kJ/kg-K)

ȕ liquid thermal expansion coefficient (10-41/K)

0.15 0.1505 0.152 0.150 32.0 94.03 0.569 0.l8

1.80 2.15 1.92 340 c 1.076 2.04 2040

2.31 2.18 2.46 381.5 1.08 4.23 1960

8.5 8.5 1.2 1.2 -0.6805

0.476

1690

1940

4.35

Hale et al. (1971); b Humphries and Griggs (1977); c Bennon and Incropera (1988); d Brent et al. (1990); e Iida and Guthrie (1988); f Incropera and DeWitt (2001); g Cengel and Boles (2002)

968 Transport Phenomena in Multiphase Systems

Table B.26 Thermophysical properties at saturation for acetone

a

T Temp. ˚C

pv saturation pressure (105 Pa)

-40 -20 0 20 40 60 80 100 120 140

0.01 0.03 0.10 0.27 0.60 1.15 2.15 4.43 6.70 10.49

hAv latent heat (kJ/kg) 660.0 615.6 564.0 552.0 536.0 517.0 495.0 472.0 426.1 394.4

Acetone, (CH)2CO, Molecular Mass: 58.1, (Tsat = 56.25 ˚C; Tm = -93.15 ˚C; Dunn and Reay, 1982) ȝv kƐ ı ȡƐ ȡv ȝƐ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface G G (kg/m³) (kg/m³) (10-3 (10-7 conductivityG conductivityaG tensionG N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3N/m) 860.0 845.0 812.0 790.0 768.0 744.0 719.0 689.6 660.3 631.8

0.03 0.10 0.26 0.64 1.05 2.37 4.30 6.94 11.02 18.61

0.800 0.500 0.395 0.323 0.269 0.226 0.192 0.170 0.148 0.132

68.0 73.0 78.0 82.0 86.0 90.0 95.0 98.0 99.0 103.0

Interpolation from Rohsenow et al. (1985); b Interpolation from Vargaftik (1975)

0.200 0.189 0.183 0.181 0.175 0.168 0.160 0.148 0.135 0.126

0.0082 0.0096 0.0110 0.0126 0.0143 0.0161 0.0178 0.0195 0.0215

31.0 27.6 26.2 23.7 21.2 18.6 16.2 13.4 10.7 8.1

cp,Ɛ liquid specific heat bG (kJ/kg-K)

cp,v vapor specific heat a (kJ/kg-K)

2.04 2.07 2.11 2.16 2.22 2.29 2.39 2.49 2.61 2.77

1.109 1.160 1.215 1.271 1.328 1.386 1.444 1.502 1.560 1.616

Table B.27 Thermophysical properties at saturation for ammonia

Appendix B. Transport Properties 969

a

T Temp. K

pv saturation pressure (106 Pa)

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390

0.008646 0.017746 0.033811 0.060439 0.10226 0.16496 0.25529 0.38100 0.55077 0.77413 1.0614 1.4235 1.8721 2.4196 3.0789 3.8641 4.7902 5.8740 7.1352 8.5977

Carey (1992)

hAv latent heat (kJ/kg) 1477 1451 1425 1398 1369 1339 1307 1273 1237 1198 1159 1113 1066 1014 958 895 825 745 649 529

Ammonia, NH3, Molecular Mass: 17.0, (Tsat = 239.9 K; Tm = 195.5 K; ASHRAE, 2001) ȝv kƐ ȡƐ ȡv ȝƐ kv liquid vapor liquid vapor liquid vapor density density viscosity viscosity thermal thermal G G (kg/m³) (kg/m³) (10-6 (10-6 conductivityG conductivityG N-s/m²) N-s/m²) (W/m-K) (W/m-K) 728.9 0.08899 407 7.64 0.709 717.5 0.1746 369 8.02 0.685 705.8 0.3190 334 8.40 0.661 0.0158 693.7 0.5489 302 8.78 0.638 0.0171 681.4 0.8972 273 9.16 0.615 0.0184 668.9 1.404 245 9.54 0.592 0.0199 656.1 2.115 220 9.93 0.569 0.0211 642.9 3.086 197 10.31 0.546 0.0224 629.2 4.380 176 10.70 0.523 0.0239 615.0 6.071 157.7 11.07 0.500 0.0256 600.2 8.247 141.0 11.45 0.477 0.0277 584.6 11.01 126.0 11.86 0.454 0.0302 568.2 14.51 113.4 12.29 0.431 0.0332 550.9 18.89 101.9 12.74 0.408 0.0368 532.4 24.40 92.1 13.22 0.385 0.0415 512.3 31.34 83.2 13.74 0.361 0.0467 490.3 40.18 75.4 14.35 0.337 0.0536 465.5 51.65 68.5 15.07 0.313 0.0614 436.5 67.16 61.1 15.96 0.286 0.0700 400.2 89.85 50.3 17.14 0.254 0.0800

ı liquid surface G tension a (10-3N/m)

33.9 31.5 29.2 26.9 24.7 22.4 20.2 18.0 15.9 13.7 11.7 9.60 7.67 5.74 3.98 2.21

cp,Ɛ liquid specific heatG (kJ/kg-K) 4.606 4.375 4.346 4.382 4.431 4.483 4.539 4.597 4.662 4.734 4.815 4.909 5.024 5.170 5.366 5.639 6.042 6.677 7.795 10.27

cp,v vapor specific heat a (kJ/kg-K) 1.979 2.033 2.083 2.151 2.237 2.343 2.467 2.611 2.776 2.963 3.180 3.428 3.725 4.088 4.545 5.144 5.978 7.217 9.312 13.86

970 Transport Phenomena in Multiphase Systems

Table B.28 Thermophysical properties at saturation for cesium

a

hAv

T Temp. K

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

500 600 700 800 900 1000 1100 1200 1300 1400 1500

0.0003 0.0056 0.0437 0.2026 0.6580 1.6800 3.6000 6.7700 11.5100 18.0200 26.7200

544.30 534.20 523.30 511.60 499.50 486.50 472.60 458.80 444.60 429.98 415.40

Cesium, Cs, Molecular Mass: 132.9, (Tsat = 943 K; Tm = 201.6 K; Ivanovskii, et al., 1982) ȡv ȝƐ ȝv kƐ ı ȡƐ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface G G G (103 (10-3 (10-4 (10-5 conductivityG conductivity aG tension kg/m³) kg/m³) N-s/m²) N-s/m²) (10-3N/m) (W/m-K) (W/m-K) 1.723 9.91 3.181 1.460 18.79 61.9 1.666 15.50 2.558 1.668 19.02 0.00530 57.1 1.609 105.20 2.163 1.893 18.79 0.00631 52.3 1.552 433.60 1.890 2.124 18.33 0.00724 47.5 1.495 1275.90 1.690 2.336 17.51 0.00807 42.7 1.438 2990.40 1.536 2.567 16.47 0.00878 37.9 1.377 5924.10 1.415 2.782 15.49 0.00942 33.1 1.311 10364.80 1.316 2.995 13.57 0.01000 28.3 1.243 16520.70 1.234 3.198 11.60 0.01060 23.5 1.174 24307.20 1.164 3.398 9.39 0.01110 18.0 1.102 34048.30 1.104 3.589 7.50 0.01150 14.0

cp,Ɛ liquid specific heat aG (kJ/kg-K) 0.232 0.224 0.219 0.217 0.222 0.231 0.239 0.248 0.256

cp,v vapor specific heat a (kJ/kg-K) 0.1982 0.2344 0.2645 0.2821 0.2878 0.2850 0.2776 0.2681 0.2582

cp,Ɛ liquid specific heatG (kJ/kg-K) 1.88 2.14 2.34 2.60 2.76 2.89 3.01

cp,v vapor specific heat (kJ/kg-K)

Vargaftik (1975)

Table B.29 Thermophysical properties at saturation for Dowtherm®

и

hAv

T Temp. ˚C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

100 150 200 250 300 350 400

0.006 0.051 0.245 0.843 2.330 5.200 10.43

345 329 314 291 264 235 207

Diphenyl mixture (Dowtherm ), Molecular Mass: 166.0, (Tsat= 258 °C; Tm = 12 °C; Vargaftik, 1975) ȝv kƐ ȝƐ kv ı ȡƐ ȡv liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-5 (10-5 conductivityG conductivityG tension (kg/m³) (kg/m³) N-s/m²) N-s/m²) (10-3N/m) (W/m-K) (W/m-K) 995 0.035 101.0 0.68 0.126 31.6 953 0.24 60.3 0.77 0.119 26.5 912 0.99 40.7 0.87 0.110 21.8 871 3.20 29.7 0.97 0.104 17.3 825 8.70 22.7 1.07 0.096 12.9 772 20.0 18.2 1.17 0.090 8.9 709 42.0 14.9 1.26 0.083 5.0

Dowtherm is an eutectic mixture of 73.5% phenulether and 26.5% diphenyl

Table B.30 Thermophysical properties at saturation for ethane Ethane, C2H6, Molecular Mass: 30.1, (Tsat= -88.6 °C; Tm = -183.3 °C; Ivanovskii et al., 1982)

a

T Temp. ˚C

pv saturation pressure (105 Pa)

-120 -100 -80 -60 -40 -20 0 20

0.096 0.600 1.700 3.700 7.200 14.000 25.000 38.000

latent heat (kJ/kg)

ȡƐ liquid density (kg/m³)

ȡv vapor density (kg/m³)

ȝƐ liquid viscosity G (10-7 N-s/m²)

ȝv vapor viscosity G (10-7 N-s/m²)

kƐ liquid thermal conductivityG (W/m-K)

530 506 480 450 414 368 304 200

582 562 540 516 488 454 414 360

0.230 0.921 2.600 6.200 12.700 25.500 46.000 85.000

2580 1800 1360 1100 900 760 660 600

49.0 55.0 61.0 67.0 73.0 79.0 85.5 91.0

0.149 0.137 0.125 0.113 0.100 0.088 0.077 0.066

hAv

kv vapor thermal conductivity aG (W/m-K)

ı liquid surface G tension -3 (10 N/m)

cp,Ɛ liquid specific heatG (kJ/kg-K)

cp,v vapor specific heat (kJ/kg-K)

0.0116 0.0138 0.0160 0.0185 0.0209

21.23 17.93 14.60 11.30 8.00 4.60 1.20 0.08

2.82 2.94 3.05 3.16 3.26 3.38 3.48

1.297 1.349 1.401 1.459 1.521 1.585 1.660 1.736

Interpolation (Rohsenow et al., 1985)

Table B.31 Thermophysical properties at saturation for ethanol Ethanol, C2H5OH, Molecular Mass: 46.0, (Tsat = 78.3 °C; Tm = -114.5 °C; Ivanovskii et al., 1982)

Appendix B. Transport Properties 971

a

T Temp. ˚C

pv saturation pressure (105 Pa)

0 20 40 60 80 100 120 140 160 180 200 220 240

0.012 0.058 0.180 0.472 1.086 2.260 4.290 7.530 12.756 19.600 29.400 42.800 60.200

latent heat (kJ/kg)

ȡƐ liquid density (103 kg/m³)

ȡv vapor density (kg/m³)

ȝƐ liquid viscosity G (10-3 N-s/m²)

ȝv vapor viscosity G (10-5 N-s/m²)

kƐ liquid thermal conductivityG (W/m-K)

kv vapor thermal conductivity aG (W/m-K)

ı liquid surface G tension (10-3N/m)

cp,Ɛ liquid specific G heat b (kJ/kg-K)

cp,v vapor specific heat c (kJ/kg-K)

1048.4 1030.0 1011.9 988.9 960.0 927.0 885.5 834.0 772.9 698.8 598.3 468.5 280.5

0.901 0.800 0.789 0.770 0.757 0.730 0.710 0.680 0.650 0.610 0.564 0.510 0.415

0.036 0.085 0.316 0.748 1.430 3.410 6.010 10.670 17.450 27.650 44.480 74.350 135.500

1.7990 1.1980 0.8190 0.5880 0.4320 0.3180 0.2430 0.1900 0.1500 0.1200 0.0950 0.0725 0.0488

0.774 0.835 0.900 0.959 1.030 1.092 1.157 1.219 1.293 1.369 1.464 1.618 1.948

0.183 0.179 0.175 0.171 0.169 0.167 0.165 0.163 0.161 0.159 0.157 0.155 0.153

0.0117 0.0139 0.0160 0.0179 0.0199 0.0219 0.0238 0.0256 0.0272 0.0288 0.0395 0.0321

24.4 22.8 21.0 19.2 17.3 15.5 13.4 11.2 9.0 6.7 4.3 2.2 0.1

2.27 2.40 2.57 2.78 3.03 3.30 3.61 3.96

1.34 1.40 1.48 1.54 1.61 1.68 1.75

hAv

Interpolation from Rohsenow et al. (1985); b Interpolation from Vargaftik (1975); c Dunn and Reay (1982)

972 Transport Phenomena in Multiphase Systems

Table B.32 Thermophysical properties at saturation for Freon®-113

a

hAv

T Temp. ˚C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-30 -20 0 10 30 50 70

