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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) 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 ρ density (kg/m3) 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 cp specific heat (kJ/Kg-K) 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 μ viscosity (10-7N-s/m²) 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 ν kinematic viscosity (10-6m2/s) 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 k thermal conductivity (10-3W/m-K) 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 α thermal diffusivity (10-6m2/s) 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 Pr Prandtl number 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) 280 300 320 340 360 380 400 450 500 550 600 650 700 750 800 ρ density (kg/m3) 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 cp specific heat (kJ/Kg-K) 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 μ viscosity (10-7N-s/m²) 140 149 156 165 173 181 190 210 231 251 270 288 305 321 337 ν kinematic viscosity (10-6m2/s) 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 k thermal conductivity (10-3W/m-K) 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 α thermal diffusivity (10-6m2/s) 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 Pr Prandtl number 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) 4.22 7 10 20 30 60 100 200 300 600 1000 ρ density (kg/m3) 16.900 7.530 5.020 2.440 1.620 0.811 0.487 0.244 0.162 0.0818 0.0487 cp specific heat (kJ/Kg-K) 9.78 5.71 5.41 5.25 5.22 5.20 5.20 5.19 5.19 5.19 5.19 μ viscosity (10-6N-s/m²) 1.25 1.76 2.26 3.58 4.63 7.12 9.78 15.1 19.9 32.2 46.3 ν kinematic viscosity (10-6m2/s) 0.0739 0.234 0.449 1.470 2.860 8.800 20.10 62.20 122.0 396.0 946.0 k thermal conductivity (10-3W/m-K) 0.011 0.014 0.018 0.027 0.034 0.053 0.074 0.118 0.155 0.251 0.360 α thermal diffusivity (10-6m2/s) 0.00064 0.00321 0.00642 0.0209 0.0403 0.125 0.291 0.932 1.830 5.940 14.20 Pr Prandtl number 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) 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 ρ density (kg/m3) 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 cp specific heat (kJ/Kg-K) 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 μ viscosity (10-7N-s/m²) 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 ν kinematic viscosity (10-6m2/s) 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 k thermal conductivity (10-3W/m-K) 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 α thermal diffusivity (10-6m2/s) 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 Pr Prandtl number 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) 100 150 200 250 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300 ρ density (kg/m3) 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 cp specific heat (kJ/Kg-K) 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 μ viscosity (10-7N-s/m²) 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 ν kinematic viscosity (10-6m2/s) 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 k thermal conductivity (10-3W/m-K) 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 α thermal diffusivity (10-6m2/s) 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 Pr Prandtl number 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) 100 150 200 250 300 350 400 450 500 550 600 700 800 900 1000 1100 1200 1300 ρ density (kg/m3) 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 cp specific heat (kJ/Kg-K) 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 μ viscosity (10-7N-s/m²) 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 ν kinematic viscosity (10-6m2/s) 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 k thermal conductivity (10-3W/m-K) 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 α thermal diffusivity (10-6m2/s) 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 Pr Prandtl number 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) 380 400 450 500 550 600 650 700 750 800 850 ρ density (kg/m3) 0.5863 0.5542 0.4902 0.4405 0.4005 0.3652 0.3380 0.3140 0.2931 0.2739 0.2579 cp specific heat (kJ/Kg-K) 2.060 2.014 1.980 1.985 1.997 2.026 2.056 2.085 2.119 2.152 2.186 μ viscosity (10-7N-s/m²) 127.1 134.4 152.5 170.4 188.4 206.7 224.7 242.6 260.4 278.6 296.9 ν kinematic viscosity (10-6m2/s) 21.68 24.25 31.11 38.68 47.04 56.60 66.48 77.26 88.84 101.7 115.1 k thermal conductivity (10-3W/m-K) 24.6 26.1 29.9 33.9 37.9 42.2 46.4 50.5 54.9 59.2 63.7 α thermal diffusivity (10-6m2/s) 20.4 23.4 30.8 38.8 47.4 57.0 66.8 77.1 88.4 100.0 113.0 Pr Prandtl number 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 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 β × 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 T (K) 20.3 273 550 70 77.4 80 90 100 110 120 89 366 230 250 300 350 400 450 500 550 β × 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 Oxygen Sodium Therminol® 60 Refrigerant-134a Glycerin C3H5(OH)3 Table B.9 Density and volume expansion coefficients of water (Mills, 1999) T (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 ρ (kg/m3) 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 β ×106 (1/K) -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 T (K) 320.00 330.00 340.00 350.00 360.00 370.00 373.15 380.00 390.00 400.00 450.00 500.00 ρ (kg/m3) 989.12 984.25 979.43 973.71 967.12 960.61 957.85 953.29 945.17 937.21 890.47 831.26 β ×106 (1/K) 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 100 150 200 250 300 400 600 800 ρ density (kg/m³) 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 Aluminum Alloy, 2024-T6, Tm = 775 K (Incropera and DeWitt, 2001) (4.5% Cu, 1.5% Mg, 0.6% Mn) k c ρ thermal conductivity specific heat density (W/m-K) (kJ/kg-K) (kg/m³) 2770 0.473 0.787 0.875 0.925 1.042 65 163 177 186 186 T Temp. K 100 200 300 400 600 Table B.12 Cartridge brass T Temp. K 100 200 300 400 600 Cartridge brass, Tm = 1188 K (Incropera and DeWitt, 2001) c ρ specific heat density (kJ/kg-K) (kg/m³) 8530 0.360 0.380 0.395 0.425 k thermal conductivity (W/m-K) 75 95 110 137 149 Table B.13 Copper T Temp. K 100 150 200 250 300 400 600 800 1000 1200 Copper, Cu, Tm = 1358 K (Rohsenow et al., 1985) c ρ specific heat density (kJ/kg-K) (kg/m³) 9009 8992 8973 8951 8930 8884 8787 8642 8568 8458 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) 480 429 413 406 401 393 379 366 352 339 962 Transport Phenomena in Multiphase Systems Table B.14 Fused silica T Temp. K 100 200 300 400 600 800 1000 1200 Silicon dioxide, SiO, Tm = 1883 K (Incropera and DeWitt, 2001) k c ρ thermal conductivity specific heat density (W/m-K) (kJ/kg-K) (kg/m³) 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 Inconel X-750, Tm = 1665 K (Incropera and DeWitt, 2001) (73% Ni, 15% Cr, 6.7% Fe) c ρ specific heat density (kJ/kg-K) (kg/m³) 8510 0.372 0.439 0.473 0.510 0.546 0.626 T Temp. K 100 200 300 400 600 800 1000 1200 1500 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 ρ 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 ρ 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) ρ 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 Niobium, Nb, Tm = 2740 K (Rohsenow et al., 1985) ρ 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 k thermal conductivity (W/m-K) 55 53 53 53 54 55 57 58 61 64 68 71 964 Transport Phenomena in Multiphase Systems Table B.20 Plain carbon