Appendix A: Constants, Units, and Conversion Factors

Appendix A: Constants, Units,and Conversion Factors

See Tables A.1, A.2 and A.3

Table A.1 Physical constants

Universal gas constant Ru ¼ 8314:34 J/(kmol K)

Boltzmann constant kb ¼ 1:38054� 10�23 J/K

Stefan–Boltzmann constant rSB ¼ 5:67� 10�8 W/(m2 K4ÞAtmospheric pressure patm ¼ 1:013� 105 Pa

Gravitational acceleration g ¼ 9:807 m/s2

Table A.2 Prefixes

Factor Prefix Symbol Factor Prefix Symbol

1018 Exa E 10−1 Deci d

1015 Peta P 10−2 Centi c

1012 Tera T 10−3 Milli m

109 Giga G 10−6 Micro l

106 Mega M 10−9 Nano n

103 Kilo k 10−12 Pico p

102 Hecto h 10−15 Femto f

10 Deka da 10−18 Atto a

© Springer Nature Switzerland AG 2020A. Faghri and Y. Zhang, Fundamentals of MultiphaseHeat Transfer and Flow, https://doi.org/10.1007/978-3-030-22137-9

747

https://doi.org/10.1007/978-3-030-22137-9

Table A.3 Conversion factors

Physical quantity Conversion factor

Acceleration ft/s2 0.30480 m/s2

m/s2 3.2808 ft/s2

Area ft2 0.092903 m2

cm2 0.15500 in2

m2 10.764 ft2

Density lbm/in3 1728.0 lbm/ft3

lbm/ft3 16.018 kg/m3

kg/m3 0.062428 lbm/ft3

g/m3 62.428 lbm/ft3

Energy Btu 1.0551 kJ

Btu 0.0002930 kW h

Btu 0.25200 kcal

ft lbf 0.0012851 Btu

kW h 3412.8 Btu

kcal 3.9683 Btu

kJ 0.94782 Btu

HP h 2544.4 Btu

Energy flux Btu/h ft2 3.1546 W/m2

kcal/h m2 0.36867 Btu/h ft2

cal/s cm2 13272.0 Btu/h ft2

W/cm2 3170.0 Btu/h ft2

W/m2 0.8598 kcal/h m2

W/m2 0.31700 Btu/h ft2

Enthalpy Btu/lbm 2324.4 J/kg

J/kg 0.00043021 Btu/lbm

Force lbf 32.1740 lbm ft/s2

lbf 4.448 N

kgf 2.2046 lbf

kgf 9.80665 N

N 0.22481 lbf

Heat transfercoefficient

Btu/h ft2 °F 5.6782 W/m2 K

kcal/h m2 °C 0.20482 Btu/h-ft2 °F

W/m2 K 0.17611 Btu/h-ft2 °F

W/m2 K 0.8598 kcal/h m2 °C

Kinematic viscosity (m)Thermal diffusivity (a)Mass diffusivity (D)

ft2/h 2.5807�10−5 m2/s

ft2/s 0.092905 m2/s

m2/s 10000 cm2/s (stokes)

m2/s 38750 ft2/h

m2/s 10.764 ft2/s

Length in 25.4 mm

ft 0.3048 m

in 0.08333 ft

mm 0.039370 in

m 3.2808 ft(continued)

748 Appendix A: Constants, Units, and Conversion Factors

Table A.3 (continued)