0.0283 0.0905 0.1500 0.2387 0.5420 1.0943 2.0120

166.88 161.48 158.68 155.83 149.93 143.82 137.46

Freon-113, C2F3Cl3, Molecular Mass: 187.4, (Tsat = 47.68 °C; Tm = -36.6 °C; Vargaftik, 1975) ȝv kƐ kv ȝƐ ı ȡv ȡƐ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-3 (10-7 conductivity aG conductivityG tension (103 kg/m³) (kg/m³) -3 N-s/m²) N-s/m²) (10 N/m) (W/m-K) (W/m-K) 1.687 0.2639 1.670 89.4 0.0889 25.3 1.643 0.7800 1.130 94.2 0.0867 22.8 1.621 1.2510 0.948 96.7 0.0822 21.5 1.598 1.9300 0.780 99.0 0.0799 20.6 1.554 4.1500 0.590 104.0 0.0754 18.1 1.508 8.0000 0.475 108.5 0.0709 0.00866 16.0 1.455 14.3000 0.401 113.0 0.0664 13.9

cp,Ɛ liquid specific G heat a (kJ/kg-K) 0.855 0.882 0.921 0.937 0.962 0.986 1.004

cp,v vapor specific heat a (kJ/kg-K) 0.587 0.597 0.621 0.627 0.647 0.667 0.689

cp,Ɛ liquid specific G heat (kJ/kg-K) 0.932 0.948 0.968 0.990 1.014 1.038 1.066 1.100

cp,v vapor specific heat (kJ/kg-K) 0.553 0.585 0.617 0.651 0.686 0.724 0.767 0.816

ASHRAE (2001)

Table B.33 Thermophysical properties at saturation for Freon®-123 hAv

T Temp. ˚C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-60 -40 -20 0 20 40 60 80

0.0081 0.0358 0.1200 0.3265 0.7561 1.5447 2.8589 4.8909

204.20 196.63 189.11 181.44 173.44 164.95 155.73 145.54

Freon-123, CHCl2CF3, Molecular Mass: 152.9, (Tsat = 27.8 °C; Tm = -107 °C; ASHRAE, 2001) ȝv kƐ ȝƐ kv ı ȡv ȡƐ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-3 (10-7 conductivityG conductivityG tension 3 (10 kg/m³) (kg/m³) -3 N-s/m²) N-s/m²) (10 N/m) (W/m-K) (W/m-K) 1.665 0.070 1.383 75.0 0.1020 0.00435 25.78 1.620 0.283 0.986 83.1 0.0961 0.00549 23.19 1.574 0.880 0.735 90.9 0.0898 0.00661 20.66 1.526 2.242 0.565 98.4 0.0837 0.00774 18.18 1.477 4.905 0.443 105.6 0.0778 0.00889 15.77 1.425 9.629 0.352 112.6 0.0724 0.01008 13.43 1.370 17.331 0.284 119.4 0.0673 0.01134 11.16 1.311 29.189 0.231 126.3 0.0626 0.01273 8.97

Table B.34 Thermophysical properties at saturation for Freon®-134a hAv

T Temp. ˚C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-60 -40 -20 0 20 40 60

0.1591 0.5121 1.3273 2.9280 5.7171 10.166 16.818

237.95 225.86 212.91 198.60 182.28 163.02 139.13

Freon-134a, CF3CH2F, Molecular Mass: 102.0, (Tsat = -26.4°C; Tm = -101 °C; ASHRAE, 2001) ȝv kƐ ȝƐ kv ı ȡv ȡƐ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-3 (10-7 conductivityG conductivityG tension 3 (10 kg/m³) (kg/m³) N-s/m²) N-s/m²) (10-3N/m) (W/m-K) (W/m-K) 1.474 0.9268 0.663 83.0 0.121 0.00656 20.80 1.418 2.769 0.472 91.2 0.111 0.00817 17.60 1.358 6.785 0.353 99.2 0.101 0.00982 14.51 1.295 14.428 0.271 107.3 0.0920 0.01151 11.56 1.225 27.778 0.211 115.81 0.0833 0.01333 8.76 1.147 50.075 0.163 125.5 0.0747 0.01544 6.13 1.053 81.413 0.124 137.9 0.0661 0.01831 3.72

cp,Ɛ liquid specific G heat (kJ/kg-K) 1.223 1.255 1.293 1.341 1.405 1.498 1.660

cp,v vapor specific heat (kJ/kg-K) 0.692 0.749 0.816 0.897 1.001 1.145 1.387

cp,Ɛ liquid specific G heat a (kJ/kg-K)

cp,v vapor specific heat a (kJ/kg-K) 0.501 0.523 0.545 0.566 0.588 0.606 0.623 0.641 0.659 0.677

Table B.35 Thermophysical properties at saturation for Freon®-21

Appendix B. Transport Properties 973

a

hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-60 -40 -20 0 20 40 60 80 100 120

0.0253 0.0954 0.2847 0.7085 1.5300 2.955 5.216 8.567 13.283 19.666

269 262 253 243 232 220 206 191 174 155

Freon-21, CHFCl2, Molecular Mass: 102.9, (Tsat = 8.90 °C; Tm = -135 °C) (Vargaftik, 1975) ȝv kƐ ı kv ȝƐ ȡv ȡƐ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-3 (10-7 conductivityG conductivity aG tension 3 (10 kg/m³) (kg/m³) -3 N-s/m²) N-s/m²) (10 N/m) (W/m-K) (W/m-K) 1.554 0.147 0.849 89 0.132 29.81 1.510 0.510 0.597 95 0.123 26.99 1.470 1.410 0.444 100 0.116 24.17 1.420 3.310 0.345 106 0.109 21.35 1.380 6.810 0.272 112 0.102 18.35 1.330 12.690 0.229 118 0.095 0.0094 15.71 1.280 21.930 0.200 124 0.087 0.0104 12.89 1.220 35.710 0.195 130 0.080 0.0113 10.07 1.160 55.860 0.180 136 0.072 0.0122 7.25 1.080 85.470 0.170 142 0.060 0.0132 4.43

Interpolation from Rohsenow et al. (1985)

0.994 1.015 1.048 1.093 1.149

974 Transport Phenomena in Multiphase Systems

Table B.36 Thermophysical properties at saturation for Freon®-22

a

hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-100 -80 -60 -40 -20 0 20 40 60

0.0199 0.1034 0.3752 1.0540 2.4560 4.9830 9.0970 15.3150 24.2360

269.29 257.43 245.42 232.92 219.40 204.28 186.89 166.22 139.94

Freon-22, CHF2Cl, Molecular Mass: 86.5, (Tsat = -40.8 °C; Tm = -160 °C; Vargaftik, 1975) ȝv kƐ ȝƐ ȡƐ kv ı ȡv liquid liquid vapor liquid vapor liquid vapor density viscosity viscosity thermal thermal surface density G G G (103 (10-4 (10-7 conductivityG conductivityG tension a (10-3 (kg/m³) kg/m³) N-s/m²) N-s/m²) N/m) (W/m-K) (W/m-K) 1.557 0.1196 6.00 80.0 0.1487 0.00446 28.1 1.514 0.561 5.00 87.5 0.1385 0.00525 24.8 1.465 1.865 4.14 95.0 0.1283 0.00612 21.5 1.412 4.885 3.49 101.7 0.1181 0.00831 18.5 1.351 10.821 3.02 110.4 0.1079 0.00929 15.0 1.285 21.285 2.67 118.7 0.0977 0.01026 11.7 1.214 38.550 2.40 126.8 0.0875 0.01123 8.7 1.132 66.225 2.19 134.5 0.0772 0.01221 5.8 1.030 111.65 2.00 142.1 0.0646 0.01318 3.3

cp,Ɛ liquid specific G heat (kJ/kg-K) 1.075 1.083 1.091 1.105 1.130 1.171 1.232 1.319 1.526

cp,v vapor specific heat (kJ/kg-K) 0.497 0.528 0.564 0.611 0.654 0.741 0.854 0.994 1.243

cp,Ɛ liquid specific G heat b (kJ/kg-K) 5.18 2.49 3.99 11.5

cp,v vapor specific heat (kJ/kg-K) 2.045 2.699 4.619 6.642

Ivanovskii et al. (1982)

Table B.37 Thermophysical properties at saturation for helium

a

hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-271 -270 -269 -268

0.06 0.32 1.00 2.29

22.8 23.6 20.9 4.0

Helium, He, Molecular Mass: 4.0, (Tsat = -268 °C; Tm = -271 °C; Dunn and Reay, 1982) ȝv kƐ ȝƐ kv ȡv ȡƐ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density G G (10-7 (10-8 conductivityG conductivity aG (kg/m³) (kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) 148.3 26.0 390 20 0.0181 0.00393 140.7 17.0 370 30 0.0224 0.00607 128.0 10.0 290 60 0.0277 0.00803 113.8 8.5 134 90 0.0350 0.00962

Touloukian et al. (1970); b Vargaftik (1975)

ı liquid surface tension G (10-3N/m) 0.26 0.19 0.09 0.01

Table B.38 Thermophysical properties at saturation for heptane

a

hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

-20 0 20 40 60 80 100 120 140 160

0.003866 0.0152 0.0472 0.1230 0.2800 0.5700 1.0606 1.8330 2.9790 4.5990

383.1 375.6 366.0 354.7 342.6 330.1 316.7 302.9 287.4 269.5

Heptane, C7H16, Molecular Mass: 100.2, (Tsat = 98.43 °C; Tm = -90.59 °C; Vargaftik, 1975) ȡv ȝƐ ȝv kƐ ı ȡƐ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface G G G (103 (103 (10-3 (10-7 conductivityG conductivity aG tensiona G kg/m³) kg/m³) N-s/m²) N-s/m²) (10-3N/m) (W/m-K) (W/m-K) 0.7172 0.6890 0.140 0.0084 0.7005 0.000070 0.5260 0.134 0.0099 0.6836 0.000200 0.4140 0.129 0.0115 20.86 0.6665 0.000500 0.3380 0.123 0.0132 18.47 0.6491 0.001100 0.2810 0.118 0.0151 16.39 0.6311 0.002000 0.2390 0.113 0.0170 14.35 0.6124 0.003597 0.1980 73.6 0.0189 12.47 0.5926 0.006075 0.1672 78.2 0.0207 10.63 0.5711 0.009785 0.1427 83.4 0.0228 8.87 0.5481 0.015110 0.1217 89.7 0.0251 7.19

cp,Ɛ liquid specific G heat (kJ/kg-K) 2.10 2.16 2.23 2.30 2.39 2.47 2.57 2.67 2.78 2.89

cp,v vapor specific heat b (kJ/kg-K) 0.83 0.87 0.92 0.97 1.02 1.05 1.09 1.16

Interpolation from Rohsenow et al. (1985); b Dunn and Reay (1982)

Table B.39 Thermophysical properties at saturation for lead

Appendix B. Transport Properties 975

a

hAv

T Temp. K

pv saturation pressure (102 Pa)

latent heat (kJ/kg)

1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500

0.0986 0.2108 0.4200 0.8010 1.3620 2.3100 3.7410 5.5500 8.2000 11.8500 16.7500 22.6000

920 920 920 920 920 920 920 920 920 920 920 920

Dunn and Reay (1982)

Lead, Pb, Molecular Mass: 207.2, (Tsat= 1740 °C; Tm = 327.5 °C; Ivanovskii et al., 1982) ȝv kƐ ȡƐ ȝƐ kv ı ȡv liquid liquid vapor liquid vapor liquid vapor density viscosity viscosity thermal thermal surface density G G G (103 (10-3 (10-5 conductivityG conductivityG tension (kg/m³) kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3N/m) 9.27 0.147 0.9122 7.46 347.28 9.14 0.296 0.8847 7.90 335.88 9.01 0.559 0.8586 8.34 324.48 8.89 1.011 0.8352 8.78 313.08 8.76 1.635 0.8143 9.21 301.68 8.63 2.648 0.7958 9.66 290.28 8,51 4.106 0.7794 10.10 278.88 8.37 5.817 0.7590 10.54 260.00 8.25 8.256 0.7410 10.98 248.00 8.12 11.480 0.7230 11.42 237.00 7.99 15.600 0.7050 11.86 225.00 7.86 20.280 0.6870 12.30 214.00

cp,Ɛ liquid specific G heat (kJ/kg-K)

cp,v vapor specific heat a (kJ/kg-K)

976 Transport Phenomena in Multiphase Systems

Table B.40 Thermophysical properties at saturation for lithium

a

hAv

T Temp. K

pv saturation pressure (102 Pa)

latent heat (kJ/kg)

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

0.1256 0.9680 5.1200 20.5000 65.8600 179.4000 426.5000 908.4000 1769.3000 3190.0000 5397.0000 8640.4000

21712 21400 21000 20740 20380 20020 19670 19330 18990 18670 18370 18080

Lithium, Li, Molecular Mass: 6.9, (Tsat = 1615 K; Tm = 453.7 K; Ivanovskii et al., 1982) ȝv kƐ ȝƐ ı kv ȡv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density G G G (10-4 (10-8 conductivityG conductivityaG tension (10-3 (10-3 kg/m³) N-s/m²) N-s/m²) N/m) (W/m-K) (W/m-K) 472.8 0.012 2.784 890.1 52.75 335.8 462.6 0.085 2.472 975.2 55.10 321.8 452.4 0.415 2.252 1055.0 57.42 0.120 307.8 442.2 1.540 2.072 1128.0 59.62 0.138 293.8 432.0 4.650 1.922 1213.0 61.94 0.156 279.8 421.7 11.960 1.795 1289.0 64.00 0.172 266.0 411.5 26.900 1.685 1368.0 66.50 0.183 252.0 401.3 54.610 1.590 1442.0 68.50 0.192 238.0 391.1 101.500 1.506 1518.0 71.00 0.198 226.0 380.9 175.100 1.432 1587.0 73.00 0.202 212.0 370.0 283.900 1.380 1666.0 75.50 0.207 198.0 360.0 436.300 1.300 1746.0 77.00 0.209 182.0

ȡƐ liquid density (kg/m³)

cp,Ɛ liquid specific G heat a (kJ/kg-K) 4.16 4.16 4.15 4.14 4.16 4.19 4.20 4.23 4.25 4.27 4.30 4.32

cp,v vapor specific heat a (kJ/kg-K) 6.956 8.171 9.114 9.723 10.019 10.049 9.891 9.611 9.259 8.871 8.481 8.098

cp,Ɛ liquid specific G heat a (kJ/kg-K) 0.1371 0.1355 0.1353 0.1364 0.1389 0.1427 0.1478

cp,v vapor specific heat a (kJ/kg-K) 1.04 1.04 1.04 1.04 1.04 1.04 1.04

Vargaftik (1975)