steel Plain Carbon Steel, Tm=1480 °C (Incropera and DeWitt, 2001) T Temp. K 300 400 600 800 1000 ρ density (kg/m³) 7854 c specific heat (kJ/kg-K) 0.434 0.487 0.559 0.685 1.169 k thermal conductivity (W/m-K) 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 ρ density (kg/m³) 7900 c specific heat (kJ/kg-K) 0.272 0.402 0.477 0.515 0.557 0.582 0.611 0.640 0.682 k thermal conductivity (W/m-K) 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) ρ 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) ρ 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 Tungsten, W, Tm = 3660 K (Rohsenow et al., 1985) ρ 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 k thermal conductivity (W/m-K) 208 192 185 180 174 159 146 137 125 118 112 108 966 Transport Phenomena in Multiphase Systems Table B.25 Phase Change Materials (PCMs) hs PCMs chemical formula latent heat (kJ/kg) Tm melting point (°C) ρℓ liquid density (kg/m³) ρs solid density (kg/m³) μℓ liquid viscosity (10-3 N-s/m²) cp,s solid specific heat (kJ/kg-K) ks solid thermal conductivity (W/mK) kℓ liquid thermal conductivity (W/mK) cp,ℓ liquid specific heat (kJ/kg-K) β liquid thermal expansion coefficient (10-41/K) 3.9 1.81 1.3 1.75 1.31 0.514 33.5 238 1.88 C14H30 C16H34 C18H38 C20H42 Ga Al H2O CH3COOH 0.358 Na2HPO4· 12H2O 36 280 1520 1446 0.476 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 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 1690 2.31 2.18 2.46 381.5 1.08 4.23 1960 1940 8.5 8.5 1.2 1.2 -0.6805 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) a 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 4.35 Appendix B Transport Properties 967 Table B.26 Thermophysical properties at saturation for acetone pv saturation pressure (105 Pa) T Temp. ˚C hv latent heat (kJ/kg) 660.0 615.6 564.0 552.0 536.0 517.0 495.0 472.0 426.1 394.4 0.0082 0.0096 0.0110 0.0126 0.0143 0.0161 0.0178 0.0195 0.0215 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 0.200 0.189 0.183 0.181 0.175 0.168 0.160 0.148 0.135 0.126 31.0 27.6 26.2 23.7 21.2 18.6 16.2 13.4 10.7 8.1 Acetone, (CH3)2CO, Molecular Mass: 58.1, (Tsat = 56.25 ˚C; Tm = -93.15 ˚C; Dunn and Reay, 1982) μv kℓ σ ρℓ ρv μℓ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface (kg/m³) (kg/m³) (10-3 (10-7 conductivity conductivitya tension N-s/m²) N-s/m²) (W/m-K) (W/m-K) (10-3N/m) cp,ℓ liquid specific heat b (kJ/kg-K) 2.04 2.07 2.11 2.16 2.22 2.29 2.39 2.49 2.61 2.77 cp,v vapor specific heat a (kJ/kg-K) 1.109 1.160 1.215 1.271 1.328 1.386 1.444 1.502 1.560 1.616 968 Transport Phenomena in Multiphase Systems 0.01 0.03 0.10 0.27 0.60 1.15 2.15 4.43 6.70 10.49 a Interpolation from Rohsenow et al. (1985); b Interpolation from Vargaftik (1975) -40 -20 0 20 40 60 80 100 120 140 Table B.27 Thermophysical properties at saturation for ammonia pv saturation pressure (106 Pa) T Temp. K hv latent heat (kJ/kg) 1477 1451 1425 1398 1369 1339 1307 1273 1237 1198 1159 1113 1066 1014 958 895 825 745 649 529 σ liquid surface tension a (10-3N/m) Appendix B. Transport Properties 969 a 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 Ammonia, NH3, Molecular Mass: 17.0, (Tsat = 239.9 K; Tm = 195.5 K; ASHRAE, 2001) μv kℓ ρℓ ρv μℓ kv liquid vapor liquid vapor liquid vapor density density viscosity viscosity thermal thermal (kg/m³) (kg/m³) (10-6 (10-6 conductivity conductivity 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 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,ℓ liquid specific heat (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 Carey (1992) Table B.28 Thermophysical properties at saturation for cesium hv latent heat (kJ/kg) 544.30 534.20 523.30 511.60 499.50 486.50 472.60 458.80 444.60 429.98 415.40 T Temp. K 0.0003 0.0056 0.0437 0.2026 0.6580 1.6800 3.6000 6.7700 11.5100 18.0200 26.7200 pv saturation pressure (105 Pa) 970 Transport Phenomena in Multiphase Systems Cesium, Cs, Molecular Mass: 132.9, (Tsat = 943 K; Tm = 201.6 K; Ivanovskii, et al., 1982) ρv μℓ μv kℓ σ ρℓ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface (103 (10-3 (10-4 (10-5 conductivity conductivity a 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,ℓ liquid specific heat a (kJ/kg-K) 0.232 0.224 0.219 0.217 0.222 0.231 0.239 0.248 0.256 pv saturation pressure (105 Pa) latent heat (kJ/kg) 345 329 314 291 264 235 207 0.006 0.051 0.245 0.843 2.330 5.200 10.43 a 500 600 700 800 900 1000 1100 1200 1300 1400 1500 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 Vargaftik (1975) Table B.29 Thermophysical properties at saturation for Dowtherm® hv T Temp. ˚C cp,v vapor specific heat (kJ/kg-K) 100 150 200 250 300 350 400 Diphenyl mixture (Dowtherm*), Molecular Mass: 166.0, (Tsat= 258 °C; Tm = 12 °C; Vargaftik, 1975) μv kℓ μℓ kv σ ρℓ ρv liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-5 (10-5 conductivity conductivity 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 cp,ℓ liquid specific heat (kJ/kg-K) 1.88 2.14 2.34 2.60 2.76 2.89 3.01 ∗ 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) pv saturation pressure (105 Pa) latent heat (kJ/kg) 530 506 480 450 414 368 304 200 0.0116 0.0138 0.0160 0.0185 0.0209 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 21.23 17.93 14.60 11.30 8.00 4.60 1.20 0.08 ρv vapor density (kg/m³) 0.096 0.600 1.700 3.700 7.200 14.000 25.000 38.000 T Temp. ˚C hv ρℓ liquid density (kg/m³) μℓ liquid viscosity (10-7 N-s/m²) kv vapor thermal conductivity a (W/m-K) μv vapor viscosity (10-7 N-s/m²) σ liquid surface tension (10-3N/m) kℓ liquid thermal conductivity (W/m-K) cp,ℓ liquid specific heat (kJ/kg-K) 2.82 2.94 3.05 3.16 3.26 3.38 3.48 cp,v vapor specific heat (kJ/kg-K) 1.297 1.349 1.401 1.459 1.521 1.585 1.660 1.736 a -120 -100 -80 -60 -40 -20 0 20 Interpolation (Rohsenow et al., 1985) Ethanol, C2H5OH, Molecular Mass: 46.0, (Tsat = 78.3 °C; Tm = -114.5 °C; Ivanovskii et al., 1982) pv saturation pressure (105 Pa) latent heat (kJ/kg) 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 0.012 0.058 0.180 0.472 1.086 2.260 4.290 7.530 12.756 19.600 29.400 42.800 60.200 Table B.31 Thermophysical properties at saturation for ethanol hv ρℓ liquid density (103 kg/m³) ρv vapor density (kg/m³) T Temp. ˚C μℓ liquid viscosity (10-3 N-s/m²) μv vapor viscosity (10-5 N-s/m²) kℓ liquid thermal conductivity (W/m-K) 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 kv vapor thermal conductivity a (W/m-K) 0.0117 0.0139 0.0160 0.0179 0.0199 0.0219 0.0238 0.0256 0.0272 0.0288 0.0395 0.0321 σ liquid surface tension (10-3N/m) 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 cp,ℓ liquid specific heat b (kJ/kg-K) 2.27 2.40 2.57 2.78 3.03 3.30 3.61 3.96 cp,v vapor specific heat c (kJ/kg-K) 1.34 1.40 1.48 1.54 1.61 1.68 1.75 0 20 40 60 80 100 120 140 160 180 200 220 240 Appendix B. Transport Properties 971 a Interpolation from Rohsenow et al. (1985); b Interpolation from Vargaftik (1975); c Dunn and Reay (1982) Table B.32 Thermophysical properties at saturation for Freon®-113 hv latent heat (kJ/kg) 166.88 161.48 158.68 155.83 149.93 143.82 137.46 T Temp. ˚C 0.0283 0.0905 0.1500 0.2387 0.5420 1.0943 2.0120 pv saturation pressure (105 Pa) a -30 -20 0 10 30 50 70 Freon-113, C2F3Cl3, Molecular Mass: 187.4, (Tsat = 47.68 °C; Tm = -36.6 °C; Vargaftik, 1975) μv kℓ kv μℓ σ ρv ρℓ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-3 (10-7 conductivity a conductivity tension (103 