Mass lbm 0.45359 kg

kg 2.2046 lbm

Mass flow rate lbm/h 0.45359 kg/h

lbm/s 3600 lbm/h

kg/s 7936.6 lbm/h

kg/h 2.2046 lbm/h

Power Btu/s 1.055 kW

Btu/h 0.293 W

W 3.412 Btu/h

W 9.48�10−4 Btu/s

HP 0.746 kW

HP 0.707 Btu/s

Pressure psi 6895 Pa

atm 1.013�105 Pa

atm 14.696 psi

bar 105 Pa

torr 1.000 mmHg

torr 133.32 Pa

psi 27.68 in H2O

ft-H2O 0.4335 psi

Specific heat, specific entropy Btu/lbm °F 4.1868 kJ/kg K

kcal/kg °C 1.000 Btu/lbm °F

kJ/kg K 0.23885 Btu/lbm °F

Temperature °F T(°C) = 5/9[T(°F) − 32] °C

°C T(°F) = 9/5 T(°C) + 32 °F

°C T(K) = T(°C) + 273.15 K

°F T(°R) = T(°F) + 459.67 °R

Thermal conductivity Btu/h ft °F 1.7307 W/m K

cal/cm s °C 418.68 W/m K

W/m K 0.5778 Btu/h ft °F

Velocity ft/s 0.30480 m/s

km/h 0.27778 m/s

mile/h 1.609 km/h

Viscosity kg/s m 1 N s/m2

posi 0.1 N s/m2

lbm/s ft 1.4882 N s/m2

lbm/h ft 4.1338�10−4 N s/m2

N s/m2 0.67195 lbm/s ft

N s/m2 2419.08 lbm/h ft

Volume L 1 dm3

L 0.001 m3

ft3 0.02832 m3

in3 16.39 cm3

yd3 0.7646 m3

m3 35.313 ft3

(continued)

Appendix A: Constants, Units, and Conversion Factors 749

Table A.3 (continued)


Volume Gal (U.S.) 3.785 L

Gal (IMP) 4.546 L

Pint (U.S.) 0.4732 L

Pint (IMP) 0.5683 L

Volume flow rate ft3/min 4.7196�10−4 m3/s

ft3/s 0.0028318 m3/s

m3/s 2118.8 ft3/min

Volumetric heat generation rate Btu/h ft3 10.35 W/m3

W/m3 0.0966 Btu/h ft3

750 Appendix A: Constants, Units, and Conversion Factors

Appendix B: Transport Properties

List of Properties Tables

Table B.1 Air at 1 atm (Bergman and Lavine 2017)Table B.2 Carbon dioxide (CO2) at 1 atm (Bergman and Lavine 2017)Table B.3 Helium (He) at 1 atm (Bejan 2013)Table B.4 Hydrogen (H2) at 1 atm (Bergman and Lavine 2017)Table B.5 Nitrogen (N2) at 1 atm (Bergman and Lavine 2017)Table B.6 Oxygen (O2) at 1 atm (Bergman and Lavine 2017)Table B.7 Water (H2O) vapor at 1 atm (Bergman and Lavine 2017)Table B.8 Volume expansion coefficients for liquids (Mills and Coimbra 2015)Table B.9 Density and volume expansion coefficients of water (Mills and Coimbra 2015)Table B.10 AluminumTable B.11 Aluminum alloy, 2024-T6Table B.12 Cartridge brassTable B.13 CopperTable B.14 Fused silicaTable B.15 Inconel® X-750Table B.16 IronTable B.17 MolybdenumTable B.18 NickelTable B.19 NiobiumTable B.20 Plain carbon steelTable B.21 Stainless steel 304Table B.22 TantalumTable B.23 TitaniumTable B.24 TungstenTable B.25 Phase Change Materials (PCMs)Table B.26 Thermophysical properties at saturation for acetoneTable B.27 Thermophysical properties at saturation for ammoniaTable B.28 Thermophysical properties at saturation for cesiumTable B.29 Thermophysical properties at saturation for Dowtherm®

Table B.30 Thermophysical properties at saturation for ethaneTable B.31 Thermophysical properties at saturation for ethanolTable B.32 Thermophysical properties at saturation for Freon®-113Table B.33 Thermophysical properties at saturation for Freon®-123Table B.34 Thermophysical properties at saturation for Freon®-134a


751

https://doi.org/10.1007/978-3-030-22137-9

Table B.35 Thermophysical properties at saturation for Freon®-21Table B.36 Thermophysical properties at saturation for Freon®-22Table B.37 Thermophysical properties at saturation for heliumTable B.38 Thermophysical properties at saturation for heptaneTable B.39 Thermophysical properties at saturation for leadTable B.40 Thermophysical properties at saturation for lithiumTable B.41 Thermophysical properties at saturation for mercuryTable B.42 Thermophysical properties at saturation for methanolTable B.43 Thermophysical properties at saturation for nitrogenTable B.44 Thermophysical properties at saturation for potassiumTable B.45 Thermophysical properties at saturation for rubidiumTable B.46 Thermophysical properties at saturation for silverTable B.47 Thermophysical properties at saturation for sodiumTable B.48 Thermophysical properties at saturation for waterTable B.49 Binary diffusion coefficients at 1 atma (Bergman and Lavine 2017)Table B.50 Diffusion coefficients in air at 1 atm (1.013 � 105 Pa)a (Mills and Coimbra 2015)Table B.51 Diffusion coefficients in solids, D ¼ D0 exp �Ea=RuTð ÞTable B.52 Schmidt number for vapors in dilute mixture in air at normal temperature, enthalpy of