Table B.41 Thermophysical properties at saturation for mercury

a

hAv

T Temp. K

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

100 200 300 400 500 600 700

0.0003745 0.02315 0.33015 2.10240 8.2220 23.46000 54.03000

303.317 300.056 296.824 293.314 289.116 283.769 276.845

Kakac et al. (1987)

Mercury, Hg, Molecular Mass: 200.6, (Tsat= 630.1 K; Tm = 234.3 K; Ivanovskii et al., 1982) ȝv kƐ ȝƐ kv ȡv ȡƐ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density G G (10-3 (10-7 conductivityG conductivityaG (kg/m³) (kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) 13351.42 0.00242 1.241 360 9.475 13111.97 0.11800 1.039 464 10.64 12873.50 1.39100 0.926 562 11.69 0.0043 12632.60 7.57200 0.853 662 12.60 0.0058 12386.00 26.00000 0.804 762 13.39 0.0073 12130.00 66.66000 0.767 862 14.04 0.0090 11863.00 140.75000 0.739 961 14.58 0.0107

ı liquid surface tension (N/m) 0.4600 0.4360 0.4050 0.3770 0.3290 0.2989 0.2687

Table B.42 Thermophysical properties at saturation for methanol Methanol, CH4O, Molecular Mass: 32.0, (Tsat = 64.7 °C; Tm = -98 °C; Vargaftik, 1975)

a

T Temp. °C

pv saturation pressure (105 Pa)

0 20 40 60 80 100 120 140 160 180 200 220 240

0.0411 0.103 0.358 0.861 1.819 3.731 6.551 10.810 17.609 16.869 38.434 56.728 79.700

hAv latent heat (kJ/kg) 1210.0 1191.1 1163.9 1130.4 1084.4 1030.0 971.3 904.3 828.0 741.1 636.4 473.1

ȡƐ liquid density (103 kg/m³) 0.8100 0.7915 0.7740 0.7555 0.7355 0.7140 0.6900 0.6640 0.6340 0.5980 0.5530 0.4900 0.2750

ȡv vapor density (103 kg/m³)

0.0001006 0.0020840 0.0039840 0.0071420 0.0121600 0.0199400 0.0318600 0.0507500 0.0863500 0.2750000

ȝƐ liquid viscosity G (10-3 N-s/m²)

ȝv vapor viscosity G (10-7 N-s/m²)

kƐ liquid thermal conductivityaG (W/m-K)

0.8170 0.5780 0.4460 0.3470 0.2710 0.2140 0.1700 0.1360 0.1090 0.0883 0.0716 0.0583 0.0460

88 95 101 108 115 123 130 136 143 150 157 166 174

0.205 0.204 0.203 0.202 0.200 0.198 0.196 0.194

kv vapor thermal conductivityaG (W/m-K)

0.00157 0.00178 0.00199 0.00220 0.00241 0.00262 0.00283 0.00303 0.00324 0.00344

ı liquid surface tension G (10-3 N/m) 24.5 22.6 20.9 19.3 17.5 15.7 13.6 11.5 9.3 6.9 4.5 2.1

cp,Ɛ liquid specific G heat (kJ/kg-K)

cp,v vapor specific heat b (kJ/kg-K)

2.42 2.46 2.52

1.37 1.44 1.50 1.57 1.70 1.86 1.92 1.92

Touloukian et al. (1970); b Dunn and Reay (1982)

Table B.43 Thermophysical properties at saturation for nitrogen Appendix B. Transport Properties 977

a

hAv

T Temp. K

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

70 80 90 100 110 120

0.3859 1.3690 3.6000 7.7750 14.6700 25.1500

205.7 194.5 180.5 162.2 137.0 95.7

ASHRAE (2001)

Nitrogen, N2, Molecular Mass: 28.0, (Tsat= -195.65 °C; Tm = 209.85 °C; Vargaftik, 1975) ȝv kƐ ȝƐ ı kv ȡv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density G G (10-5 (10-7 conductivityG conductivityaG tension (103 kg/m³) G N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3 N/m) 0.838 0.0019 2010 48.00 0.1420 0.0066 10.53 0.790 0.0060 1390 55.20 0.1280 0.0077 8.27 0.746 0.0150 1160 62.00 0.1120 0.0091 6.16 0.691 0.0320 810 68.80 0.0955 0.0111 4.00 0.626 0.0620 740 75.60 0.0802 0.0138 2.00 0.528 0.1245 640 82.10 0.0628 0.0195 0.20

ȡƐ liquid density (103 kg/m³)

cp,Ɛ liquid specific G heat (kJ/kg-K) 1.935 1.964 2.028 2.176 2.566

cp,v vapor specific heat a (kJ/kg-K) 1.08 1.14 1.26 1.47 1.97 4.14

978 Transport Phenomena in Multiphase Systems

Table B.44 Thermophysical properties at saturation for potassium Potassium, K, Molecular Mass: 39.1, (Tsat = 1032.2 K; Tm = 336.4 K; Vargaftik, 1975) T Temp. K

pv saturation pressure (105 Pa)

600 700 800 900 1000 1100 1200 1300 1400 1500

0.0009258 0.01022 0.06116 0.2441 0.7322 1.864 3.913 7.304 12.44 20.0

latent heat (kJ/kg)

ȡƐ liquid density (kg/m³)

ȡv vapor density (10-3 kg/m³)

ȝƐ liquid viscosity G (10-4 N-s/m²)

2143 2108 2068 2023 1970 1924 1872 1820 1765 1711

766.9 743.3 719.6 695.7 671.6 647.3 622.9 598.4 573.6 548.8

0.69 6.68 36.44 134.80 380.20 871.90 1703.00 2969.10 4768.70 7062.10

2.380 1.981 1.707 1.507 1.354 1.233 1.135 1.053 0.984 0.925

hAv

ȝv vapor viscosity G (10-7 N-s/m²)

kƐ liquid thermal conductivityG (W/m-K)

kv vapor thermal conductivity aG (W/m-K)

ı liquid surface tension G (10-3N/m)

cp,Ɛ liquid specific G heat (kJ/kg-K)

134 148 163 178 196 212 228 242

43.85 40.72 37.58 34.45 31.32 28.19 25.05 22.00 19.00 16.00

0.0142 0.0175 0.0205 0.0228 0.0248 0.0266 0.0280 0.0293 0.0303

98.2 92.2 86.2 80.2 74.2 68.2 62.2 56.2 53.0 47.0

0.771 0.762 0.761 0.769 0.792 0.819 0.846 0.873 0.899 0.924

ı liquid surface tension G (10-3N/m) 81.6 75.7 69.8 63.9 58.0 51.3 44.5 37.7 30.9 26.0 19.0

cp,Ɛ liquid specific G heat (kJ/kg-K) 0.369 0.362 0.357 0.353 0.353 0.360 0.373 0.385 0.399 0.408 0.418

cp,v vapor specific heat (10-1 kJ/kgK) 0.8194 0.9646 1.066 1.116 1.121 1.100 1.064 1.022 0.9796

Table B.45 Thermophysical properties at saturation for rubidium hAv

T Temp. K

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

500 600 700 800 900 1000 1100 1200 1300 1400 1500

0.0001733 0.003664 0.03174 0.1584 0.5476 1.467 3.295 6.466 11.43 18.6 28.5

889.6 870.9 849.7 827.3 804.6 782.2 759.6 737.0 714.5 694.0 674.0

Rubidium, Rb, Molecular Mass: 85.5, (Tsat = 959.2 K; Tm = 312.7 K; Vargaftik, 1975) ȝƐ ȝv kƐ kv ȡv ȡƐ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density G G (10-4 (10-4 conductivityG conductivityG (kg/m³) ( kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) 1386 0.0003585 3.23 29.8 1340 0.006386 2.58 0.112 27.8 0.0073 1294 0.04819 2.18 0.135 25.9 0.0089 1248 0.2145 1.89 0.158 24.1 0.0103 1202 0.6726 1.69 0.183 22.2 0.0115 1156 1.658 1.53 0.208 20.3 0.0125 1110 3.437 1.40 0.244 18.5 0.0133 1064 6.274 1.30 0.268 16.7 0.0141 1018 10.36 1.21 0.289 15.0 0.0149 972 12.35 1.14 0.314 13.6 0.0156 926 22.22 1.08 0.336 12.0 0.0160

cp,v vapor specific heat (kJ/kg-K) 0.3353 0.4100 0.4679 0.4979 0.5035 0.4937 0.4762 0.4558 0.4354 0.4130 0.3900

Table B.46 Thermophysical properties at saturation for silver

a

hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500

0.01008 0.02420 0.05300 0.10800 0.20600 0.38300 0.63500 0.86000 1.36000 2.53000 3.84000

298 298 298 298 298 298 298 298 298 298 298

Brennan and Kroliczek (1979)

Silver, Ag, Molecular Mass: 107.9, (Tsat = 2212 °C; Tm = 960.5 °C; Ivanovskii et al., 1982) ȝƐ ȝv kƐ kv ı ȡv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density G G G (10-3 (10-6 conductivity a conductivityG tension ( kg/m³) G N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3N/m) 8782 0.0076 2.88 61.69 191.3 827.5 8683 0.01698 2.47 64.69 192.7 810.1 8585 0.03548 2.08 67.69 194.1 792.1 8485 0.06823 1.75 70.69 195.5 775.3 8385 0.12300 1.44 73.69 196.9 757.9 8289 0.21880 1.17 76.69 198.3 740.5 8190 0.35480 0.90 79.69 199.7 723.1 8092 0.57540 0.67 82.69 705.7 8000 0.87100 0.44 85.69 638.0 7894 1.23000 0.24 88.69 680.0 7796 1.82000 0.05 91.69 665.0

ȡƐ liquid density (kg/m³)

cp,Ɛ liquid specific G heat (kJ/kg-K)

cp,v vapor specific heat (kJ/kg-K)

Appendix B. Transport Properties 979

980 Transport Phenomena in Multiphase Systems

Table B.47 Thermophysical properties at saturation for sodium

a

hAv

T Temp. K

pv saturation pressure (102 Pa)

latent heat (kJ/kg)

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

0.047 0.951 8.760 48.760 192.200 584.280 1465.400 3165.000 6097.400 10716.600 17495.900 26919.900 39350.000

4429 4341 4237 4131 4026 3925 3829 3742 3656 3577 3500 3425 3353

Sodium, Na, Molecular Mass: 23.0, (Tsat = 1151.2 K; Tm = 371.0 K; Ivanovskii et al., 1982) ȝv kƐ kv ȝƐ ı ȡƐ ȡv liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density G G G (10-4 (10-8 conductivity conductivityaG tension -3 (kg/m³) (10 kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3N/m) 873.2 0.022 3.276 1480 75.17 172.1 849.4 0.396 2.690 1660 70.53 0.0277 162.1 825.6 3.270 2.298 1827 65.88 0.0343 152.1 801.8 16.500 2.018 2010 61.25 0.0406 142.1 778.0 59.980 1.809 2211 56.60 0.0455 132.1 754.2 168.100 1.645 2398 51.96 0.0492 122.1 730.4 396.600 1.514 2577 47.00 0.0522 112.1 706.6 804.500 1.407 2763 42.50 0.0547 102.1 682.8 1459.200 1.317 2938 37.50 0.0570 92.1 658.0 2424.800 1.240 3117 33.00 0.0592 82.0 635.2 3750.900 1.176 3281 28.50 72.0 611.4 5482.400 1.117 3449 24.00 62.0 587.6 7627.700 1.067 3620 19.00 52.0

cp,Ɛ liquid specific G heat a (kJ/kg-K) 1.30 1.27 1.26 1.25 1.26 1.27 1.29

cp,v vapor specific heat a (10-1 kJ/kg-K) 1.793 2.244 2.555 2.700 2.709 2.632 2.508 2.365 2.228 2.095

Vargaftik (1975)

Table B.48 Thermophysical properties at saturation for water hAv

T Temp. °C

pv saturation pressure (105 Pa)

latent heat (kJ/kg)

20 40 60 80 100 120 140 160 180 200

0.023368 0.073749 0.199190 0.473590 1.013250 1.985400 3.613600 6.180400 10.02700 15.55100

2453.8 2406.5 2358.4 2308.9 2251.2 2202.9 2144.9 2082.2 2014.0 1939.0

Water, H2O, Molecular Mass: 18.0, (Tsat = 100 °C; Tm = 0.0 °C; Vargaftik, 1975) ȝv kƐ kv ȝƐ ȡv liquid vapor liquid vapor vapor viscosity viscosity thermal thermal density G G G (10-7 (10-7 conductivity conductivityaG (kg/m³) N-s/m²) N-s/m²) (W/m-K) (W/m-K) 999.0 0.01729 10015 88.5 0.602 0.0188 993.05 0.05110 6513 96.6 0.630 0.0201 983.28 0.13020 4630 105.0 0.653 0.0216 971.82 0.29320 3510 113.0 0.669 0.0231 958.77 0.59740 2790 121.0 0.680 0.0248 943.39 1.12100 2300 128.0 0.685 0.0267 925.93 1.96560 1950 135.0 0.687 0.0288 907.44 3.25890 1690 142.0 0.684 0.0313 887.31 5.15970 1493 149.0 0.676 0.0341 865.05 7.86530 1338 156.0 0.664 0.0375

ȡƐ liquid density (kg/m³)

ı liquid surface tension G (10-3/m) 72.88 69.48 66.07 62.69 58.91 54.96 50.79 46.51 42.19 37.77

cp,Ɛ liquid specific G heat a (kJ/kg-K) 4.182 4.179 4.185 4.197 4.216 4.245 4.285 4.339 4.408 4.497

cp,v vapor specific heat a (kJ/kg-K) 1.874 1.894 1.924 1.969 2.034 2.124 2.245 2.406 2.615 2.883

Polynomial Temperature-Property Relation In Tables B.49 í Table B.70, coefficients for a fifth-degree polynomial temperatureproperty relation are given for each of the working fluids and properties listed in Tables Tables B.26 í Table B.48 (excluding helium). A least-squares polynomial regression method was used to derive these coefficients. Thermophysical properties given in Tables B.26 í B.48 were used with an International Math and Statistics Library subroutine, RCURV, to generate the coefficients. For properties that vary rapidly over part of the temperature range, such as vapor pressure, vapor density, and viscosity, a logarithmic transformation of the dependent variable was used to calculate the coefficients as well as a standard polynomial form (Ott, 1984). These two polynomial forms are Logarithmic: ln(φ ) = α 0 + α1T + α 2T 2 + α 3T 3 + α 4T 4 + α 5T 5

Standard: φ = α 0 + α1T + α 2T 2 + α 3T 3 + α 4T 4 + α 5T 5 where ȥ is the fluid property, Įi are the coefficients, and T is the temperature. The determination of which polynomial form to use was based on the average error between the input values and the calculated values, which was defined as 1 n φ − φˆ Average Error =

n

¦ i =1

i

i

φi

where φi is the input value (from Tables B.26 – B.48), φˆi is the calculated value of the fluid property, and n is the number of input values. This average error is given in Tables B.49 í B.70 in the column entitled Error (%). For the majority of the fluid properties, the logarithmic transformation produced the lowest average error. When the standard polynomial form is used, the superscript c is given beside the property symbol in the tables and is noted at the bottom of each table.