kg/m³) (kg/m³) N-s/m²) N-s/m²) (10-3N/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,ℓ liquid specific 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 ASHRAE (2001) Table B.33 Thermophysical properties at saturation for Freon®-123 hv latent heat (kJ/kg) 204.20 196.63 189.11 181.44 173.44 164.95 155.73 145.54 972 Transport Phenomena in Multiphase Systems pv saturation pressure (105 Pa) 0.0081 0.0358 0.1200 0.3265 0.7561 1.5447 2.8589 4.8909 Freon-123, CHCl2CF3, Molecular Mass: 152.9, (Tsat = 27.8 °C; Tm = -107 °C; ASHRAE, 2001) μv kℓ μℓ kv σ ρv ρℓ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-3 (10-7 conductivity conductivity tension 3 (10 kg/m³) (kg/m³) N-s/m²) N-s/m²) (10-3N/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 cp,ℓ liquid specific heat (kJ/kg-K) 0.932 0.948 0.968 0.990 1.014 1.038 1.066 1.100 T Temp. ˚C -60 -40 -20 0 20 40 60 80 cp,v vapor specific heat (kJ/kg-K) 0.553 0.585 0.617 0.651 0.686 0.724 0.767 0.816 Table B.34 Thermophysical properties at saturation for Freon®-134a hv latent heat (kJ/kg) 237.95 225.86 212.91 198.60 182.28 163.02 139.13 T Temp. ˚C 0.1591 0.5121 1.3273 2.9280 5.7171 10.166 16.818 pv saturation pressure (105 Pa) -60 -40 -20 0 20 40 60 Freon-134a, CF3CH2F, Molecular Mass: 102.0, (Tsat = -26.4°C; Tm = -101 °C; ASHRAE, 2001) μv kℓ μℓ kv σ ρv ρℓ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-3 (10-7 conductivity conductivity 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,ℓ liquid specific 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 Table B.35 Thermophysical properties at saturation for Freon®-21 hv latent heat (kJ/kg) T Temp. °C pv saturation pressure (105 Pa) cp,ℓ liquid specific heat a (kJ/kg-K) Appendix B. Transport Properties 973 a -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) μv kℓ σ kv μℓ ρv ρℓ liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-3 (10-7 conductivity conductivity a tension 3 (10 kg/m³) (kg/m³) N-s/m²) N-s/m²) (10-3N/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 0.994 1.015 1.048 1.093 1.149 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 Interpolation from Rohsenow et al. (1985) Table B.36 Thermophysical properties at saturation for Freon®-22 hv latent heat (kJ/kg) 269.29 257.43 245.42 232.92 219.40 204.28 186.89 166.22 139.94 T Temp. °C 0.0199 0.1034 0.3752 1.0540 2.4560 4.9830 9.0970 15.3150 24.2360 pv saturation pressure (105 Pa) a -100 -80 -60 -40 -20 0 20 40 60 Freon-22, CHF2Cl, Molecular Mass: 86.5, (Tsat = -40.8 °C; Tm = -160 °C; Vargaftik, 1975) μv kℓ ρℓ μℓ kv σ ρv liquid liquid vapor liquid vapor liquid vapor density viscosity viscosity thermal thermal surface density (103 (10-4 (10-7 conductivity conductivity 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,ℓ liquid specific 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 Ivanovskii et al. (1982) 974 Transport Phenomena in Multiphase Systems pv saturation pressure (105 Pa) latent heat (kJ/kg) 22.8 23.6 20.9 4.0 0.06 0.32 1.00 2.29 Table B.37 Thermophysical properties at saturation for helium hv T Temp. °C a Touloukian et al. (1970); b Vargaftik (1975) -271 -270 -269 -268 Helium, He, Molecular Mass: 4.0, (Tsat = -268 °C; Tm = -271 °C; Dunn and Reay, 1982) μv kℓ μℓ kv ρv ρℓ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density (10-7 (10-8 conductivity conductivity a (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 σ liquid surface tension (10-3N/m) 0.26 0.19 0.09 0.01 cp,ℓ liquid specific 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 Table B.38 Thermophysical properties at saturation for heptane hv latent heat (kJ/kg) 383.1 375.6 366.0 354.7 342.6 330.1 316.7 302.9 287.4 269.5 T Temp. °C 0.003866 0.0152 0.0472 0.1230 0.2800 0.5700 1.0606 1.8330 2.9790 4.5990 pv saturation pressure (105 Pa) a Interpolation from Rohsenow et al. (1985); b Dunn and Reay (1982) -20 0 20 40 60 80 100 120 140 160 Heptane, C7H16, Molecular Mass: 100.2, (Tsat = 98.43 °C; Tm = -90.59 °C; Vargaftik, 1975) ρv μℓ μv kℓ σ ρℓ kv liquid vapor liquid vapor liquid vapor liquid density density viscosity viscosity thermal thermal surface (103 (103 (10-3 (10-7 conductivity conductivity a tensiona kg/m³) kg/m³) N-s/m²) N-s/m²) (W/m-K) (10-3N/m) (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,ℓ liquid specific 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 Table B.39 Thermophysical properties at saturation for lead hv latent heat (kJ/kg) 920 920 920 920 920 920 920 920 920 920 920 920 T Temp. K 0.0986 0.2108 0.4200 0.8010 1.3620 2.3100 3.7410 5.5500 8.2000 11.8500 16.7500 22.6000 pv saturation pressure (102 Pa) cp,ℓ liquid specific heat (kJ/kg-K) cp,v vapor specific heat a (kJ/kg-K) Appendix B. Transport Properties 975 a 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 Lead, Pb, Molecular Mass: 207.2, (Tsat= 1740 °C; Tm = 327.5 °C; Ivanovskii et al., 1982) μv kℓ ρℓ μℓ kv σ ρv liquid liquid vapor liquid vapor liquid vapor density viscosity viscosity thermal thermal surface density (103 (10-3 (10-5 conductivity conductivity 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 Dunn and Reay (1982) Table B.40 Thermophysical properties at saturation for lithium hv latent heat (kJ/kg) 21712 21400 21000 20740 20380 20020 19670 19330 18990 18670 18370 18080 ρℓ liquid density (kg/m³) T Temp. K 0.1256 0.9680 5.1200 20.5000 65.8600 179.4000 426.5000 908.4000 1769.3000 3190.0000 5397.0000 8640.4000 pv saturation pressure (102 Pa) 976 Transport Phenomena in Multiphase Systems Lithium, Li, Molecular Mass: 6.9, (Tsat = 1615 K; Tm = 453.7 K; Ivanovskii et al., 1982) μv kℓ μℓ σ kv ρv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density (10-4 (10-8 conductivity conductivitya 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 cp,ℓ liquid specific 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 pv saturation pressure (105 Pa) latent heat (kJ/kg) 303.317 300.056 296.824 293.314 289.116 283.769 276.845 0.0003745 0.02315 0.33015 2.10240 8.2220 23.46000 54.03000 a 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 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 Vargaftik (1975) Table B.41 Thermophysical properties at saturation for mercury hv T Temp. K a 100 200 300 400 500 600 700 Mercury, Hg, Molecular Mass: 200.6, (Tsat= 630.1 K; Tm = 234.3 K; Ivanovskii et al., 1982) μv kℓ μℓ kv ρv ρℓ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density (10-3 (10-7 conductivity conductivitya (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 σ liquid surface tension (N/m) 0.4600 0.4360 0.4050 0.3770 0.3290 0.2989 0.2687 cp,ℓ liquid specific 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 Kakac et al. (1987) Table B.42 Thermophysical properties at saturation for methanol Methanol, CH4O, Molecular Mass: 32.0, (Tsat = 64.7 °C; Tm = -98 °C; Vargaftik, 1975) pv saturation pressure (105 Pa) 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 0.0001006 0.0020840 0.0039840 0.0071420 0.0121600 0.0199400 0.0318600 0.0507500 0.0863500 0.2750000 0.00157 0.00178 0.00199 0.00220 0.00241 0.00262 0.00283 0.00303 0.00324 0.00344 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 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 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 T Temp. °C hv ρℓ liquid density (103 kg/m³) ρv vapor density (103 kg/m³) μℓ liquid viscosity (10-3 N-s/m²) kv vapor thermal