vaporization and boiling point at 1 atma (Mills and Coimbra 2015)Table B.53 Schmidt numbers for dilute solution in water at 300 Ka (Mills and Coimbra 2015)Table B.54 Solubility and permeability of gases in solids (Mills and Coimbra 2015)Table B.55 Henry’s constant for selected gases in water at moderate pressurea

Table B.56 Solubility of selected gases and solids (Bergman and Lavine 2017)Table B.57 Solubility of inorganic compounds in watera (Mills and Coimbra 2015)Table B.58 Equilibrium compositions for the NH3-water system (Mills and Coimbra 2015)Table B.59 Equilibrium compositions for the SO2-water system

a (Mills and Coimbra 2015)Table B.60 Thermodynamic properties of water vapor-air mixtures at 1 atm (Mills and Coimbra 2015)

752 Appendix B: Transport Properties

Table B.1 Air at 1 atm (Bergman and Lavine 2017)

T Temp.(K)

qDensity(kg/m3)

cpSpecificheat(kJ/Kg-K)

lViscosity(10−7 N s/m2)

mKinematicviscosity(10−6 m2/s)

kThermalconductivity(10−3 W/m K)

aThermaldiffusivity(10−6 m2/s)

PrPrandtlnumber

100 3.5562 1.032 71.1 2.00 9.34 2.54 0.786

150 2.3364 1.012 103.4 4.426 13.8 5.84 0.758

200 1.7458 1.007 132.5 7.59 18.1 10.3 0.737

250 1.3947 1.006 159.6 11.44 22.3 15.9 0.72

300 1.1614 1.007 184.6 15.89 26.3 22.5 0.707

350 0.995 1.009 208.2 20.92 30.0 29.9 0.700

400 0.8711 1.014 230.1 26.41 33.8 38.3 0.690

450 0.7740 1.021 250.7 32.39 37.3 47.2 0.686

500 0.6964 1.030 270.1 38.79 40.7 56.7 0.684

550 0.6329 1.040 288.4 45.57 43.9 66.7 0.683

600 0.5804 1.051 305.8 52.69 46.9 76.9 0.685

650 0.5356 1.063 322.5 60.21 49.7 87.3 0.690

700 0.4975 1.075 338.8 68.10 52.4 98 0.695

750 0.4643 1.087 354.6 76.37 54.9 109 0.702

800 0.4354 1.099 369.8 84.93 57.3 120 0.709

850 0.4097 1.110 384.3 93.80 59.6 131 0.716

900 0.3868 1.121 398.1 102.9 62.0 143 0.720

950 0.3666 1.131 411.3 112.2 64.3 155 0.723

1000 0.3482 1.141 424.4 121.9 66.7 168 0.726

1100 0.3166 1.159 449 141.8 71.5 195 0.728

1200 0.2902 1.175 473 162.9 76.3 224 0.728

1300 0.2679 1.189 496 185.1 82 238 0.719

1400 0.2488 1.207 530 213 91 303 0.703

1500 0.2322 1.23 557 240 100 350 0.685

1600 0.2177 1.248 584 268 106 390 0.688

1700 0.2049 1.267 611 298 113 435 0.685

1800 0.1935 1.286 637 329 120 482 0.683

1900 0.1833 1.307 663 362 128 534 0.677

2000 0.1741 1.337 689 396 137 589 0.672

2100 0.1658 1.372 715 431 147 646 0.667

2200 0.1582 1.417 740 468 160 714 0.655

2300 0.1513 1.478 766 506 175 783 0.647

2400 0.1448 1.558 792 547 196 869 0.63

2500 0.1389 1.665 818 589 222 960 0.613

3000 0.1135 2.726 955 841 486 1570 0.536

Appendix B: Transport Properties 753

Table B.2 Carbon dioxide (CO2) at 1 atm (Bergman and Lavine 2017)

T Temp.(K)

qDensity(kg/m3)

cpSpecificheat(kJ/kg K)