Transport Phenomena in Multiphase Systems 981

Table B.49 Coefficients of temperature-property relations for acetone Propertya pv (105Pa) hAv (kJ/kg)

ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚CG -40 – 140 ˚CG -40 – 140 ˚C -20 – 140 ˚CG -40 – 140 ˚CG -40 – 140 ˚CG -40 – 140 ˚CG

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error (%)

-2.3250

5.4550-2

b

-2.0375-4

-1.8017-6

3.4981-8

-1.3904-10

3.03

6.3491

-2.7168-3

2.9698-5

-1.2474-8

-4.0319-9

1.8757-11

0.65

6.7037

-1.6696-3

1.0073-6

1.2383-7

-2.1854-9

8.5364-12

0.15

-1.3402

4.2408-2

-1.7210-4

2.1825-6

-2.1680-8

7.5011-11

3.53

-9.4164-1G

-1.0496-2G

8.1436-5G

-1.7996-6G

1.7421-8G

-5.5176-11G

0.67

4.3519G

2.6016-3G

-3.5279-6G

2.1574-7G

-3.5172-9G

1.3856-11G

0.43

-1.6958

-1.1504-3

1.2496-5

-3.0675-7

2.9314-10

4.9935-12

0.30

-4.6467G

7.1871-3G

-2.0976-5G

4.6070-7G

-5.4286-9G

1.9213-11G

0.07

3.2514G

-3.9116-3G

-1.0745-5G

-4.2728-7G

4.4000-9G

-1.7122-11

0.59

7.4631-1G

1.0064-3G

6.3091-6G

3.0226-8G

-5.0475-10G

2.2060-12G

0.09

1.9452-1G

2.2900-3G

-8.6330-7G

-2.0672-8G

1.9250-10G

6.5969-13G

0.01

2

3

4

5

Polynomial function, ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 5.4550-2 signifies 5.4550×10-2

Table B.50 Coefficients of temperature-property relations for ammonia Propertya 6

pv (10 Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-6Ns/m²)G ȝv (10-6Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ıc (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a

Temp. 200 – 390 K 200 – 390 K 200 – 390 K 200 – 390 K 200 – 390 K 200 – 390 K 200 – 390 K 200 – 390 K 240 – 390 K 200 – 390 K 200 – 390 K

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error (%)

-62.865G

7.0518-1 G

-3.4742-3G

9.3187-6G

-1.3074-8G

7.5491-12G

0.20

11507

-183.01

1.3511

-4.9982-3b

9.1651-6

-6.7220-9

0.22

15.720

-1.6835-1

1.2492-3

-4.6323-6

8.5208-9

-6.2525-12

0.10

-72.638

9.5217-1

-5.3865-3

1.6458-5

-2.6195-8

1.7156-11

0.83

52.913G

-8.5184-1G

6.2226-3G

-2.2649-5

4.0580-8

-2.8649-11

1.07

-3.6761G

9.0960-2G

-6.2940-4G

2.3334-6G

-4.4046-9G

3.3532-12G

0.13

13.276G

-2.4537-1G

1.7877-3G

-6.5246-6G

1.1785-8G

-8.4743-12G

0.22

-6.8670

-4.7528-2

8.9143-4

-4.7431-6

1.0675-8

-8.6786-12

0.62

338.91G

-4.1174G

2.4029-2G

-7.3673-5G

1.1159-7G

-6.6186-11G

0.63

-14.697G

3.7537-1G

-3.2928-3G

1.3844-5G

-2.8160-8G

2.2354-11G

1.03

-57.892G

1.1165G

-8.4409-3G

3.1568-5G

-5.8318-8G

4.2728-11G

0.62

2

3

4

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 7.0518-1 signifies 7.0518×10 c Polynomial Function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b

982 Transport Phenomena in Multiphase Systems

Table B.51 Coefficients of temperature-property relations for cesium Propertya 5

pv (10 Pa)

hAv (kJ/kg) ȡƐ (10³kg/m³) ȡv (103 kg/m³) ȝƐ (104 Ns/m²)G ȝv(10-5 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G -3

ı (10 N/m)G cp,Ɛ(kJ/kg K)G cp,v(kJ/kg K)G a b

Temp. 500– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K 600– 1500 K 500– 1500 K 500– 1300 K 500– 1300 K

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-53.928G

1.8416-1 G

-2.7524-4G

2.2324-7G

-9.3633-11G

1.5913-14G

0.60

6.4024

-2.9921-4

3.7633-7

-4.8691-10

2.3849-13

-4.4136-17

0.02

6.2290-1G

2.3515-4G

-1.4219-6G

1.7272-9G

-1.0157-12G

2.1514-16G

0.04

80.341G

-4.6134-1G

1.0114-3G

-1.0297-6G

5.0263-10

-9.5176-14

12.3

3.9271G

-1.0375-2G

1.4165-5G

-1.1074-8G

4.5511-12G

-7.6390-16G

0.07

-2.5093-1G

6.4837-4G

2.5339-6G

-3.4459-9G

1.8081-12G

-3.5142-16G

0.10

-9.6746-2

1.7377-2

-3.8386-5

4.1234-8

-2.1629-11

4.3126-15

0.41

-6.8268G

2.1282-3G

4.3815-6G

-8.7917-9G

5.6219-12G

-1.2482-15G

0.05

2.5845G

1.0553-2G

-2.5491-5G

2.7594-8G

-1.4440-11G

2.8376-15G

0.51

-3.94420G

1.6920-2G

-4.2949-5G

5.0613-8G

-2.8084-11G

5.9744-15G

0.17

-1.6680G

-5.9431-3G

2.4441-5G

-3.3498-8G

1.9721-11G

-4.3077-15G

0.08

2

3

4

5

Polynomial Function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 1.8416-1 signifies 1.8416×10

Table B.52 Coefficients of temperature-property relations for Dowtherm® Propertya 5

pv (10 Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-5Ns/m²)G ȝv (10-5 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °CG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-13.659G

1.3474-1 G

-6.8307-4G

2.2792-6G

-4.1046-9G

2.9887-12G

0.27

6.2599

-9.1562-3

7.6261-5

-3.1904-7

5.9931-10

-4.2875-13

0.06

6.9789

-5.5143-4

-3.6109-6

1.9442-8

-4.6172-11

3.1349-14

0.01

-11.565

1.3514-1

-7.4914-4

2.6390-6

-4.8454-9

3.5407-12

0.05

6.5143G

-2.8763-2G

1.3375-4G

-4.3101-7G

7.6306-10G

-5.5244-13G

0.08

100– 400 °CG

-4.7238-1G

-1.7885-3G

4.1595-5G

-1.8502-7G

3.7586-10G

2.9462-13G

0.01

100– 400 °CG

-2.1714G

4.1094-3G

-4.6356-5G

1.8565-7G

-3.5315-10G

2.5537-13G

0.33

G

G

G

G

G

G

G

4.3058G

-1.7285-2G

1.4156-4G

-6.7840-7G

1.5240-9G

-1.3701-12G

0.16

-3.1706-1

2.0074-2

-1.6404-4

7.2357-7

-1.5446-9

1.2569-12

0.34

G

G

G

G

100– 400 °CG 100– 400 °C G

G 2

3

4

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 1.3474-1 signifies 1.3474×10-1

Appendix B. Transport Properties 983

Table B.53 Coefficients of temperature-property relations for ethane Propertya

Temp.

Į0G

Į1G

Į2G

Į3G

Į4 G

pv (105Pa)

-120– 20 °C

3.2181G

2.5604-2bG

-2.0481-4G

-1.6186-6G

1.1732-8G

1.9164-10G

0.42

hAv (kJ/kg)

-120– 20 °C -120– 20 °C -120– 20 °C -120– 20 °C -120– 20 °C -120– 20 °C -60– 20 °C -120– 20 °C -120– 0 °C -120– 20 °C

5.7153

-1.3766-2

-2.6378-4

-3.8474-6

-2.9487-8

-8.7228-11

0.16

6.0252

-5.5940-3

-5.4609-5

-5.7691-7

-4.0348-9

-1.1902-11

0.06

3.8345

2.9745-2

-1.0357-5

1.6498-6

1.8172-8

1.0060-10

0.66

6.4915G

-6.1186-3G

5.8535-5

5.1235-7

2.7979-9

-3.7143-12

0.20

4.4479G

3.6435-3G

-1.6045-5G

-3.3600-7G

-3.8411-9G

-1.3189-11G

0.06

-2.5644G

-7.0141-3G

-2.1420-5G

-45965-7G

-6.1947-9G

-2.4827-11G

0.08

-3.9900G

7.0307-3G

-2.4476-5G

-8.7918-7G

-1.1320-8G

G

0.01

1.9473-1G

-9.3444-2G

-1.7344-3G

-1.8129-5G

-9.1194-8G

-1.6900-10G

1.04

1.2471G

1.0319-3G

-3.4135-5G

-7.0981-7G

-6.2492-9G

-1.9064-11G

0.05

5.0629-1G

2.2657-3G

9.9616-7G

-3.3084-8G

-3.3255-10G

-8.7290-13G

0.05

ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-7Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

2

3

4

Į5 G

Error(%)

5

Polynomial Function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 2.5604-2 signifies 2.5604×10-2

Table B.54 Coefficients of temperature-property relations for ethanol Propertya pv (105Pa)

hAv

c

(kJ/kg) ȡƐ (103kg/m³) ȡv (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-5 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ıc (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a

Temp. 0– 240 °CG 0– 240 °CG 0– 240 °CG 0– 240 °C 0– 240 °CG 0– 240 °CG 0– 240 °CG 0– 220 °CG 0– 240 °CG 0– 140 °CG 0– 120 °CG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-4.4114G

8.7650-2 G

-6.3182-4G

3.9958-6G

-1.4340-8G

2.0359-11G

1.24

1048.6

-1.0921

1.0651-2

-2.0693-4

1.1231-6

-2.4928-9

0.12

-1.07911G

-7.7201-3G

1.5906-4G

-1.6139-6

7.1873-9

-1.2075-11

0.50

-3.3681

5.2492-2

5.1630-5

-1.9542-6

8.6893-9

-1.1451-11

4.95

5.8942-1G

-2.2540-2G

1.0283-4G

-8.8574-7G

4.7884-9G

-9.7493-12G

0.39

-2.57591G

4.5249-3G

-3.1212-5G

3.9144-7G

-2.3733-9G

5.1450-12G

0.29

-1.6976G

-1.2505-3G

7.5291-7G

5.2361-8G

-3.4986-10G

6.4599-13G

0.10

-4.4346G

3.3797-3G

2.1001-4G

-3.4778-6G

2.0462-8

-4.0325-11

3.75

24.419G

-8.1477-2G

-1.1450-4G

8.6540-7G

-7.6432-9G

1.9148-11G

2.15

-4.4424-10G

1.5104-12G

0.01

1.6850-8G

-5.3880-11G

0.11

0.81763

2.6793-3G

1.3888-5G

-4.385611G

2.9255-1G

1.2271-3G

8.0938-5G

-1.8513-6G

2

3

4

5

Polynomial Function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 8.7650-2 signifies 8.7650×10-2 c Polynomial Function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b

984 Transport Phenomena in Multiphase Systems

Table B.55 Coefficients of temperature-property relations for Freon®-113 Propertya pv c (105Pa) hAv (kJ/kg) ȡƐ (103kg/m³) ȡv c (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv c (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G