conductivitya (W/m-K) μv vapor viscosity (10-7 N-s/m²) kℓ liquid thermal conductivitya (W/m-K) cp,ℓ liquid specific heat (kJ/kg-K) 2.42 2.46 2.52 cp,v vapor specific heat b (kJ/kg-K) 1.37 1.44 1.50 1.57 1.70 1.86 1.92 1.92 a Touloukian et al. (1970); b Dunn and Reay (1982) 0 20 40 60 80 100 120 140 160 180 200 220 240 σ liquid surface tension (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 Table B.43 Thermophysical properties at saturation for nitrogen hv latent heat (kJ/kg) 205.7 194.5 180.5 162.2 137.0 95.7 ρℓ liquid density (103 kg/m³) T Temp. K 0.3859 1.3690 3.6000 7.7750 14.6700 25.1500 pv saturation pressure (105 Pa) Appendix B. Transport Properties 977 a 70 80 90 100 110 120 Nitrogen, N2, Molecular Mass: 28.0, (Tsat= -195.65 °C; Tm = 209.85 °C; Vargaftik, 1975) μv kℓ μℓ σ kv ρv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density (10-5 (10-7 conductivity conductivitya tension (103 kg/m³) 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 cp,ℓ liquid specific 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 ASHRAE (2001) 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) pv saturation pressure (105 Pa) latent heat (kJ/kg) 2143 2108 2068 2023 1970 1924 1872 1820 1765 1711 134 148 163 178 196 212 228 242 0.0142 0.0175 0.0205 0.0228 0.0248 0.0266 0.0280 0.0293 0.0303 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 43.85 40.72 37.58 34.45 31.32 28.19 25.05 22.00 19.00 16.00 98.2 92.2 86.2 80.2 74.2 68.2 62.2 56.2 53.0 47.0 ρv vapor density (10-3 kg/m³) 0.0009258 0.01022 0.06116 0.2441 0.7322 1.864 3.913 7.304 12.44 20.0 T Temp. K hv ρℓ liquid density (kg/m³) μℓ liquid viscosity (10-4 N-s/m²) kv vapor thermal conductivity a (W/m-K) σ liquid surface tension (10-3N/m) μv vapor viscosity (10-7 N-s/m²) kℓ liquid thermal conductivity (W/m-K) cp,ℓ liquid specific heat (kJ/kg-K) 0.771 0.762 0.761 0.769 0.792 0.819 0.846 0.873 0.899 0.924 600 700 800 900 1000 1100 1200 1300 1400 1500 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 978 Transport Phenomena in Multiphase Systems pv saturation pressure (105 Pa) latent heat (kJ/kg) 889.6 870.9 849.7 827.3 804.6 782.2 759.6 737.0 714.5 694.0 674.0 0.0001733 0.003664 0.03174 0.1584 0.5476 1.467 3.295 6.466 11.43 18.6 28.5 Table B.45 Thermophysical properties at saturation for rubidium hv T Temp. K 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Rubidium, Rb, Molecular Mass: 85.5, (Tsat = 959.2 K; Tm = 312.7 K; Vargaftik, 1975) μv kℓ μℓ kv ρv ρℓ liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal density density (10-4 (10-4 conductivity conductivity (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 σ liquid surface tension (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,ℓ liquid specific 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 (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 hv latent heat (kJ/kg) 298 298 298 298 298 298 298 298 298 298 298 ρℓ liquid density (kg/m³) T Temp. °C 0.01008 0.02420 0.05300 0.10800 0.20600 0.38300 0.63500 0.86000 1.36000 2.53000 3.84000 pv saturation pressure (105 Pa) cp,ℓ liquid specific heat (kJ/kg-K) cp,v vapor specific heat (kJ/kg-K) a 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 Silver, Ag, Molecular Mass: 107.9, (Tsat = 2212 °C; Tm = 960.5 °C; Ivanovskii et al., 1982) μv kℓ kv μℓ σ ρv liquid vapor liquid vapor liquid vapor viscosity viscosity thermal thermal surface density (10-3 (10-6 conductivity a conductivity tension ( kg/m³) 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 Brennan and Kroliczek (1979) Appendix B. Transport Properties 979 Table B.47 Thermophysical properties at saturation for sodium hv latent heat (kJ/kg) 4429 4341 4237 4131 4026 3925 3829 3742 3656 3577 3500 3425 3353 T Temp. K 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 pv saturation pressure (102 Pa) 980 Transport Phenomena in Multiphase Systems Sodium, Na, Molecular Mass: 23.0, (Tsat = 1151.2 K; Tm = 371.0 K; Ivanovskii et al., 1982) μv kℓ kv μℓ σ ρℓ ρv liquid vapor liquid vapor liquid liquid vapor viscosity viscosity thermal thermal surface density density (10-4 (10-8 conductivity conductivitya 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,ℓ liquid specific heat a (kJ/kg-K) 1.30 1.27 1.26 1.25 1.26 1.27 1.29 pv saturation pressure (105 Pa) latent heat (kJ/kg) 2453.8 2406.5 2358.4 2308.9 2251.2 2202.9 2144.9 2082.2 2014.0 1939.0 0.023368 0.073749 0.199190 0.473590 1.013250 1.985400 3.613600 6.180400 10.02700 15.55100 a 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 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 hv ρℓ liquid density (kg/m³) T Temp. °C 20 40 60 80 100 120 140 160 180 200 Water, H2O, Molecular Mass: 18.0, (Tsat = 100 °C; Tm = 0.0 °C; Vargaftik, 1975) μv kℓ kv μℓ ρv liquid vapor liquid vapor vapor viscosity viscosity thermal thermal density (10-7 (10-7 conductivity conductivitya (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 σ liquid surface tension (10-3/m) 72.88 69.48 66.07 62.69 58.91 54.96 50.79 46.51 42.19 37.77 cp,ℓ liquid specific 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 − 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 − Table B.48 (excluding helium). A least-squares polynomial regression method was used to derive these coefficients. Thermophysical properties given in Tables B.26 − 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 ψ is the fluid property, αi 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 ˆ 1 n φ −φ Average Error = n ∑ i =1 i i φi ˆ where φi is the input value (from Tables B.26 – B.48), φi 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 − 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) h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-3Ns/m²) μv (10-7Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Temp. -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -20 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C -40 – 140 ˚C α0 -2.3250 6.3491 6.7037 -1.3402 -9.4164-1 4.3519 -1.6958 -4.6467 3.2514 7.4631-1 1.9452-1 α1 5.4550-2 b α2 -2.0375-4 2.9698-5 1.0073-6 -1.7210-4 8.1436-5 -3.5279-6 1.2496-5 -2.0976-5 -1.0745-5 6.3091-6 -8.6330-7 2 3 α3 -1.8017-6 -1.2474-8 1.2383-7 2.1825-6 -1.7996-6 2.1574-7 -3.0675-7 4.6070-7 -4.2728-7 3.0226-8 -2.0672-8 4 5 α4 3.4981-8 -4.0319-9 -2.1854-9 -2.1680-8 1.7421-8 -3.5172-9 2.9314-10 -5.4286-9 4.4000-9 -5.0475-10 1.9250-10 α5 -1.3904-10 1.8757-11 8.5364-12 7.5011-11 -5.5176-11 1.3856-11 4.9935-12 1.9213-11 -1.7122-11 2.2060-12 6.5969-13 Error (%) 3.03 0.65 0.15 3.53 0.67 0.43 0.30 0.07 0.59 0.09 0.01 -2.7168-3 -1.6696-3 4.2408-2 -1.0496-2 2.6016-3 -1.1504-3 7.1871-3 -3.9116-3 1.0064-3 2.2900-3 Polynomial function, ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 5.4550-2 signifies 5.4550×10-2 Propertya pv (10 Pa) 6 Table B.50 Coefficients of temperature-property relations for ammonia 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 α0 -62.865 11507 15.720 -72.638 52.913 -3.6761 13.276 -6.8670 338.91 -14.697 -57.892 α1 7.0518-1 -183.01 -1.6835-1 9.5217-1 -8.5184-1 9.0960-2 -2.4537-1 -4.7528-2 -4.1174 3.7537-1 1.1165 b α2 -3.4742-3 1.3511 1.2492-3 -5.3865-3 6.2226-3 -6.2940-4 1.7877-3 8.9143-4 2.4029-2 -3.2928-3 -8.4409-3 2 3 α3 9.3187-6 -4.9982-3b -4.6323-6 1.6458-5 -2.2649-5 2.3334-6 -6.5246-6 -4.7431-6 -7.3673-5 1.3844-5 3.1568-5 4 5 α4 -1.3074-8 9.1651-6 8.5208-9 -2.6195-8 4.0580-8 -4.4046-9 