Temp. -30–70 °CG

Į0G 1.5513-1bG

Į1G 5.5834-3G

Į2G 1.9778-4G

Į3G 2.8601-6G

Į4 G -5.7513-8

Į5 G Error(%) 5.3363-10G 1.45

-30–70 °C

5.0647

-1.0499-3

-2.6927-5

-6.1850-7

2.7966-8

-2.3520-10

0.10

-30–70 °C

4.8109-1

-7.0767-4

-1.9487-5

-4.7513-7

2.1984-8

-1.9019-10

0.09

-30–70 °C

1.2915

4.3043-2

1.4813-3

2.0168-5

-5.0204-7

4.6851-9

1.35

-30–70 °CG

-8.8373-2G

-9.8086-3G

-2.0540-4G

-6.0984-6G

3.1638-7

-2.7593-9G

1.57

-30–70 °CG

4.5742G

1.3980-3G

3.4991-5G

9.1946-7G

-4.4771-8

3.8285-10G

0.12

-30–70 °CG

-2.4988G

-2.7661-3G

-3.9035-6G

2.0723-8G

-4.4813-10

1.8509-12G

0.01

50 °CG

8.66-3G

G

G

G

G

G

-30–70 °C

3.0672

-3.0787-3

-8.9997-5

-2.0623-6

9.4964-8

-8.0415-10

-30–70 °CG

-8.1787-2G

1.7608-3G

-1.6786-5G

2.3976-7G

-30–70 °CG

-4.7900-1G

1.6029-3G

a

-1.1241-5G 2

3

5.9003-8G 4

-8.1962-10 -1.0574-11G 5.3622-9

-5.9305-11G

0.04 0.02 0.12

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 1.5513-1 signifies 1.5513×10-1 c Polynomial function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b

Table B.56 Coefficients of temperature-property relations for Freon®-123 Propertya

Temp. -60– pv (10 Pa) 80 °CG -60– hAv (kJ/kg) 80 °C -60– ȡƐ (103kg/m³) 80 °CG -60– ȡv c (kg/m³) 80 °C -60– ȝƐ (10-3Ns/m²)G 80 °CG -60– ȝv (10-7 Ns/m²)G 80 °CG kƐ -60– (W/m-K)G 80 °CG -60– kv (W/m-K)G 80 °CG -60– ı 80 °CG (10-3 N/m)G cp,Ɛ -60– 80 °CG (kJ/kgK)G cp,v -60– 80 °CG (kJ/kgK)G 5

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-1.1195

4.5666-2

b

-1.9934-4

8.5444-7

-3.5199-9

1.1017-11

0.01

5.2009

-2.1509-3

-4.5252-6

-2.7239-8

-7.7727-11

-7.0220-13

0.00

4.2279-1

-1.5851-3

-2.6844-6

-1.1732-8

-6.3028-11

1.7371-13

0.01

2.2395

9.5368-2

1.6184-3

1.3321-5

4.9021-8

4.0765-11

0.05

-5.7105-1

-1.2631-2

2.4428-5

-1.3376-7

1.2093-9

-6.4471-12

0.04

4.5890

3.7376-3

-1.0586-5

3.4387-8

-6.7932-11

1.0880-12

0.01

-2.4809

-3.5937-3

-1.4384-6

2.9439-8

-3.4971-10

1.7944-12

0.02

-4.8616

7.3399-3

-2.2812-5

1.4868-7

-1.1456-9

8.3612-12

0.01

2.9004

-6.7246-3

-1.8095-5

-6.1639-8

-3.3005-10

-2.3405-12

0.00

-9.8440-3

1.1580-3

7.2577-7

-1.3957-8

3.0203-10

8.1384-13

0.01

-4.2964-1

2.6267-3

-6.5433-8

2.8020-8

7.5571-11

-2.5335-13

0.02

a

Polynomial function: ln(Property) = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b The notation 4.5666-2 signifies 4.5666×10-2 c Polynomial function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5

Appendix B. Transport Properties 985

Table B.57 Coefficients of temperature-property relations for Freon®-134a Propertya

Temp. -60– pv (10 Pa) 60 °CG -60– hAv (kJ/kg) 60 °C -60– ȡƐ (103kg/m³) 60 °C -60– ȡv c (kg/m³) 60 °C -60– ȝƐ (10-3Ns/m²)G 60 °CG -60– ȝv (10-7 Ns/m²)G 60 °CG -60– kƐ (W/m-K)G 60 °CG -60– kv c (W/m-K)G 60 °CG -60– ı 60 °C (10-3 N/m)G cp,Ɛ -60– 60 °CG (kJ/kgK)G cp,v -60– 60 °CG (kJ/kgK)G c

5

Į0G

Į1G

Į2G b

Į3G

Į4 G

Į5 G

Error(%)

1.4766-3

9.1273-6

1.8868-8

-1.0026-11

0.03

-3.8266-3

-1.9182-5

-1.3660-7

-1.4190-9

-1.1862-11

0.01

2.5819-1

-2.5548-3

-8.4503-6

-5.3400-8

-6.1301-10

-4.3062-12

0.01

1.4323+1

4.9951-1

7.6087-3

6.5242-5

-4.1610-8

-4.9125-9

0.56

-1.3047

-1.2721-2

1.3074-5

-3.6304-7

6.4168-10

4.3908-12

0.05

4.6756

3.8342-3

-2.6263-6

8.7893-8

5.0768-10

6.1839-12

0.00

-2.3865

-4.7587-3

-4.9980-6

-1.5376-7

-7.5506-10

2.1118-11

0.02

1.1516-2

8.6892-5

1.2320-7

2.0313-9

3.6695-11

2.8646-13

0.02

2.4473

-1.2448-2

-5.9505-5

-4.0640-7

-4.5286-9

-3.3364-11

0.01

2.9357-1

2.0423-3

1.1431-5

7.9461-8

1.4916-9

1.6785-11

0.01

-1.0828-1

5.0590-3

1.6049-5

1.1362-7

2.3121-9

2.5170-11

0.02

2.9283

1.0610-1

5.2912

a

Polynomial function: ln(Property) = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b The notation 1.0610-1 signifies 1.0610×10-1 c Polynomial function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 Table B.58 Coefficients of temperature-property relations for Freon®-21 Propertya pv (105Pa)

Temp. -60– 120 °CG

hAv

-60– 120 °C

(kJ/kg) ȡƐ (103kg/m³) ȡv (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

-60– 120 °CG -60– 120 °C -60– 120 °CG -60– 120 °CG -60– 120 °CG -40– 120 °CG -60– 120 °CG -20– 120 °CG -60– 120 °CG

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-3.4451-1bG

4.1751-2G

-1.7642-4G

7.1705-7G

-2.5411-9G

5.6934-12G

0.01

5.4933

-2.1700-3

-7.6996-6

-1.3706-8

-2.9105-10

2.2108-13

0.04

3.5332-1G

-1.5737-3G

-2.9329-6G

-8.1168-9G

4.8930-11G

-1.6497-12G

0.11

1.1960

3.9035-2

-1.5967-4

7.1148-7

-2.7682-9

8.5168-12

0.05

-1.0724G

-1.2269-2G

4.5152-5G

2.0188-7G

2.3391-9G

-2.8723-11G

0.77

4.6629G

2.7294-3G

-2.5030-7G

-1.3902-9G

-5.2580-10G

3.2451-12G

0.10

-2.2136G

-3.2496-3G

-1.2739-5G

1.8600-8G

2.1809-9G

-2.0491-11G

0.22

-4.9866G

1.0894-2G

-9.0477-5G

4.7958-7G

-8.3962-10G

0.0G

0.01

3.0590G

-6.7747-3G

-2.2547-5G

-2.2853-9

-1.7098-10

-1.5797-11

0.18

1.4889-2G

1.3267-3G

1.3973-5G

-1.0390-8G

-2.8225-10G

0.0G

0.01

-5.6775-1G

1.8572-3G

-5.0100-6G

-5.1476-9G

3.2243-10G

-1.2404-12G

0.06

2

4

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 3.4451-1 signifies 3.4451×10-1

986 Transport Phenomena in Multiphase Systems

Table B.59 Coefficients of temperature-property relations for Freon®-22 Propertya pv (105Pa)

Temp. -100– 60 °CG

hAv

-100– 60 °C

(kJ/kg) ȡƐ (103kg/m³) ȡv (kg/m³) ȝƐ (10-4Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

-100– 60 °CG -100– 60 °C -100– 60 °CG -100– 60 °CG -100– 60 °CG -100– 60 °CG -100– 60 °CG -100– 60 °CG -100– 60 °CG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

1.6060G

3.2529-2 G

-1.3092-4G

5.4844-7G

-2.3659-9G

1.7589-11G

0.02

5.3194

-3.9023-3

-2.0700-5

-1.8940-7

-1.7339-9

-7.7266-12

0.03

2.5101-1G

-2.6444-3G

-8.8462-6G

-6.2742-8

-1.0131-9

-5.4408-12

0.02

3.0582

3.1512-2

-1.0338-4

6.3370-7

-1.2757-9

2.3553-11

0.01

9.8169-1G

-5.6143-3G

2.2490-5G

-1.5992-7G

-4.0714-10G

9.5286-12G

0.07

4.7763G

3.5563-3G

-9.2066-6G

-8.9021-8G

7.9195-10G

1.1511-11G

0.14

-2.3264G

-5.1094-3G

-1.0280-5G

-1.1905-7G

-2.4990-9G

-1.4352-11G

0.09

-4.5693

4.3334-3

-3.1493-5

6.8438-7

-3.1372-10

-6.2585-11

1.60

2.4636G

-1.3560-2G

-7.1002-5G

-4.6908-7G

-5.7002-9G

-3.2763-11G

0.31

1.5887-1G

1.9513-3G

1.3013-5G

1.5071-7G

3.7021-9

2.4147-11

0.16

-3.0127-1

6.0931-3

2.9892-5

9.8627-8

1.1367-9

1.0353-11

0.51

2

4

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 3.2529-2 signifies 3.2529×10-2

Table B.60 Coefficients of temperature-property relations for heptane Propertya pv (105Pa)

Temp. -20– 160 °CG

hAv

-20– 160 °C

(kJ/kg) ȡƐ (103kg/m³) ȡv (103kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

-20– 160 °CG -0 – 160 °CG -20– 160 °CG 100– 160 °CG -20– 80 °C -20– 160 °CG -20– 160 °CG -20– 160 °CG -20– 160 °CG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-4.1875G

6.2035-2 G

-2.8899-4G

1.3328-6G

-4.8688-9G

8.7514-12G

0.07

5.9286

-1.1575-3

-8.0368-6

3.0846-8

3.8138-11

-8.8137-13

0.01

-0.35593G

-1.2011-3G

-1.1416-6G

4.0160-9G

-8.1251-11G

1.2225-13G

0.01

-9.5679G

5.4885-2G

-6.8200-5G

-2.6778-6

2.4493-8

-6.4331-11

0.81

-6.4586-1G

-1.2617-2G

5.1105-5G

-2.0879-7G

-4.8532-10G

4.0509-12G

0.38

3.8877G

6.1806-3G

-3.0481-5G

9.7703-8G

0.0G

0.0G

0.01

-2.0099

-1.6511-3

-1.7251-6

-9.2954-7

2.2360-8

-1.4260-10

0.01

-4.6160G

7.7908-3G

-1.5605-5G

1.158-7G

-1.4660-9G

5.4467-12G

0.14

3.1702G

-7.2045-3G

3.7806-5G

-4.8714-7G

2.3540-9G

-5.3416-12

0.06

7.7016-1G

1.4975-3G

3.6697-6G

-2.9931-8G

2.3965-10G

-7.3288-13G

0.07

-1.3938-1G

2.6295-3G

1.1500-5G

-1.7062-7G

-1.4205-9G

1.5923-11G

0.11

2

4

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 6.2035-2 signifies 6.2035×10-2

Appendix B. Transport Properties 987

Table B.61 Coefficients of temperature-property relations for lead Propertya pv (102Pa)

Temp. 1400– 2500 KG

hAv

1400– 2500 K

(kJ/kg) ȡƐ (103kg/m³) ȡv (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-5 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Į0G 4.6336G

Į1G -5.2565-2

b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

7.4881-5

-4.3022-8

1.1552-11

-1.1994-15

0.89

920

1400– 2500 KG 1400– 2500 K 1400– 2500 KG 1400– 2500 KG

3.6048G

-3.2801-3G

3.2902-6G

-1.7002-9G

4.3394-13G

-4.3951-17G

0.03

8.3434

-5.9172-2

8.0693-5

-4.5861-8

1.2260-11

-1.2705-15

0.83

-3.5423G

1.0984-2G

-1.2825-5G

7.0970-9G

-1.9132-12G

2.0177-16G

0.15

-6.17011G

4.9129-3G

-4.1177-6G

1.9835-9G

-4.9092-13

4.8791-17

0.02

G

G

G

G

G

G

G

G

G

G

G

G

G

G

1400– 2500 KG

25.135G

-4.9401-2G

5.0275-5G

-2.5283-8G

6.2419-12G

-6.0685-16G

G

G

G

G

G

G

G

G

G

G

G 2

G 3

4

0.32

G 5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 5.2565-2 signifies 5.2565×10-2

Table B.62 Coefficients of temperature-property relations for lithium Propertya pv (102Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (10-3kg/m³) ȝƐ (10-4Ns/m²)G ȝv (10-8 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3 N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 900– 2000 KG 900– 2000 K 900– 2000 K 900– 2000 KG 900– 2000 KG 900– 2000 KG 900– 2000 KG 1100– 2000 KG 900– 2000 KG 900– 2000 KG 900– 2000 KG

Polynomial function:

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-65.397G

1.5599-1bG

-1.5201-4G

8.1778-8G

-2.3065-11G

2.6663-15G

0.79

10.701

-2.3108-3

3.1400-6

-2.2140-9

7.5364-13

-9.9447-17

0.09

6.0669

8.3105-4

-1.5042-6

1.0686-9

-3.7709-13

5.1832-17

0.02

-68.241G

1.6057-1G

-1.6084-4G

8.8500-8G

-2.5450-11G

2.9917-15G

0.30

9.4544G

-2.7505-2G

3.6732-5

-2.5268-8

8.6852-12

-1.1841-15

0.16

2.8973G

1.1891-2G

-1.5340-5G

1.0624-8G

-3.7032-12G

5.1272-16G

0.13

4.2556G

-2.5537-3G

5.0480-6G

-4.0821-9G

1.5784-12G

-2.3730-16G

0.12

20.694G

-8.4269-2G

1.1754-4G

-7.8416-8G

2.5440-11G

-3.2371-15G

0.52

7.8595G

-7.2138-3G

1.0848-5G

-8.4472-9G

3.2074-12G

-4.7997-16G

0.11

1.4122-1G

5.1039-3G

-7.8268-6G

5.7796-9G

-2.0587-12G

2.8515-16

0.01

-3.7092G

1.2156-2G

-8.1715-6G

1.6862-9G

2.3686-13G

-9.6999-17G

0.04

2

3

4

ln(Property) = α 0 + α 1T + α 2 T + α 3 T + α 4 T + α 5 T 

The notation 1.5599-1 signifies 1.5599×10

988 Transport Phenomena in Multiphase Systems

5

Table B.63 Coefficients of temperature-property relations for mercury Propertya pv (105Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 100– 700 KG 100– 700 K 100– 700 K 100– 700 K 100– 700 KG 100– 700 KG 100– 700 K 300– 700 K 100– 700 K 100– 700 K 100– 700 KG

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-14.575G

8.4718-2G

-2.0927-4G

3.3495-7G

-2.9993-10

1.1264-13G

0.15

5.7260

-1.1371-4

6.3434-9

1.3279-10

-4.0224-13

1.4867-16

0.01

9.5173

-1.7845-4

-1.2298-8

4.1107-11

-1.2592-13

6.5094-17

0.01

-12.403

8.1209-2

-2.0418-4

3.2816-7

-2.9379-10

1.1027-13

0.13

4.9966-1G

-3.5741-3G

8.5984-6G

-1.3495-8G

1.1914-11G

-4.4337-15G

0.03

5.5053G

4.7804-3

-1.1839-5

2.3678-8

-2.5687-11

1.1088-14

0.04

2.1052G

1.5928-3G

-1.6980-6G

1.2601-9G

-7.9198-13

2.9427-16G

0.01

-8.2112G

1.8371-2G

-4.5018-5G

5.6262-8G

-2.6760-11

0.0G

0.01

-6.11231

-2.8045-3

1.5740-5

-4.7357-8

6.0220-11

-2.7769-14

0.58

-1.9647G

-2.7998-4G

5.8783-7G

-2.655810G

4.0363-13G

-2.6814-16G

0.01

3.9221-2G

0.0G

0.0G

0.0G

0.0G

0.00

0.0G 2

3

4

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 8.4718-2 signifies 8.4718×10-2

Table B.64 Coefficients of temperature-property relations for methanol Propertya pv (105Pa)

hAv (kJ/kg) ȡƐ (103kg/m³) ȡv (103 kg/m³) ȝƐ (10-3Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 0– 240 ˚CG 0– 240 ˚C 60– 220 ˚C 0– 240 ˚CG 0– 240 ˚CG 0– 240 ˚CG 0– 140 ˚CG 40– 220 ˚CG 0– 220 ˚CG 0– 40 ˚CG 0– 140 ˚CG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-3.2260G

5.2299-2 G

1.0307-4G

-2.9204-6G

1.4369-8

-2.2852-11G

3.52

7.1001

-1.6650-3

4.2482-5

-8.2591-7

5.2087-9

-1.1710-11

0.39

-2.00541

-5.5461-3

1.8492-4

-2.6081-6

1.4646-8

-2.8794-11

1.96

-67.300G

2.1944G

-3.0858-2G

2.1359-4G

-7.2014-7G

9.4732-10G

6.77

-2.05291

-1.8685-2

1.2225-4

-1.0701-6

4.5665-9

-7.2697-12

0.35

4.4794G

3.3930-3G

4.0163-6G

-7.3376-8G

2.4641-10G

-2.1042-13G

0.28

-1.5847G

-4.0650-4G

1.1186-5G

-2.2761-7G

1.6087-9G

-3.9220-12

0.03

-6.7646G

8.9038-3G

-3.5238-5G

1.4232-7G

-4.0030-10

5.0729-13G

0.03

3.2019G

-6.2365-3G

1.1123-4G

-1.7652-6G

1.0660-8G

-2.4530-11G

0.65

8.8377-1G

6.2710-4

9.6297-6

0.0

0.0

0.0

0.01

3.1404-1G

5.0100-3G

-1.7365-4G

3.4376-6G

-2.5001-8G

5.9705-11G

0.40

2

4

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 5.2299-2 signifies 5.2299×10-2

Appendix B. Transport Properties 989

Table B.65 Coefficients of temperature-property relations for nitrogen Propertya pv (105Pa)

Temp. 70–120 KG

Į0G -43.782G

Į1G 1.5669G

Į2G G -2.3774-2b

Į3G 1.9698-4G

Į4 G -8.5268-7G

Į5 G 1.5176-9G

Error(%) 0.49

hAv

70–120 K

40.773

-2.0285

4.6388-2

-5.2896-4

3.0054-6

-6.8292-9

0.22

70–120 KG

35.567G

-1.9499G

4.2463-2G

-4.6083-4G

2.4889-6G

-5.3639-9G

0.22

70–120 KG

-67.907G

2.8270G

-5.5599-2G

5.8348-4G

-3.1442-6G

6.8695-9G

0.08

70–120 KG

948.70G

-51.222G

1.1060G

-1.1838-2G

6.2780-5G

-1.3198-7G

4.14

70–120 KG

-2.9587G

2.9150-1G

-5.1900-3G

4.8252-5G

-2.2449-7G

4.1366-10G

0.03

70–120 KG

32.320G

-1.9406G

4.3870-2G

-4.9230-4G

2.7304-6G

-6.0054-9G

0.50

70–120 KG

-84.477G

4.4031G

-9.7414-2G

1.0725-3G

-5.8607-6G

1.2734-8G

3.35

70–120 KG

548.30G

-31.026G

7.0194-1G

-7.9006-3G

4.4236-5G

-9.8671-8G

0.57

70–110 KG

6.5809G

-2.9472-1G

5.5008-3G

-4.5869-5G

1.4529-7

0.0

0.05

70–120 KG

-431.10G

24.938G

-5.7258-1G

6.5396-3G

-3.7167-5G

8.4167-8G

0.10

2

4

(kJ/kg) ȡƐ (103kg/m³ ) ȡv (103 kg/m³) ȝƐ (105 Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/mK)G kv (W/mK)G ı (103 N/m)G cp,Ɛ (kJ/kgK)G cp,v c (kJ/kgK)G a

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 2.3774-2 signifies 2.3774×10 c Polynomial Function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b

Table B.66 Coefficients of temperature-property relations for potassium Propertya pv (105Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (10-3 kg/m³) ȝƐ (10-4Ns/m²)G ȝv (10-7 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3N/m)G cp,Ɛ (kJ/kgK)G cp,v (10-1kJ/kg K)G a b

Temp. 600– 1500 KG 600– 1500 K 600– 1500 K 600– 1500 KG 600– 1500 KG 800– 1500 KG 600– 1500 KG 700– 1500 KG 600– 1500 KG 600– 1500 KG 600– 1500 KG

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-60.792G

2.0072-1 G

-2.9607-4G

2.3898-7G

-1.0021-10

1.7070-14G

0.41

7.4437

1.3335-3

-2.6188-6

2.2227-9

-9.95606-13

1.6216-16

0.05

6.8171

-2.9903-4

6.4906-8

-1.128510

4.9791-14

-1.0285-17

0.01

-43.901G

1.5060-1G

-1.9914-4G

1.4552-7G

-5.6005-11

8.8657-15G

0.36

3.7145G

-9.2264-3G

1.1332-5G

-8.1123-9G

3.0732-12

-4.7794-16

0.02

-2.7247G

3.1905-2G

-5.5202-5G

4.8605-8G

-2.1075-11

3.5833-15G

0.14

4.6283G

-3.1884-3G

5.6190-6G

-6.0362-9G

3.0539-12G

-6.3262-16G

0.04

-9.5175

1.5278-2

-1.5544-5

7.1481-9

-1.0428-12

-1.0113-16

0.14

9.5646G

-2.5629-2G

5.2720-5G

-5.3832-8G

2.6602-11G

-5.1195-15G

0.51

-1.5299G

8.1223-3G

-1.9186-5G

2.0925-8G

-1.0612-11

2.0459-15G

0.11

-2.2283G

2.9093-3G

6.2200-6G

-1.3592-8G

8.6984-12G

-1.8919-15G

0.05

Polynomial function: ln(Property) = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 The notation 2.0072-1 signifies 2.0072×10-1

990 Transport Phenomena in Multiphase Systems

Table B.67 Coefficients of temperature-property relations for rubidium Propertya pv (105Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ (10-4Ns/m²)G ȝv (10-4 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 500– 1500 KG 500– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K 600– 1500 K 500– 1500 K 600– 1500 K 500– 1500 K 500– 1500 K 500– 1500 K

Į0G

Į1G b

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-55.657G

1.8743-1 G

-2.7675-4G

2.2191-7G

-9.2037-11

1.5478-14G

0.57

6.7318

6.7485-4

-1.7798-6

1.7134-9

-8.4612-13

1.6787-16

0.02

7.3881

-2.8698-4

-3.4371-8

-1.584911

3.9560-15

-2.0966-18

0.01

-66.172

2.5978-1

-4.5141-4

4.1965-7

-1.9911-10

3.7782-14

3.00

4.0558G

-1.0855-2G

1.4889-5G

-1.1567-8G

4.6581-12G

-7.5589-16G

0.12

-9.8418

3.6490-2

-7.1293-5

7.1688-8

-3.5422-11

6.8223-15

0.56

4.7043G

-6.4659-3G

1.3165-5G

-1.4204-8G

7.2430-12G

-1.4313-15G

0.17

-6.6733G

1.4823-3G

8.4641-6G

-1.5050-8G

9.5117-12G

-2.1186-15G

0.08

7.9250G

-1.9554-2G

4.3014-5G

-4.7024-8G

2.4631-11G

-5.0586-15G

0.73

-2.3892G

8.5914-3G

-1.9597-5G

2.0443-8G

-9.8727-12

1.8050-15G

0.21

-3.3670G

6.0154-3G

-5.4747-7G

-7.5127-9G

6.2261-12

-1.5185-15

0.15

2

4

3

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 1.8743-1 signifies 1.8743×10

Table B.68 Coefficients of temperature-property relations for silver

a

Propertya pv (105Pa) hAv (kJ/kg)

Temp. 1500– 2500 KG

ȡƐ (kg/m³) ȡv (kg/m³) ȝƐ c -3 (10 Ns/m²)G ȝv (10-6 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G

1500– 2500 KG 1500– 2500 KG 1500– 2500 KG 1500– 2500 KG 1500– 2100 KG

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

263.11G

-7.1135-1bG

7.2544-4G

-3.5810-7G

8.6526-11G

-8.2124-15G

3.94

8.5176

1.6679-3

-1.7069-6

8.0584-10

-1.8715-13

1.7012-17

0.02

-173.43

3.9882-1

-3.8988-4

1.9489-7

-4.8845-11

4.8792-15

4.93

-5.38641G

3.1996-2

-4.6751-5

2.7477-8

-7.5466-12

8.0128-16

1.14

2.9330G

1.2850-3G

-4.9599-7G

1.4551-10G

-2.5305-14

1.9217-18G

0.01

5.1376G

8.2034-5G

-3.2260-9G

1.2246-13G

0.0G

0.0G

0.01

G

G

G

1500– 2500 KG

3.1881G

1.7708-2G

-2.7287-5G

1.8780-8G

-6.0622-12

7.4708-16G

1.18

G

G

G

G

G

G

G 2

3

4

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation 7.1135-1 signifies 7.1135×10-1 c Polynomial Function: Property = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 b

Appendix B. Transport Properties 991

Table B.69 Coefficients of temperature-property relations for sodium Propertya pv (102Pa)

hAv (kJ/kg) ȡƐ (kg/m³) ȡv (10-3kg/m³) ȝƐ (10-4Ns/m²)G ȝv (10-8 Ns/m²)G kƐ (W/m-K)G kv (W/m-K)G ı (10-3N/m)G cp,Ɛ (kJ/kgK)G cp,v (kJ/kgK)G a b

Temp. 600– 1800 KG 600– 1800 K 600– 1800 K 600– 1800 KG 600– 1800 KG 600– 1800 KG 600– 1800 KG 700– 1500 KG 600– 1800 KG 600– 1200 KG 600– 1500 KG

Į0G

Į1G

Į2G

Į3G

Į4 G

Į5 G

Error(%)

-57.346G

1.8129-1bG

-2.2487-4G

1.5164-7G

-5.2957-11

7.5006-15

0.98

8.2271

1.1086-3

-2.1757-6

1.6631-9

-6.0973-13

8.7109-17

0.02

6.9583

-3.9865-4

2.6890-7

-2.584310

1.0321-13

-1.6518-17

0.02

-57.566

0.18157

-2.2885-4

1.5614-7

-5.5058-11

7.8615-15

1.25

4.1428G

-9.2518-3G

1.0570-5G

-6.9077-9G

2.3709-12G

-3.3213-16G

0.05

6.4857G

1.6476-3G

-6.37865-7G

3.8144-10G

-2.3380-13

5.4972-17G

0.16

6.0146G

-7.4369-3G

1.3548-5G

-1.2912-8G

5.8860-12G

-1.0619-15G

0.21

-2.9716G

-1.3227-2G

3.8083-5G

-4.1771-8G

2.0652-11G

-3.8556-15G

0.17

5.5631G

-1.0484-3G

1.1969-6G

-1.3563-9

6.7582-13

-1.4750-16

0.02

2.4330G

-1.1431-2G

2.4444-5G

-2.6701-8G

1.4701-11G

-3.2175-15G

0.13

-4.3532G

1.5451-2G

-1.5104-5G

5.0582-9G

2.9861-13G

-3.5328-16G

0.04

Polynomial function: ln(Property) = Į0 + Į1T +Į2T2 + Į3T3 + Į4T4 + Į5T5 The notation 1.8129-1 signifies 1.8129×10

Table B.70 Coefficients of temperature-property relations for water Propertya

Temp.