1.1785-8 1.0675-8 1.1159-7 -2.8160-8 -5.8318-8 α5 7.5491-12 -6.7220-9 -6.2525-12 1.7156-11 -2.8649-11 3.3532-12 -8.4743-12 -8.6786-12 -6.6186-11 2.2354-11 4.2728-11 Error (%) 0.20 0.22 0.10 0.83 1.07 0.13 0.22 0.62 0.63 1.03 0.62 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-6Ns/m²) μv (10-6Ns/m²) kℓ (W/m-K) kv (W/m-K) σc (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 7.0518-1 signifies 7.0518×10-1 c Polynomial Function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 982 Transport Phenomena in Multiphase Systems Table B.51 Coefficients of temperature-property relations for cesium Propertya pv (10 Pa) 5 h v (kJ/kg) ρℓ (10³kg/m³) ρv (103 kg/m³) μℓ (104 Ns/m²) μv(10-5 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10 N/m) cp,ℓ(kJ/kgK) cp,v(kJ/kgK) -3 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 α0 -53.928 6.4024 6.2290-1 80.341 3.9271 -2.5093-1 -9.6746-2 -6.8268 2.5845 -3.94420 -1.6680 α1 1.8416-1 b α2 -2.7524-4 3.7633-7 -1.4219-6 1.0114-3 1.4165-5 2.5339-6 -3.8386-5 4.3815-6 -2.5491-5 -4.2949-5 2.4441-5 2 3 α3 2.2324-7 -4.8691-10 1.7272-9 -1.0297-6 -1.1074-8 -3.4459-9 4.1234-8 -8.7917-9 2.7594-8 5.0613-8 -3.3498-8 4 5 α4 -9.3633-11 2.3849-13 -1.0157-12 5.0263-10 4.5511-12 1.8081-12 -2.1629-11 5.6219-12 -1.4440-11 -2.8084-11 1.9721-11 α5 1.5913-14 -4.4136-17 2.1514-16 -9.5176-14 -7.6390-16 -3.5142-16 4.3126-15 -1.2482-15 2.8376-15 5.9744-15 -4.3077-15 Error(%) 0.60 0.02 0.04 12.3 0.07 0.10 0.41 0.05 0.51 0.17 0.08 -2.9921-4 2.3515-4 -4.6134-1 -1.0375-2 6.4837-4 1.7377-2 2.1282-3 1.0553-2 1.6920-2 -5.9431-3 a b Polynomial Function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 1.8416-1 signifies 1.8416×10-1 Table B.52 Coefficients of temperature-property relations for Dowtherm® Propertya pv (10 Pa) 5 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-5Ns/m²) μv (10-5 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Temp. 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °C 100– 400 °C α0 -13.659 6.2599 6.9789 -11.565 6.5143 -4.7238-1 -2.1714 α1 1.3474-1 b α2 -6.8307-4 7.6261-5 -3.6109-6 -7.4914-4 1.3375-4 4.1595-5 -4.6356-5 α3 2.2792-6 -3.1904-7 1.9442-8 2.6390-6 -4.3101-7 -1.8502-7 1.8565-7 α4 -4.1046-9 5.9931-10 -4.6172-11 -4.8454-9 7.6306-10 3.7586-10 -3.5315-10 α5 2.9887-12 -4.2875-13 3.1349-14 3.5407-12 -5.5244-13 2.9462-13 2.5537-13 Error(%) 0.27 0.06 0.01 0.05 0.08 0.01 0.33 -9.1562-3 -5.5143-4 1.3514-1 -2.8763-2 -1.7885-3 4.1094-3 100– 400 °C 100– 400 °C 4.3058 -3.1706-1 -1.7285-2 2.0074-2 1.4156-4 -1.6404-4 -6.7840-7 7.2357-7 1.5240-9 -1.5446-9 -1.3701-12 1.2569-12 0.16 0.34 Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 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 pv (105Pa) Temp. -120– 20 °C -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 α0 3.2181 5.7153 6.0252 3.8345 6.4915 4.4479 -2.5644 -3.9900 1.9473-1 1.2471 5.0629-1 α1 2.5604-2b -1.3766-2 -5.5940-3 2.9745-2 -6.1186-3 3.6435-3 -7.0141-3 7.0307-3 -9.3444-2 1.0319-3 2.2657-3 α2 -2.0481-4 -2.6378-4 -5.4609-5 -1.0357-5 5.8535-5 -1.6045-5 -2.1420-5 -2.4476-5 -1.7344-3 -3.4135-5 9.9616-7 2 3 α3 -1.6186-6 -3.8474-6 -5.7691-7 1.6498-6 5.1235-7 -3.3600-7 -45965-7 -8.7918-7 -1.8129-5 -7.0981-7 -3.3084-8 4 5 α4 1.1732-8 -2.9487-8 -4.0348-9 1.8172-8 2.7979-9 -3.8411-9 -6.1947-9 -1.1320-8 -9.1194-8 -6.2492-9 -3.3255-10 α5 1.9164-10 -8.7228-11 -1.1902-11 1.0060-10 -3.7143-12 -1.3189-11 -2.4827-11 Error(%) 0.42 0.16 0.06 0.66 0.20 0.06 0.08 0.01 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-7Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b -1.6900-10 -1.9064-11 -8.7290-13 1.04 0.05 0.05 Polynomial Function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 2.5604-2 signifies 2.5604×10-2 Table B.54 Coefficients of temperature-property relations for ethanol Propertya pv (105Pa) Temp. 0– 240 °C 0– 240 °C 0– 240 °C 0– 240 °C 0– 240 °C 0– 240 °C 0– 240 °C 0– 220 °C 0– 240 °C 0– 140 °C 0– 120 °C α0 -4.4114 1048.6 -1.07911 -3.3681 5.8942-1 -2.57591 -1.6976 -4.4346 24.419 0.81763 2.9255-1 α1 8.7650-2 -1.0921 -7.7201-3 5.2492-2 -2.2540-2 4.5249-3 -1.2505-3 3.3797-3 -8.1477-2 2.6793-3 1.2271-3 b α2 -6.3182-4 1.0651-2 1.5906-4 5.1630-5 1.0283-4 -3.1212-5 7.5291-7 2.1001-4 -1.1450-4 1.3888-5 8.0938-5 2 3 α3 3.9958-6 -2.0693-4 -1.6139-6 -1.9542-6 -8.8574-7 3.9144-7 5.2361-8 -3.4778-6 8.6540-7 -4.385611 -1.8513-6 4 5 α4 -1.4340-8 1.1231-6 7.1873-9 8.6893-9 4.7884-9 -2.3733-9 -3.4986-10 2.0462-8 -7.6432-9 -4.4424-10 1.6850-8 α5 2.0359-11 -2.4928-9 -1.2075-11 -1.1451-11 -9.7493-12 5.1450-12 6.4599-13 -4.0325-11 1.9148-11 1.5104-12 -5.3880-11 Error(%) 1.24 0.12 0.50 4.95 0.39 0.29 0.10 3.75 2.15 0.01 0.11 hv c (kJ/kg) ρℓ (103kg/m³) ρv (kg/m³) μℓ (10-3Ns/m²) μv (10-5 Ns/m²) kℓ (W/m-K) kv (W/m-K) σc (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial Function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 8.7650-2 signifies 8.7650×10-2 c Polynomial Function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 984 Transport Phenomena in Multiphase Systems Table B.55 Coefficients of temperature-property relations for Freon®-113 Propertya pv c (105Pa) h v (kJ/kg) ρℓ (103kg/m³) ρv c (kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv c (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Temp. -30–70 °C -30–70 °C -30–70 °C -30–70 °C -30–70 °C -30–70 °C -30–70 °C 50 °C -30–70 °C -30–70 °C -30–70 °C α0 1.5513-1b 5.0647 4.8109-1 1.2915 -8.8373-2 4.5742 -2.4988 8.66-3 3.0672 -8.1787-2 -4.7900-1 α1 5.5834-3 -1.0499-3 -7.0767-4 4.3043-2 -9.8086-3 1.3980-3 -2.7661-3 α2 1.9778-4 -2.6927-5 -1.9487-5 1.4813-3 -2.0540-4 3.4991-5 -3.9035-6 α3 2.8601-6 -6.1850-7 -4.7513-7 2.0168-5 -6.0984-6 9.1946-7 2.0723-8 α4 -5.7513-8 2.7966-8 2.1984-8 -5.0204-7 3.1638-7 -4.4771-8 -4.4813-10 α5 5.3363-10 -2.3520-10 -1.9019-10 4.6851-9 -2.7593-9 3.8285-10 1.8509-12 Error(%) 1.45 0.10 0.09 1.35 1.57 0.12 0.01 -3.0787-3 1.7608-3 1.6029-3 2 -8.9997-5 -1.6786-5 -1.1241-5 3 4 -2.0623-6 2.3976-7 5.9003-8 5 9.4964-8 -8.0415-10 0.04 0.02 0.12 -8.1962-10 -1.0574-11 5.3622-9 -5.9305-11 Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 1.5513-1 signifies 1.5513×10-1 c Polynomial function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 Table B.56 Coefficients of temperature-property relations for Freon®-123 Propertya pv (10 Pa) 5 h v (kJ/kg) ρℓ (103kg/m³) ρv c (kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a Temp. -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C -60– 80 °C α0 -1.1195 5.2009 4.2279-1 2.2395 -5.7105-1 4.5890 -2.4809 -4.8616 2.9004 -9.8440-3 -4.2964-1 α1 4.5666-2 b α2 -1.9934-4 -4.5252-6 -2.6844-6 1.6184-3 2.4428-5 -1.0586-5 -1.4384-6 -2.2812-5 -1.8095-5 7.2577-7 -6.5433-8 α3 8.5444-7 -2.7239-8 -1.1732-8 1.3321-5 -1.3376-7 3.4387-8 2.9439-8 1.4868-7 -6.1639-8 -1.3957-8 2.8020-8 α4 -3.5199-9 -7.7727-11 -6.3028-11 4.9021-8 1.2093-9 -6.7932-11 -3.4971-10 -1.1456-9 -3.3005-10 3.0203-10 7.5571-11 α5 1.1017-11 -7.0220-13 1.7371-13 4.0765-11 -6.4471-12 1.0880-12 1.7944-12 8.3612-12 -2.3405-12 8.1384-13 -2.5335-13 Error(%) 0.01 0.00 0.01 0.05 0.04 0.01 0.02 0.01 0.00 0.01 0.02 -2.1509-3 -1.5851-3 9.5368-2 -1.2631-2 3.7376-3 -3.5937-3 7.3399-3 -6.7246-3 1.1580-3 2.6267-3 Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 b The notation 4.5666-2 signifies 4.5666×10-2 c Polynomial function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 Appendix B. Transport Properties 985 