20– 200 ˚CG 20– hAv (kJ/kg) 200 ˚C 20– ȡƐ (kg/m³) 200 ˚C 20– ȡv (kg/m³) 200 ˚C 20– ȝƐ (10-7Ns/m²)G 200 ˚CG ȝv 20– (10-7 Ns/m²)G 200 ˚CG 20– kƐ (W/m-K)G 200 ˚CG 20– kv (W/m-K)G 200 ˚CG 20– ı 200 ˚CG (10-3N/m)G cp,Ɛ 20– 200 ˚CG (kJ/kgK)G cp,v 20– 200 ˚CG (kJ/kgK)G pv (105Pa)

a b

Į1G

Į2G

Į3G

-5.0945G

7.2280G

-2.8625-4 bG

9.2341-7G

-2.0295-9G

2.1645-12G

0.01

7.8201

-5.8906-4

-9.1355-6

8.4738-8

-3.9635-10

5.9150-13

0.05

6.9094

-2.0146-5

-5.9868-6

2.5921-8

-9.3244-11

1.2103-13

0.02

-5.3225

6.8366-2

-2.7243-4

8.4522-7

-1.6558-9

1.5514-12

0.01

9.7620G

-3.1154-2

2.0029-4

-9.5815-7

2.7772-9

-3.5075-12

0.02

4.3995G

3.8789-3G

2.1181-5G

-3.4406-7G

1.6730-9G

-2.8030-12G

0.04

-5.6528-1G

3.1743-3G

-1.4392-5G

-1.3224-8G

2.5534-10G

-6.4454-13G

0.04

-4.0406G

3.2288-3G

5.3383-6G

-6.7139-8G

4.0967-10G

-6.9579-13G

0.07

4.3438G

-3.0664-3G

2.0743-5G

-2.5499-7G

1.0377-9G

-1.7156-12G

0.03

1.4338G

-2.2638-4G

4.2819-6G

-2.7411-8G

1.4699-10G

-2.2589-13G

0.01

6.2084-1G

3.1420-4G

1.6110-6G

4.0156-8G

3.4841-11G

-2.0709-13G

0.01

2

4

3

Į4 G

5

Polynomial function: ln(Property) = Į0 + Į1T +Į2T + Į3T + Į4T + Į5T The notation -2.8625-4 signifies -2.8625×10-4

992 Transport Phenomena in Multiphase Systems

Į5 G

Error (%)

Į0G

Table B.71 Binary diffusion coefficients at 1 atma (Incropera and DeWitt 2001) Substance A

Substance B

T(K)

DAB (m2/s)

NH3

Air

298

0.28 × 10-4

H2O

Air

298

0.26 × 10-4

CO2

Air

298

0.16 × 10-4

H2

Air

298

0.41 × 10-4

O2

Air

298

0.21 × 10-4

Acetone

Air

273

0.11 × 10-4

Benzene

Air

298

0.88 × 10-5

Naphthalene

Air

300

0.62 × 10-5

Ar

N2

293

0.19 × 10-4

H2

O2

273

0.70 × 10-4

H2

N2

273

0.68 × 10-4

H2

CO2

273

0.55 × 10-4

CO2

N2

293

0.16 × 10-4

CO2

O2

273

0.14 × 10-4

O2

N2

273

0.18 × 10-4

Dilute

Caffeine

H2O

298

0.63 × 10-9

solutions

Ethanol

H2O

298

0.12 × 10-8

Glucose

H2 O

298

0.69 × 10-9

Glycerol

H2O

298

0.94 × 10-9

Acetone

H2O

298

0.13 × 10-8

CO2

H2O

298

0.20 × 10-8

O2

H2O

298

0.24 × 10-8

H2

H2O

298

0.63 × 10-8

N2

H2O

298

0.26 × 10-8

O2

Rubber

298

0.21 × 10-9

N2

Rubber

298

0.15 × 10-9

CO2

Rubber

298

0.11 × 10-9

He

SiO2

293

0.4 × 10-13

H2

Fe

293

0.26 × 10-12

Cd

Cu

293

0.27 x 10-18

Al

Cu

293

0.13 x 10-33

Gases

Solids

a

Assuming ideal gas behavior, the pressure and temperature dependence of the diffusion coefficient for a binary mixture of gases may be estimated form the relation DAB ∝ p-1 T 3/2.

Appendix B. Transport Properties 993

Table B.72 Diffusion coefficients in air at 1 atm (1.013 × 105 Pa)a (Mills, 1999) T [K] 200 300 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000

O2 0.095 0.188 0.325 0.475 0.646 0.838 1.05 1.26 1.52 2.06 2.66 3.32 4.03 4.80

CO2 0.074 0.157 0.263 0.385 0.537 0.684 0.857 1.05 1.24 1.69 2.17 2.75 3.28 3.94

Binary Diffusion Coefficient (m2/s × 104) CO C7H16 H2 NO 0.098 0.036 0.375 0.088 0.202 0.075 0.777 0.180 0.332 0.128 1.25 0.303 0.485 0.194 1.71 0.443 0.659 0.270 2.44 0.603 0.854 0.354 3.17 0.782 1.06 0.442 3.93 0.978 1.28 0.538 4.77 1.18 1.54 0.641 5.69 1.41 2.09 0.881 7.77 1.92 2.70 1.13 9.90 2.45 3.37 1.41 12.5 3.04 4.10 1.72 15.2 3.70 4.87 2.06 18.0 4.48

SO2 0.058 0.126 0.214 0.326 0.440 0.576 0.724 0.887 1.06 1.44 1.87 2.34 2.85 3.36

He 0.363 0.713 1.14 1.66 2.26 2.91 3.64 4.42 5.26 7.12 9.20 11.5 13.9 16.6

a

Owing to the practical importance of water vapor-air mixtures, engineers have used convenient empirical formulas for DH 2 O air. A formula that has been widely used is 1.685

§ p ·§ T · m2/s; DH 2 O, air = 1.97 × 10−5 ¨ 0 ¸ ¨ ¸ 273K < T < 373K © p ¹© T0 ¹ where p0 = 1 atm; T0 = 256 K. The following formula has also found increasing use (Marrero and Mason,1972);

DH 2 O air = 1.87 × 10−10 T = 2.75 × 10−9

2.072

p

;

T 1.632 ; p

280K < T < 450K 450K < T < 1070K

for p in atmospheres and T in Kelvins. Over the temperature range 290-330 K, the discrepancy between the two formulas is less than 2.5%. For small concentrations of water vapor in air, the older formula gives a constant value of ScH2 O air = 0.61 over the temperature range 273-373 K. On the other hand, the Marrero and Mason (1972) formula gives values of Sc H 2O air that vary from 0.63 at 280 K to 0.57 at 373 K.

994 Transport Phenomena in Multiphase Systems

Table B.73 Diffusion coefficients in solids, D = D0 exp ( − Ea / RuT ) (Mills, 1999) D0 System Oxygen-Pyrex glass Oxygen-fused silica glass Oxygen-titanium Oxygen-titanium alloy (Ti-6Al-4V) Oxygen-zirconium Hydrogen-iron Hydrogen-Į-titanium Hydrogen-ȕ-titanium Hydrogen-zirconium Hydrogen-Zircaloy-4 Deuterium-Pyrex glass Deuterium-fused silica glass Helium-Pyrex glass Helium-fused silica glass Helium-borosilicate Neon-borosilicate Carbon-FCC iron Carbon-BCC iron a

Eaa

2

m /s

kJ/kmol

6.19 × 10−8 2.61 × 10−9 5.0 × 10−3 5.82 × 10−2 4.68 × 10−5 7.60 × 10−8 1.80 × 10−6 1.95 × 10−7 1.09 × 10−7 1.27 × 10−5 6.19 × 10−8 2.61 × 10−9 4.76 × 10−8 5.29 × 10−8 1.94 × 10−8 1.02 × 10−10 2.3 × 10−5 1.1 × 10−6

4.69 × 104 3.77 × 104 2.13 × 105 2.59 × 105 7.06 × 105 5.60 × 103 5.18 × 104 2.78 × 104 4.81 × 104 6.05 × 105 4.69 × 104 3.77 × 104 2.72 × 104 2.55 × 104 2.34 × 104 3.77 × 104 1.378 × 105 8.75 × 104

Activation energy

Appendix B. Transport Properties 995

Table B.74 Schmidt number for vapors in dilute mixture in air at normal temperature, enthalpy of vaporization, and boiling point at 1 atma (Mills, 1999) hAv

Boiling point

Vapor

Formula

Scb

J/kg × 10-6

temperature K

Acetone

CH3COCH3

1.42

0.527

329

Ammonia

NH3

0.61

1.370

240

Benzene

C6H6

1.79

0.395

354 194

Chemical

a

b

c

Carbon dioxide

CO2

1.00

0.398

Carbon monoxide

CO

0.77

0.217

81

Chlorine

Cl2

1.42

0.288

238

Ethanol

CH3CH2OH

1.32

0.854

352

Helium

He

0.22

Heptane

C7H16

2.0

0.340

372

4.3

Hydrogen

H2

0.20

0.454

20.3

Hydrogen sulfide

H2S

0.94

0.548

213

Methanol

CH3OH

0.98

1.100

338

Napthalenec

C10H8

2.35

0.567

491

Nitric oxide

NO

0.87

0.465

121

Octane

C8H18

2.66

0.303

399

Oxygen

O2

0.83

0.214

90.6

Pentane

C5H12

1.49

0.357

309

Sulfur dioxide

SO2

1.24

0.398

263

Water vapor

H2O

0.61

2.257

373

With the Clausius-Clapeyron relation, one may estimate vapor pressure as ­° Mh § 1 1 · ½° psat  exp ® − Av ¨ − ¸ ¾ atm, for T  TBP °¯ Ru © T TBP ¹ °¿ The Schmidt number is defined as Sc = μ / ρ D = v / D . Since the vapors are in small concentrations, values for ȝ, ȡ and v can be taken as pure air values.

Cho et al. (1992); hAv = 0.567 × 106 J/K is at 300 K.

996 Transport Phenomena in Multiphase Systems

Table B.75 Schmidt numbers for dilute solution in water at 300 Ka (Mills, 1999) Solute Helium Hydrogen Nitrogen Water Nitric Oxide Carbon monoxide Oxygen Ammonia Carbon dioxide Hydrogen sulfide Ethylene Methane Nitrous oxide Sulfur dioxide Sodium chloride Sodium hydroxide Acetic acid Acetone Methanol Ethanol Chlorine Benzene Ethylene glycol n-Propanol i-Propanol Propane Aniline Benzoic acid Glycerol Sucrose a

Molecular mass, M (kg/kmol) 4.003 2.016 28.02 18.016 30.01 28.01 32.00 17.03 44.01 34.08 28.05 16.04 44.02 64.06 58.45 40.00 60.05 58.08 32.04 46.07 70.90 78.11 62.07 60.09 60.09 44.09 93.13 122.12 92.09 342.3

Schmidt number, Sc 120 190 280 340 350 360 400 410 420 430 450 490 490 520 540 490 620 630 640 640 670 720 720 730 730 750 800 830 1040 1670

For other temperatures use Sc / Sc300 K  ( μ 2 / ρT ) /( μ 2 / ρT )300 K , where ȝ and ȡ are for water, and T is absolute

temperature. For chemically similar solutes of different molecular weights use Sc 2 / Sc1  ( M 2 / M1 )0.4 . A table of ( μ 2 / ρT ) /( μ 2 / ρT )300 K for water follows. T[K]

( μ 2 / ρT ) /( μ 2 / ρT )300 K

T [K]

( μ 2 / ρT ) /( μ 2 / ρT )300 K

290 300 310 320 330

1.66 1.00 0.623 0.429 0.296

340 350 360 370

0.221 0.167 0.123 0.097

Spalding (1963).

Appendix B. Transport Properties 997

Table B.76 Solubility and permeability of gases in solids (Mills, 1999) Gas

Solid

T(K)

S ′ [m3 (STP)/m3 atm] or S’a

H2

Vulcanized rubber

300

Vulcanized neoprene

290

Silicone rubber Natural rubber Polyethylene Polycarbonate Fused silica

300 300 300 300 400

Nickel

800 360 440

He

Silicone rubber Natural rubber Polycarbonate Nylon 66 Teflon Fused silica

300 300 300 300 300 300

0.053 × 10-10 4.2 × 10-10 0.37 × 10-10 0.065 × 10-10 0.091 × 10-10

S ′′ ≅ 0.035 S ′′ ≅ 0.030 S ′′ ≅ 0.202 S ′′ ≅ 0.192 2.3 × 10-10 0.24 × 10-10 0.11 × 10-10 0.0076 × 10-10 0.047 × 10-10

390 680

S ′ = 0.0059

1.0 × 10-12

300

S ′ = 0.070

0.15 × 10-10

Pyrex glass

300

7740 glass (94% SiO2+B2O3+P2O5 5% Na2O+Li2+K2O 1% other oxides) 7056 glass (90% SiO2+B2O3+P2O5 8% Na2O+Li2+K2O 1% PbO, 0.5% other oxides) Vulcanized rubber

470

800

Silicone rubber Natural rubber Polyethylene Polycarbonate Silicone-polycarbonate copolymer (57% silicone) Ethyl cellulose

0.34 × 10-10

S ′′ ≅ 0.018 S ′′ ≅ 0.026 S ′′ ≅ 0.006 S ′′ ≅ 0.024 S ′ = 0.0084 S ′ = 0.0038 S ′ = 0.0046 S ′ = 0.0039

800

O2

S ′ = 0.040 S ′ = 0.051

Permeabilityb m3(STP)/m2s (atm/m)

580 720

4.6 × 10-13 1.6 × 10-12 6.4 × 10-12 1.2 × 10-14

300 300 300 300 300

3.8 × 10-10 0.18 × 10-10 4.2 × 10-12 0.011 × 10-10 1.2 × 10-10

300

0.09 × 10-10

998 Transport Phenomena in Multiphase Systems

Table B.76 Solubility and permeability of gases in solids (Mills, 1999) (cont’d) Gas

Solid

T(K)

N2

Vulcanized rubber Silicone rubber Natural rubber Silicone-polycarbonate copolymer (57% silicone) Teflon® Vulcanized rubber Silicone rubber Natural rubber Silicone-polycarbonate copolymer (57% silicone)

300 300 300

CO2

S ′ [m3 (STP)/m3 atm] or S’a

Permeabilityb m3(STP)/m2s (atm/m)

S ′ = 0.035

0.054 × 10-10 1.9 × 10-10 0.062 × 10-10

300

0.53 × 10-10

300 300 300 300

0.019 × 10-10 1.0 × 10-10 21 × 10-10 1.0 × 10-10

S ′ = 0.90

300

7.4 × 10-10

Nylon 66

300

0.0013 × 10-10

H2O Ne

Cellophane Fused silica

310 300-1200

Ar

Fused silica

900-1200

0.91-1.8 × 10-10

S ′′ ≅ 0.002 S ′′ ≅ 0.01

Solubility S ′ = Volume of solute gas (0 °C, 1 atm) dissolved in unit volume of solid when the gas is at 1 atm partial pressure. Solubility coefficient S ′′ = c1, g / c2 .

a

b

Permeability K = DAB S ′ .

From various sources, including Geankoplis (1993), Doremus (1973), and Altemose (1961).

Appendix B. Transport Properties 999

Table B.77 Henry’s constant for selected gases in water at moderate pressurea

H = p A,i / x A,i (bars) T (K) 273 280 290 300 310 320 323 a

NH3 21 23 26 30 ----

Cl2 265 365 480 615 755 860 890

H2S 260 335 450 570 700 835 870

SO2 165 210 315 440 600 800 850

CO2 710 960 1300 1730 2175 2650 2870

CH4 22,880 27,800 35,200 42,800 50,000 56,300 58,000

O2 25,500 30,500 37,600 45,700 52,500 56,800 58,000

H2 58,000 61,500 66,500 71,600 76,000 78,600 79,000

Incropera and DeWitt (2001) and Spalding (1963).

Table B.78 The solubility of selected gases and solids (Incropera and DeWitt, 2001) Gas O2 N2 CO2 He H2

Solid Rubber Rubber Rubber SiO2 Ni

T (K) 298 298 298 293 358

1000 Transport Phenomena in Multiphase Systems

S = c A, s / p A, g (kmol/m3-bar) 3.12 x 10-3 1.56 x 10-3 40.15 x 10-3 0.45 x 10-3 9.01 x 10-3

Table B.79 Solubility of inorganic compounds in watera (Mills, 1999) Solute Aluminum sulfate Calcium bicarbonate Calcium chloride Calcium hydroxide Potassium chloride Potassium nitrate Potassium sulfate Sodium bicarbonate Sodium carbonate Sodium chloride Sodium nitrate Sodium sulfate

a

Formula

Solid Phase

Al2(SO4)3

18H2O

Ca(HCO3)2

-

273.15 280 31.2

32.8

290

300

310

320

T (K) 330

340

350

360

370

373.15

35.5

39.1

44.3

50.3

57.0

63.9

70.8

78.3

84.6

89.0

18.10 18.33

18.40

16.15 16.30 16.53 16.75 16.98 17.20 17.43 17.65 17.88

CaCl2

6H2O

59.5

63.3

71.5

CaCl2

2H2O

-

-

-

Ca(OH)2

93.3 137.2 -

-

-

-

-

-

-

-

-

134.6 140.2 145.3

150.9 157.0

159.0

-

0.185 0.179 0.168 0.157 0.145 0.132 0.120 0.109 0.098

0.088 0.080

0.077

KCl

-

27.6

29.9

33.1

36.1

39.1

41.8

53.1

55.8

56.7

KNO3

-

13.3

18.5

28.2

41.3

58.2

78.7 102.3 129.2 159.2

191.6 232.1

246.0

K2SO4

-

7.35

8.63 10.51 12.38 14.20 15.95 17.64 19.25 20.88

22.36 23.69

24.1

NaHCO3

-

6.9

7.76

9.14 10.63 12.20 13.90 15.79

-

-

-

-

-

Na2O3

10H2O

7

10.8

18.7

Na2CO3

1H2O

-

-

NaCl

-

35.7

35.8

NaNO2

-

73

78

Na2SO4

10H2O

5.0

Na2SO4 Na2SO4

7H2O -

19.5 -

44.6

47.4

50.2

33.4

-

-

-

-

-

-

-

-

-

-

49.1

47.8

46.7

46.2

45.9

45.7

45.55

45.5

35.9

36.2

36.5

36.9

37.2

37.6

38.2

38.8

39.5

39.8

85

93

101

111

121

132

144

159

175

180

7.7

16.1

34.1

-

-

-

-

-

-

-

-

26.7 -

39.6 -

-

49.6

47.4

45.7

43.7

44.0

43.3

42.7

42.5

Solubility expressed in kilograms of anhydrous substance that is soluble in 100 kg water.

Appendix B. Transport Properties 1001

Table B.80 Equilibrium compositions for the NH3-water system (Mills, 1999)

x A,A

p A, g (atm) 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0

290 K 0.030 0.056 0.078 0.096 0.11 0.18 0.26 0.31 0.35 -

300 K 0.019 0.036 0.052 0.064 0.079 0.14 0.21 0.26 0.29 0.32

310 K 0.012 0.024 0.035 0.046 0.056 0.099 0.16 0.20 0.23 0.27

320 K 0.008 0.016 0.024 0.032 0.040 0.057 0.12 0.16 0.19 0.22

330 K 0.006 0.012 0.017 0.023 0.029 0.052 0.092 0.13 0.15 0.17

Table B.81 Equilibrium compositions for the SO2-water systema (Mills, 1999)

x A,A × 103

p A, g (atm) 0.001 0.003 0.01 0.03 0.1 0.3 1.0 a

290 K 0.12 0.25 0.62 1.4 4.1 11.0 33.0

300 K 0.084 0.18 0.42 1.1 2.9 7.9 24.0

310 K 0.059 0.13 0.31 0.73 2.0 5.6 18.0

Notice that Henry’s law is invalid for the SO2-water system, even at very dilute concentrations.

1002 Transport Phenomena in Multiphase Systems

320 K 0.042 0.093 0.22 0.51 1.4 3.9 12.0

Table B.82 Thermodynamic properties of water vapor-air mixtures at 1 atm (Mills, 1999) Specific Volume (m3/kg) Temp. (°C) 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 a b

Saturation Mass Fraction 0.007608 0.008136 0.008696 0.009289 0.009918 0.01058 0.01129 0.01204 0.01283 0.01366 0.01455 0.01548 0.01647 0.01751 0.01861 0.01978 0.02100 0.02229 0.02366 0.02509 0.02660 0.02820 0.02987 0.03164 0.03350 0.03545 0.03751 0.03967 0.04194 0.04432 0.04683 0.04946 0.05222 0.05512 0.05817 0.06137 0.06472 0.06842 0.07193 0.07580

Enthalpya, b (KJ/kg)

Dry Air

Saturated Air

Liquid Water

Dry Air

Saturated Air

0.8018 0.8046 0.8075 0.8103 0.8131 0.8160 0.8188 0.8217 0.8245 0.8273 0.8302 0.8330 0.8359 0.8387 0.8415 0.8444 0.8472 0.8500 0.8529 0.8557 0.8586 0.8614 0.8642 0.8671 0.8699 0.8728 0.8756 0.8784 0.8813 0.8841 0.8870 0.8898 0.8926 0.8955 0.8983 0.9012 0.9040 0.9068 0.9097 0.9125

0.8054 0.8086 0.8117 0.8148 0.8180 0.8212 0.8244 0.8276 0.8309 0.8341 0.8374 0.8408 0.8441 0.8475 0.8510 0.8544 0.8579 0.8615 0.8650 0.8686 0.8723 0.8760 0.8798 0.8836 0.8874 0.8914 0.8953 0.8994 0.9035 0.9077 0.9119 0.9162 0.9206 0.9251 0.9297 0.9343 0.9391 0.9439 0.9489 0.9539

42.13 46.32 50.52 54.71 58.90 63.08 67.27 71.45 75.64 79.82 83.99 88.17 92.35 96.53 100.71 104.89 109.07 113.25 117.43 121.61 125.79 129.97 134.15 138.32 142.50 146.68 150.86 155.04 159.22 163.40 167.58 171.76 175.94 180.12 184.29 188.47 192.65 196.83 201.01 205.19

10.059 11.065 12.071 13.077 14.083 15.089 16.095 17.101 18.107 19.113 20.120 21.128 22.134 23.140 24.147 25.153 26.159 27.166 28.172 29.178 30.185 31.191 32.198 33.204 34.211 35.218 36.224 37.231 38.238 39.245 40.252 41.259 42.266 43.273 44.280 45.287 46.294 47.301 48.308 49.316

29.145 31.481 33.898 36.401 38.995 41.684 44.473 47.367 50.372 53.493 56.736 60.107 63.612 67.259 71.054 75.004 79.116 83.400 87.862 92.511 97.357 102.408 107.674 113.166 118.893 124.868 131.100 137.604 144.389 151.471 158.862 166.577 174.630 183.037 191.815 200.980 210.550 220.543 230.980 241.881

The enthalpies of dry air and liquid water are set equal to zero at a datum temperature of 0 °C The enthalpy of an unsaturated water vapor-air mixture can be calculated as

h = hdry air + (m1 / m1, sat )(hsat − hdry air ) .

Appendix B. Transport Properties 1003

References Altemose, V.O., 1961, “Helium Diffusion through Glass,” Journal of Applied Physics, Vol. 32, pp. 1309-1316. American Society of Heating, Refrigerating and Air Conditioning Engineers, 2001, ASHRAE Handbook of Fundamentals, ASHRAE, New York, NY. Bejan, A., 1994, Convection Heat Transfer, 2nd ed., John Wiley & Sons, New York, NY. Bennon, W.D., and Incropera, F.P., 1988, “Developing Laminar Mixed Convection with Solidification in a Vertical Channel,” ASME Journal of Heat Transfer, Vol. 110, pp. 410-415. Brennan, P.J., and Kroliczek, E.J., 1979, Heat Pipe Design Handbook, Vol. 2, prepared for NASA Goddard by B&K Engineering, Inc., Suite 825, One Investment Place, Towson, MD. Carey, V.P., 1992, Liquid-Vapor Phase-Change Phenomena, Hemisphere, Washington, D.C. Cengel, Y.A., and Boles, M.A., 2002, Thermodynamics – An Engineering Approach, 4th ed., McGraw-Hill, New York, NY. Cho, C., Irvine, T.F., Jr., and Karni, J., 1992, “Measurement of the Diffusion Coefficient of Naphthalene into Air,” International Journal of Heat and Mass Transfer, Vol. 35, pp. 957-966. Doremus, R.H., 1973, Glass Science, Wiley, New York. Dunn, P. and Reay, D.A., 1982, Heat Pipes, Pergamon Press, New York. Geankoplis, C. J., 1993, Transport Processes and Unit Operations, 3rd edition, Prentice-Hall, Englewood Cliffs, NJ. Hale, D.V., Hoovers, M.J., and O’Nell, M.J., 1971, Phase Change Materials Handbook, NASA-CR-61363. Humphries, W.R., and Griggs, E.I., 1977, A Design Handbook for Phase Change Thermal Control and Energy Storage Devices, NASA-TP-1074. Iida, T., and Guthrie, R.I.L., 1988, The Physical Properties of Liquid Metals, Oxford University Press, Oxford, UK. Incropera, F.P., and DeWitt, D.P., 2001, Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley & Sons, New York, NY. Ivanovskii, M.N., Sorokin, V.P., and Yagodkin, I.V., 1982, The Physical Principles of Heat Pipes, Clarendon Press, Oxford, UK.

1004 Transport Phenomena in Multiphase Systems

Kakac, S., Shah, R.K., and Aung, W., eds., 1987, Handbook of Single-Phase Convective Heat Transfer, John Wiley & Sons, New York, NY. Marrero, T.R., and Mason, E.A., 1972, “Gaseous Diffusion Coefficients,” Journal of Physical and Chemical Reference Data, Vol. pp. 1, 3-118. Mills, A.F., 1999, Basic Heat and Mass Transfer, 2nd Ed., Prentice Hall, Upper Saddle River, NJ. Ott, L., 1984, An Introduction to Statistical Methods and Data Analysis, Duxbury Press, Boston, MA. Rohsenow, W.N., Hartnett, J.P., and Ganic, E.N. eds., 1985, Handbook of Heat Transfer Fundamentals, McGraw-Hill, New York, NY. Spalding, D.B., 1963, Convective Mass Transfer, McGraw-Hill, New York, NY. Touloukian, Y.S., Liley, P.E., and Saxena, S.C., eds., 1970, Thermophysical Properties of Matter, Vol. 3, Plenum, New York, NY. Vargaftik, N.B., 1975, Handbook of Physical Properties of Liquids and Gases, Hemisphere, New York, NY.

Appendix B. Transport Properties 1005