Table B.57 Coefficients of temperature-property relations for Freon®-134a Propertya pv (10 Pa) c 5 h v (kJ/kg) ρℓ (10 kg/m³) ρv c (kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv c (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a 3 Temp. -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C -60– 60 °C α0 2.9283 5.2912 2.5819-1 1.4323+1 -1.3047 4.6756 -2.3865 1.1516-2 2.4473 2.9357-1 -1.0828-1 α1 1.0610-1 b α2 1.4766-3 -1.9182-5 -8.4503-6 7.6087-3 1.3074-5 -2.6263-6 -4.9980-6 1.2320-7 -5.9505-5 1.1431-5 1.6049-5 α3 9.1273-6 -1.3660-7 -5.3400-8 6.5242-5 -3.6304-7 8.7893-8 -1.5376-7 2.0313-9 -4.0640-7 7.9461-8 1.1362-7 α4 1.8868-8 -1.4190-9 -6.1301-10 -4.1610-8 6.4168-10 5.0768-10 -7.5506-10 3.6695-11 -4.5286-9 1.4916-9 2.3121-9 α5 -1.0026-11 -1.1862-11 -4.3062-12 -4.9125-9 4.3908-12 6.1839-12 2.1118-11 2.8646-13 -3.3364-11 1.6785-11 2.5170-11 Error(%) 0.03 0.01 0.01 0.56 0.05 0.00 0.02 0.02 0.01 0.01 0.02 -3.8266-3 -2.5548-3 4.9951-1 -1.2721-2 3.8342-3 -4.7587-3 8.6892-5 -1.2448-2 2.0423-3 5.0590-3 Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 b The notation 1.0610-1 signifies 1.0610×10-1 c Polynomial function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 Table B.58 Coefficients of temperature-property relations for Freon®-21 Propertya pv (105Pa) Temp. -60– 120 °C -60– 120 °C -60– 120 °C -60– 120 °C -60– 120 °C -60– 120 °C -60– 120 °C -40– 120 °C -60– 120 °C -20– 120 °C -60– 120 °C α0 -3.4451-1b 5.4933 3.5332-1 1.1960 -1.0724 4.6629 -2.2136 -4.9866 3.0590 1.4889-2 -5.6775-1 α1 4.1751-2 -2.1700-3 -1.5737-3 3.9035-2 -1.2269-2 2.7294-3 -3.2496-3 1.0894-2 -6.7747-3 1.3267-3 1.8572-3 α2 -1.7642-4 -7.6996-6 -2.9329-6 -1.5967-4 4.5152-5 -2.5030-7 -1.2739-5 -9.0477-5 -2.2547-5 1.3973-5 -5.0100-6 2 3 α3 7.1705-7 -1.3706-8 -8.1168-9 7.1148-7 2.0188-7 -1.3902-9 1.8600-8 4.7958-7 -2.2853-9 -1.0390-8 -5.1476-9 4 5 α4 -2.5411-9 -2.9105-10 4.8930-11 -2.7682-9 2.3391-9 -5.2580-10 2.1809-9 -8.3962-10 -1.7098-10 -2.8225-10 3.2243-10 α5 5.6934-12 2.2108-13 -1.6497-12 8.5168-12 -2.8723-11 3.2451-12 -2.0491-11 0.0 -1.5797-11 0.0 -1.2404-12 Error(%) 0.01 0.04 0.11 0.05 0.77 0.10 0.22 0.01 0.18 0.01 0.06 hv (kJ/kg) ρℓ (103kg/m³) ρv (kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T 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 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C -100– 60 °C α0 1.6060 5.3194 2.5101-1 3.0582 9.8169-1 4.7763 -2.3264 -4.5693 2.4636 1.5887-1 -3.0127-1 α1 3.2529-2 b α2 -1.3092-4 -2.0700-5 -8.8462-6 -1.0338-4 2.2490-5 -9.2066-6 -1.0280-5 -3.1493-5 -7.1002-5 1.3013-5 2.9892-5 2 3 α3 5.4844-7 -1.8940-7 -6.2742-8 6.3370-7 -1.5992-7 -8.9021-8 -1.1905-7 6.8438-7 -4.6908-7 1.5071-7 9.8627-8 4 5 α4 -2.3659-9 -1.7339-9 -1.0131-9 -1.2757-9 -4.0714-10 7.9195-10 -2.4990-9 -3.1372-10 -5.7002-9 3.7021-9 1.1367-9 α5 1.7589-11 -7.7266-12 -5.4408-12 2.3553-11 9.5286-12 1.1511-11 -1.4352-11 -6.2585-11 -3.2763-11 2.4147-11 1.0353-11 Error(%) 0.02 0.03 0.02 0.01 0.07 0.14 0.09 1.60 0.31 0.16 0.51 hv (kJ/kg) ρℓ (103kg/m³) ρv (kg/m³) μℓ (10-4Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b -3.9023-3 -2.6444-3 3.1512-2 -5.6143-3 3.5563-3 -5.1094-3 4.3334-3 -1.3560-2 1.9513-3 6.0931-3 Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T 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 °C -20– 160 °C -20– 160 °C -0 – 160 °C -20– 160 °C 100– 160 °C -20– 80 °C -20– 160 °C -20– 160 °C -20– 160 °C -20– 160 °C α0 -4.1875 5.9286 -0.35593 -9.5679 -6.4586-1 3.8877 -2.0099 -4.6160 3.1702 7.7016-1 -1.3938-1 α1 6.2035-2 b α2 -2.8899-4 -8.0368-6 -1.1416-6 -6.8200-5 5.1105-5 -3.0481-5 -1.7251-6 -1.5605-5 3.7806-5 3.6697-6 1.1500-5 2 3 α3 1.3328-6 3.0846-8 4.0160-9 -2.6778-6 -2.0879-7 9.7703-8 -9.2954-7 1.158-7 -4.8714-7 -2.9931-8 -1.7062-7 4 5 α4 -4.8688-9 3.8138-11 -8.1251-11 2.4493-8 -4.8532-10 0.0 2.2360-8 -1.4660-9 2.3540-9 2.3965-10 -1.4205-9 α5 8.7514-12 -8.8137-13 1.2225-13 -6.4331-11 4.0509-12 0.0 -1.4260-10 5.4467-12 -5.3416-12 -7.3288-13 1.5923-11 Error(%) 0.07 0.01 0.01 0.81 0.38 0.01 0.01 0.14 0.06 0.07 0.11 hv (kJ/kg) ρℓ (103kg/m³) ρv (103kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b -1.1575-3 -1.2011-3 5.4885-2 -1.2617-2 6.1806-3 -1.6511-3 7.7908-3 -7.2045-3 1.4975-3 2.6295-3 Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T 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 K 1400– 2500 K 1400– 2500 K 1400– 2500 K 1400– 2500 K 1400– 2500 K α0 4.6336 920 3.6048 8.3434 -3.5423 -6.17011 -3.2801-3 -5.9172-2 1.0984-2 4.9129-3 3.2902-6 8.0693-5 -1.2825-5 -4.1177-6 -1.7002-9 -4.5861-8 7.0970-9 1.9835-9 4.3394-13 1.2260-11 -1.9132-12 -4.9092-13 -4.3951-17 -1.2705-15 2.0177-16 4.8791-17 0.03 0.83 0.15 0.02 α1 -5.2565-2 b α2 7.4881-5 α3 -4.3022-8 α4 1.1552-11 α5 -1.1994-15 Error(%) 0.89 hv (kJ/kg) ρℓ (103kg/m³) ρv (kg/m³) μℓ (10-3Ns/m²) μv (10-5 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b 1400– 2500 K 25.135 -4.9401-2 5.0275-5 -2.5283-8 6.2419-12 -6.0685-16 0.32 Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 The notation 5.2565-2 signifies 5.2565×10-2 Table B.62 Coefficients of temperature-property relations for lithium Propertya pv (102Pa) Temp. 900– 2000 K 900– 2000 K 900– 2000 K 900– 2000 K 900– 2000 K 900– 2000 K 900– 2000 K 1100– 2000 K 900– 2000 K 900– 2000 K 900– 2000 K α0 -65.397 10.701 6.0669 -68.241 9.4544 2.8973 4.2556 20.694 7.8595 1.4122-1 -3.7092 α1 1.5599-1b -2.3108-3 8.3105-4 1.6057-1 -2.7505-2 1.1891-2 -2.5537-3 -8.4269-2 -7.2138-3 5.1039-3 1.2156-2 2 α2 -1.5201-4 3.1400-6 -1.5042-6 -1.6084-4 3.6732-5 -1.5340-5 5.0480-6 1.1754-4 1.0848-5 -7.8268-6 -8.1715-6 3 4 α3 8.1778-8 -2.2140-9 1.0686-9 8.8500-8 -2.5268-8 1.0624-8 -4.0821-9 -7.8416-8 -8.4472-9 5.7796-9 1.6862-9 5 α4 -2.3065-11 7.5364-13 -3.7709-13 -2.5450-11 8.6852-12 -3.7032-12 1.5784-12 2.5440-11 3.2074-12 -2.0587-12 2.3686-13 α5 2.6663-15 -9.9447-17 5.1832-17 2.9917-15 -1.1841-15 5.1272-16 -2.3730-16 -3.2371-15 -4.7997-16 2.8515-16 -9.6999-17 Error(%) 0.79 0.09 0.02 0.30 0.16 0.13 0.12 0.52 0.11 0.01 0.04 h v (kJ/kg) ρℓ (kg/m³) ρv (10-3kg/m³) μℓ (10-4Ns/m²) μv (10-8 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3 N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α 0 + α 1T + α 2 T + α 3 T + α 4 T + α 5 T -1 The notation 1.5599-1 signifies 1.5599×10 988 Transport Phenomena in Multiphase Systems Table B.63 Coefficients of temperature-property relations for mercury Propertya pv (105Pa) Temp. 100– 700 K 100– 700 K 100– 700 K 100– 700 K 100– 700 K 100– 700 K 100– 700 K 300– 700 K 100– 700 K 100– 700 K 100– 700 K α0 -14.575 5.7260 9.5173 -12.403 4.9966-1 5.5053 2.1052 -8.2112 -6.11231 -1.9647 3.9221-2 α1 8.4718-2 -1.1371-4 -1.7845-4 8.1209-2 -3.5741-3 4.7804-3 1.5928-3 1.8371-2 -2.8045-3 -2.7998-4 0.0 2 α2 -2.0927-4 6.3434-9 -1.2298-8 -2.0418-4 8.5984-6 -1.1839-5 -1.6980-6 -4.5018-5 1.5740-5 5.8783-7 0.0 3 4 α3 3.3495-7 1.3279-10 4.1107-11 3.2816-7 -1.3495-8 2.3678-8 1.2601-9 5.6262-8 -4.7357-8 -2.655810 0.0 5 α4 -2.9993-10 -4.0224-13 -1.2592-13 -2.9379-10 1.1914-11 -2.5687-11 -7.9198-13 -2.6760-11 6.0220-11 4.0363-13 0.0 α5 1.1264-13 1.4867-16 6.5094-17 1.1027-13 -4.4337-15 1.1088-14 2.9427-16 0.0 -2.7769-14 -2.6814-16 0.0 Error(%) 0.15 0.01 0.01 0.13 0.03 0.04 0.01 0.01 0.58 0.01 0.00 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 8.4718-2 signifies 8.4718×10-2 Table B.64 Coefficients of temperature-property relations for methanol Propertya pv (105Pa) Temp. 0– 240 ˚C 0– 240 ˚C 60– 220 ˚C 0– 240 ˚C 0– 240 ˚C 0– 240 ˚C 0– 140 ˚C 40– 220 ˚C 0– 220 ˚C 0– 40 ˚C 0– 140 ˚C α0 -3.2260 7.1001 -2.00541 -67.300 -2.05291 4.4794 -1.5847 -6.7646 3.2019 8.8377-1 3.1404-1 α1 5.2299-2 b α2 1.0307-4 4.2482-5 1.8492-4 -3.0858-2 1.2225-4 4.0163-6 1.1186-5 -3.5238-5 1.1123-4 9.6297-6 -1.7365-4 2 3 α3 -2.9204-6 -8.2591-7 -2.6081-6 2.1359-4 -1.0701-6 -7.3376-8 -2.2761-7 1.4232-7 -1.7652-6 0.0 3.4376-6 4 5 α4 1.4369-8 5.2087-9 1.4646-8 -7.2014-7 4.5665-9 2.4641-10 1.6087-9 -4.0030-10 1.0660-8 0.0 -2.5001-8 α5 -2.2852-11 -1.1710-11 -2.8794-11 9.4732-10 -7.2697-12 -2.1042-13 -3.9220-12 5.0729-13 -2.4530-11 0.0 5.9705-11 Error(%) 3.52 0.39 1.96 6.77 0.35 0.28 0.03 0.03 0.65 0.01 0.40 h v (kJ/kg) ρℓ (103kg/m³) ρv (103 kg/m³) μℓ (10-3Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b -1.6650-3 -5.5461-3 2.1944 -1.8685-2 3.3930-3 -4.0650-4 8.9038-3 -6.2365-3 6.2710-4 5.0100-3 Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T 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 K 70–120 K 70–120 K 70–120 K 70–120 K 70–120 K 70–120 K 70–120 K 70–120 K 70–110 K 70–120 K α0 -43.782 40.773 35.567 -67.907 948.70 -2.9587 32.320 -84.477 548.30 6.5809 -431.10 α1 1.5669 -2.0285 -1.9499 2.8270 -51.222 2.9150-1 -1.9406 4.4031 -31.026 -2.9472-1 24.938 α2 -2.3774-2b 4.6388-2 4.2463-2 -5.5599-2 1.1060 -5.1900-3 4.3870-2 -9.7414-2 7.0194-1 5.5008-3 -5.7258-1 2 3 α3 1.9698-4 -5.2896-4 -4.6083-4 5.8348-4 -1.1838-2 4.8252-5 -4.9230-4 1.0725-3 -7.9006-3 -4.5869-5 6.5396-3 4 5 α4 -8.5268-7 3.0054-6 2.4889-6 -3.1442-6 6.2780-5 -2.2449-7 2.7304-6 -5.8607-6 4.4236-5 1.4529-7 -3.7167-5 α5 1.5176-9 -6.8292-9 -5.3639-9 6.8695-9 -1.3198-7 4.1366-10 -6.0054-9 1.2734-8 -9.8671-8 0.0 8.4167-8 Error(%) 0.49 0.22 0.22 0.08 4.14 0.03 0.50 3.35 0.57 0.05 0.10 hv (kJ/kg) ρℓ (103kg/m³ ) ρv (103 kg/m³) μℓ (105 Ns/m²) μv (10-7 Ns/m²) kℓ (W/mK) kv (W/mK) σ (103 N/m) cp,ℓ (kJ/kg-K) cp,v c (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 2.3774-2 signifies 2.3774×10-2 c Polynomial Function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 Table B.66 Coefficients of temperature-property relations for potassium Propertya pv (105Pa) Temp. 600– 1500 K 600– 1500 K 600– 1500 K 600– 1500 K 600– 1500 K 800– 1500 K 600– 1500 K 700– 1500 K 600– 1500 K 600– 1500 K 600– 1500 K α0 -60.792 7.4437 6.8171 -43.901 3.7145 -2.7247 4.6283 -9.5175 9.5646 -1.5299 -2.2283 α1 2.0072-1 b α2 -2.9607-4 -2.6188-6 6.4906-8 -1.9914-4 1.1332-5 -5.5202-5 5.6190-6 -1.5544-5 5.2720-5 -1.9186-5 6.2200-6 α3 2.3898-7 2.2227-9 -1.128510 1.4552-7 -8.1123-9 4.8605-8 -6.0362-9 7.1481-9 -5.3832-8 2.0925-8 -1.3592-8 α4 -1.0021-10 -9.95606-13 4.9791-14 -5.6005-11 3.0732-12 -2.1075-11 3.0539-12 -1.0428-12 2.6602-11 -1.0612-11 8.6984-12 α5 1.7070-14 1.6216-16 -1.0285-17 8.8657-15 -4.7794-16 3.5833-15 -6.3262-16 -1.0113-16 -5.1195-15 2.0459-15 -1.8919-15 Error(%) 0.41 0.05 0.01 0.36 0.02 0.14 0.04 0.14 0.51 0.11 0.05 h v (kJ/kg) ρℓ (kg/m³) ρv (10-3 kg/m³) μℓ (10-4Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (10-1kJ/kgK) 1.3335-3 -2.9903-4 1.5060-1 -9.2264-3 3.1905-2 -3.1884-3 1.5278-2 -2.5629-2 8.1223-3 2.9093-3 a b Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 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) Temp. 500– 1500 K 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 α0 -55.657 6.7318 7.3881 -66.172 4.0558 -9.8418 4.7043 -6.6733 7.9250 -2.3892 -3.3670 α1 1.8743-1 b α2 -2.7675-4 -1.7798-6 -3.4371-8 -4.5141-4 1.4889-5 -7.1293-5 1.3165-5 8.4641-6 4.3014-5 -1.9597-5 -5.4747-7 2 3 α3 2.2191-7 1.7134-9 -1.584911 4.1965-7 -1.1567-8 7.1688-8 -1.4204-8 -1.5050-8 -4.7024-8 2.0443-8 -7.5127-9 4 5 α4 -9.2037-11 -8.4612-13 3.9560-15 -1.9911-10 4.6581-12 -3.5422-11 7.2430-12 9.5117-12 2.4631-11 -9.8727-12 6.2261-12 α5 1.5478-14 1.6787-16 -2.0966-18 3.7782-14 -7.5589-16 6.8223-15 -1.4313-15 -2.1186-15 -5.0586-15 1.8050-15 -1.5185-15 Error(%) 0.57 0.02 0.01 3.00 0.12 0.56 0.17 0.08 0.73 0.21 0.15 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-4Ns/m²) μv (10-4 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b 6.7485-4 -2.8698-4 2.5978-1 -1.0855-2 3.6490-2 -6.4659-3 1.4823-3 -1.9554-2 8.5914-3 6.0154-3 Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation 1.8743-1 signifies 1.8743×10-1 Table B.68 Coefficients of temperature-property relations for silver Propertya pv (105Pa) h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ c (10-3Ns/m²) μv (10-6 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Temp. 1500– 2500 K 1500– 2500 K 1500– 2500 K 1500– 2500 K 1500– 2500 K 1500– 2100 K α0 263.11 α1 -7.1135-1b α2 7.2544-4 α3 -3.5810-7 α4 8.6526-11 α5 -8.2124-15 Error(%) 3.94 8.5176 -173.43 -5.38641 2.9330 5.1376 1.6679-3 3.9882-1 3.1996-2 1.2850-3 8.2034-5 -1.7069-6 -3.8988-4 -4.6751-5 -4.9599-7 -3.2260-9 8.0584-10 1.9489-7 2.7477-8 1.4551-10 1.2246-13 -1.8715-13 -4.8845-11 -7.5466-12 -2.5305-14 0.0 1.7012-17 4.8792-15 8.0128-16 1.9217-18 0.0 0.02 4.93 1.14 0.01 0.01 1500– 2500 K 3.1881 1.7708-2 -2.7287-5 1.8780-8 -6.0622-12 7.4708-16 1.18 Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 The notation 7.1135-1 signifies 7.1135×10-1 c Polynomial Function: Property = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 Appendix B. Transport Properties 991 Table B.69 Coefficients of temperature-property relations for sodium Propertya pv (102Pa) Temp. 600– 1800 K 600– 1800 K 600– 1800 K 600– 1800 K 600– 1800 K 600– 1800 K 600– 1800 K 700– 1500 K 600– 1800 K 600– 1200 K 600– 1500 K α0 -57.346 8.2271 6.9583 -57.566 4.1428 6.4857 6.0146 -2.9716 5.5631 2.4330 -4.3532 α1 1.8129-1b 1.1086-3 -3.9865-4 0.18157 -9.2518-3 1.6476-3 -7.4369-3 -1.3227-2 -1.0484-3 -1.1431-2 1.5451-2 α2 -2.2487-4 -2.1757-6 2.6890-7 -2.2885-4 1.0570-5 -6.37865-7 1.3548-5 3.8083-5 1.1969-6 2.4444-5 -1.5104-5 α3 1.5164-7 1.6631-9 -2.584310 1.5614-7 -6.9077-9 3.8144-10 -1.2912-8 -4.1771-8 -1.3563-9 -2.6701-8 5.0582-9 α4 -5.2957-11 -6.0973-13 1.0321-13 -5.5058-11 2.3709-12 -2.3380-13 5.8860-12 2.0652-11 6.7582-13 1.4701-11 2.9861-13 α5 7.5006-15 8.7109-17 -1.6518-17 7.8615-15 -3.3213-16 5.4972-17 -1.0619-15 -3.8556-15 -1.4750-16 -3.2175-15 -3.5328-16 Error(%) 0.98 0.02 0.02 1.25 0.05 0.16 0.21 0.17 0.02 0.13 0.04 hv (kJ/kg) ρℓ (kg/m³) ρv (10-3kg/m³) μℓ (10-4Ns/m²) μv (10-8 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T2 + α3T3 + α4T4 + α5T5 The notation 1.8129-1 signifies 1.8129×10-1 Error (%) 0.01 0.05 0.02 0.01 0.02 0.04 0.04 0.07 0.03 0.01 0.01 Table B.70 Coefficients of temperature-property relations for water Propertya pv (105Pa) Temp. 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C 20– 200 ˚C α0 -5.0945 7.8201 6.9094 -5.3225 9.7620 4.3995 -5.6528-1 -4.0406 4.3438 1.4338 6.2084-1 α1 7.2280 -5.8906-4 -2.0146-5 6.8366-2 -3.1154-2 3.8789-3 3.1743-3 3.2288-3 -3.0664-3 -2.2638-4 3.1420-4 α2 -2.8625-4 b -9.1355-6 -5.9868-6 -2.7243-4 2.0029-4 2.1181-5 -1.4392-5 5.3383-6 2.0743-5 4.2819-6 1.6110-6 2 3 α3 9.2341-7 8.4738-8 2.5921-8 8.4522-7 -9.5815-7 -3.4406-7 -1.3224-8 -6.7139-8 -2.5499-7 -2.7411-8 4.0156-8 4 5 α4 -2.0295-9 -3.9635-10 -9.3244-11 -1.6558-9 2.7772-9 1.6730-9 2.5534-10 4.0967-10 1.0377-9 1.4699-10 3.4841-11 α5 2.1645-12 5.9150-13 1.2103-13 1.5514-12 -3.5075-12 -2.8030-12 -6.4454-13 -6.9579-13 -1.7156-12 -2.2589-13 -2.0709-13 h v (kJ/kg) ρℓ (kg/m³) ρv (kg/m³) μℓ (10-7Ns/m²) μv (10-7 Ns/m²) kℓ (W/m-K) kv (W/m-K) σ (10-3N/m) cp,ℓ (kJ/kg-K) cp,v (kJ/kg-K) a b Polynomial function: ln(Property) = α0 + α1T +α2T + α3T + α4T + α5T The notation -2.8625-4 signifies -2.8625×10-4 992 Transport Phenomena in Multiphase Systems Table B.71 Binary diffusion coefficients at 1 atma (Incropera and DeWitt 2001) Substance A Gases NH3 H2O CO2 H2 O2 Acetone Benzene Naphthalene Ar H2 H2 H2 CO2 CO2 O2 Dilute solutions Caffeine Ethanol Glucose Glycerol Acetone CO2 O2 H2 N2 Solids O2 N2 CO2 He H2 Cd Al a Substance B Air Air Air Air Air Air Air Air N2 O2 N2 CO2 N2 O2 N2 H2O H2O H2 O H2O H2O H2O H2O H2O H2O Rubber Rubber Rubber SiO2 Fe Cu Cu T(K) 298 298 298 298 298 273 298 300 293 273 273 273 293 273 273 298 298 298 298 298 298 298 298 298 298 298 298 293 293 293 293 DAB (m2/s) 0.28 × 10-4 0.26 × 10-4 0.16 × 10-4 0.41 × 10-4 0.21 × 10-4 0.11 × 10-4 0.88 × 10-5 0.62 × 10-5 0.19 × 10-4 0.70 × 10-4 0.68 × 10-4 0.55 × 10-4 0.16 × 10-4 0.14 × 10-4 0.18 × 10-4 0.63 × 10-9 0.12 × 10-8 0.69 × 10-9 0.94 × 10-9 0.13 × 10-8 0.20 × 10-8 0.24 × 10-8 0.63 × 10-8 0.26 × 10-8 0.21 × 10-9 0.15 × 10-9 0.11 × 10-9 0.4 × 10-13 0.26 × 10-12 0.27 x 10-18 0.13 x 10-33 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 ⎛ p ⎞⎛ T ⎞ m2/s; DH 2 O, air = 1.97 × 10−5 ⎜ 0 ⎟ ⎜ ⎟ 273K < T < 373K ⎝ p ⎠⎝ T0 ⎠ where p0 = 1 atm; T0 = 256 K. The following formula has also found increasing use (Marrero and Mason,1972); 1.685 DH 2 O air = 1.87 × 10−10 T = 2.75 × 10−9 2.072 p ; 280K < T < 450K 450K < T < 1070K T 1.632 ; p 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-α-titanium Hydrogen-β-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 kJ/kmol m /s 2 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) Chemical Vapor Acetone Ammonia Benzene Carbon dioxide Carbon monoxide Chlorine Ethanol Helium Heptane Hydrogen Hydrogen sulfide Methanol Napthalenec Nitric oxide Octane Oxygen Pentane Sulfur dioxide Water vapor a hv Scb 1.42 0.61 1.79 1.00 0.77 1.42 1.32 0.22 2.0 0.20 0.94 0.98 2.35 0.87 2.66 0.83 1.49 1.24 0.61 0.340 0.454 0.548 1.100 0.567 0.465 0.303 0.214 0.357 0.398 2.257 J/kg × 10-6 0.527 1.370 0.395 0.398 0.217 0.288 0.854 Boiling point temperature K 329 240 354 194 81 238 352 4.3 372 20.3 213 338 491 121 399 90.6 309 263 373 Formula CH3COCH3 NH3 C6H6 CO2 CO Cl2 CH3CH2OH He C7H16 H2 H2 S CH3OH C10H8 NO C8H18 O2 C5H12 SO2 H2O b With the Clausius-Clapeyron relation, one may estimate vapor pressure as ⎧ Mh v ⎛ 1 1 ⎞⎫ ⎪ ⎪ psat exp ⎨ − ⎜− ⎟ ⎬ atm, for T ∼ TBP ⎪ Ru ⎝ T TBP ⎠ ⎪ ⎩ ⎭ The Schmidt number is defined as Sc = μ / ρ D = v / D . Since the vapors are in small concentrations, values for μ, ρ and v can be taken as pure air values. c Cho et al. (1992); h v = 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 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 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 For other temperatures use Sc / Sc300 K ( μ 2 / ρT ) /( μ 2 / ρT )300 K , where μ and ρ are for water, and T is absolute ( M 2 / M1 )0.4 . A table temperature. For chemically similar solutes of different molecular weights use Sc 2 / Sc1 of ( μ 2 / ρT ) /( μ 2 / ρT )300 K for water follows. T[K] 290 300 310 320 330 ( μ 2 / ρT ) /( μ 2 / ρT )300 K 1.66 1.00 0.623 0.429 0.296 T [K] 340 350 360 370 ( μ 2 / ρT ) /( μ 2 / ρT )300 K 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 H2 Solid Vulcanized rubber Vulcanized neoprene Silicone rubber Natural rubber Polyethylene Polycarbonate Fused silica Nickel T(K) 300 290 300 300 300 300 400 800 360 440 He Silicone rubber Natural rubber Polycarbonate Nylon 66 Teflon Fused silica Pyrex glass 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 Silicone rubber Natural rubber Polyethylene Polycarbonate Silicone-polycarbonate copolymer (57% silicone) Ethyl cellulose 300 300 300 300 300 300 800 300 800 470 580 720 390 680 300 300 300 300 300 300 300 S ′ [m3 (STP)/m3 atm] or S’a Permeabilityb m3(STP)/m2s (atm/m) 0.34 × 10-10 0.053 × 10-10 4.2 × 10-10 0.37 × 10-10 0.065 × 10-10 0.091 × 10-10 S ′ = 0.040 S ′ = 0.051 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 S ′′ ≅ 0.018 S ′′ ≅ 0.026 S ′′ ≅ 0.006 S ′′ ≅ 0.024 S ′ = 0.0084 S ′ = 0.0038 S ′ = 0.0046 S ′ = 0.0039 S ′ = 0.0059 S ′ = 0.070 4.6 × 10-13 1.6 × 10-12 6.4 × 10-12 1.2 × 10-14 1.0 × 10-12 0.15 × 10-10 3.8 × 10-10 0.18 × 10-10 4.2 × 10-12 0.011 × 10-10 1.2 × 10-10 0.09 × 10-10 O2 998 Transport Phenomena in Multiphase Systems Table B.76 Solubility and permeability of gases in solids (Mills, 1999) (cont’d) Gas N2 Solid Vulcanized rubber Silicone rubber Natural rubber Silicone-polycarbonate copolymer (57% silicone) Teflon® Vulcanized rubber Silicone rubber Natural rubber Silicone-polycarbonate copolymer (57% silicone) Nylon 66 H2O Ne Ar a T(K) 300 300 300 300 300 300 300 300 300 300 310 300-1200 900-1200 S ′ [m3 (STP)/m3 atm] or S’a Permeabilityb m3(STP)/m2s (atm/m) 0.054 × 10-10 1.9 × 10-10 0.062 × 10-10 0.53 × 10-10 0.019 × 10-10 1.0 × 10-10 21 × 10-10 1.0 × 10-10 7.4 × 10-10 0.0013 × 10-10 0.91-1.8 × 10-10 S ′ = 0.035 CO2 S ′ = 0.90 Cellophane Fused silica Fused silica 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 . Permeability K = DAB S ′ . b 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 ---- C l2 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 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 1000 Transport Phenomena in Multiphase Systems 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 Formula Al2(SO4)3 Ca(HCO3)2 CaCl2 CaCl2 Ca(OH)2 KCl KNO3 K2SO4 NaHCO3 Na2O3 Na2CO3 NaCl NaNO2 Na2SO4 Na2SO4 Na2SO4 a Solid Phase 18H2O 6H2O 2H2O 10H2O 1H2O 10H2O 7H2O - 273.15 280 31.2 32.8 290 35.5 300 39.1 310 44.3 320 50.3 T (K) 330 57.0 340 63.9 350 70.8 360 78.3 370 84.6 373.15 89.0 18.40 159.0 0.077 56.7 246.0 24.1 45.5 39.8 180 42.5 16.15 16.30 16.53 16.75 16.98 17.20 17.43 17.65 17.88 59.5 63.3 71.5 93.3 137.2 - 18.10 18.33 - 134.6 140.2 145.3 150.9 157.0 0.088 0.080 53.1 55.8 0.185 0.179 0.168 0.157 0.145 0.132 0.120 0.109 0.098 27.6 13.3 7.35 6.9 7 35.7 73 5.0 19.5 29.9 18.5 33.1 28.2 36.1 41.3 39.1 58.2 41.8 44.6 47.4 50.2 78.7 102.3 129.2 159.2 191.6 232.1 22.36 23.69 45.7 38.8 159 43.3 45.55 39.5 175 42.7 8.63 10.51 12.38 14.20 15.95 17.64 19.25 20.88 7.76 10.8 35.8 78 7.7 26.7 9.14 10.63 12.20 13.90 15.79 18.7 35.9 85 16.1 39.6 33.4 36.2 93 34.1 49.1 36.5 101 49.6 47.8 36.9 111 47.4 46.7 37.2 121 45.7 46.2 37.6 132 43.7 45.9 38.2 144 44.0 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) p A, g (atm) 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 x A, 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) p A, g (atm) 0.001 0.003 0.01 0.03 0.1 0.3 1.0 a x A, × 103 290 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 18.0 320 K 0.042 0.093 0.22 0.51 1.4 3.9 12.0 Notice that Henry’s law is invalid for the SO2-water system, even at very dilute concentrations. 1002 Transport Phenomena in Multiphase Systems 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 Enthalpya, b (KJ/kg) Liquid Water 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 Dry Air 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 Saturated Air 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 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 Dry 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 Saturated Air 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 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