PrPrandtlnumber

280 1.9022 0.830 140 7.36 15.20 9.63 0.765

300 1.7730 0.851 149 8.40 16.55 11.00 0.766

320 1.6609 0.872 156 9.39 18.05 12.50 0.754

340 1.5618 0.891 165 10.60 19.70 14.20 0.746

360 1.4743 0.908 173 11.70 21.20 15.80 0.741

380 1.3961 0.926 181 13.00 22.75 17.60 0.737

400 1.3257 0.942 190 14.30 24.30 19.50 0.737

450 1.1782 0.981 210 17.80 28.30 24.50 0.728

500 1.0594 1.020 231 21.80 32.50 30.10 0.725

550 0.9625 1.050 251 26.10 36.60 36.20 0.721

600 0.8826 1.080 270 30.60 40.70 42.70 0.717

650 0.8143 1.100 288 35.40 44.50 49.70 0.712

700 0.7564 1.130 305 40.30 48.10 56.30 0.717

750 0.7057 1.150 321 45.50 51.70 63.70 0.714

800 0.6614 1.170 337 51.00 55.10 71.20 0.716

Table B.3 Helium (He) at 1 atm (Bejan 2013)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

4.22 16.900 9.78 1.25 0.0739 0.011 0.00064 1.15

7 7.530 5.71 1.76 0.234 0.014 0.00321 0.73

10 5.020 5.41 2.26 0.449 0.018 0.00642 0.70

20 2.440 5.25 3.58 1.470 0.027 0.0209 0.70

30 1.620 5.22 4.63 2.860 0.034 0.0403 0.71

60 0.811 5.20 7.12 8.800 0.053 0.125 0.70

100 0.487 5.20 9.78 20.10 0.074 0.291 0.69

200 0.244 5.19 15.1 62.20 0.118 0.932 0.67

300 0.162 5.19 19.9 122.0 0.155 1.830 0.67

600 0.0818 5.19 32.2 396.0 0.251 5.940 0.67

1000 0.0487 5.19 46.3 946.0 0.360 14.20 0.67


Table B.4 Hydrogen (H2) at 1 atm (Bergman and Lavine 2017)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

100 0.24255 11.230 42.1 17.4 67 24.6 0.707

150 0.16156 12.600 56.0 34.7 101 49.6 0.699

200 0.12115 13.540 68.1 56.2 131 79.9 0.704

250 0.09693 14.060 78.9 81.4 157 115 0.707

300 0.08078 14.310 89.6 111 183 158 0.701

350 0.06924 14.430 98.8 143 204 204 0.700

400 0.06059 14.480 108.2 179 226 258 0.695

450 0.05386 14.500 117.2 218 247 316 0.689

500 0.04848 14.520 126.4 261 266 378 0.691

550 0.04407 14.530 134.3 305 285 445 0.685

600 0.04040 14.550 142.4 352 305 519 0.678

700 0.03463 14.610 157.8 456 342 676 0.675

800 0.03030 14.700 172.4 569 378 849 0.670

900 0.02694 14.830 186.5 692 412 1030 0.671

1000 0.02424 14.990 201.3 830 448 1230 0.673

1100 0.02204 15.170 213.0 966 488 1460 0.662

1200 0.02020 15.370 226.2 1120 528 1700 0.659

1300 0.01865 15.590 238.5 1279 568 1955 0.655

1400 0.01732 15.810 250.7 1447 610 2230 0.650

1500 0.01616 16.020 262.7 1626 655 2530 0.643

1600 0.01520 16.280 273.7 1801 697 2815 0.639

1700 0.01430 16.580 284.9 1992 742 3130 0.637

1800 0.01350 16.960 296.1 2193 786 3435 0.639

1900 0.01280 17.490 307.2 2400 835 3730 0.643

2000 0.01210 18.250 318.2 2630 878 3975 0.661

Table B.5 Nitrogen (N2) at 1 atm (Bergman and Lavine 2017)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

100 3.4388 1.070 68.8 2.00 9.58 2.6 0.768

150 2.2594 1.050 100.6 4.45 13.9 5.86 0.759

200 1.6883 1.043 129.2 7.65 18.3 10.4 0.736

250 1.3488 1.042 154.9 11.48 22.2 15.8 0.727

300 1.1233 1.041 178.2 15.86 25.9 22.1 0.716

350 0.9625 1.042 200.0 20.78 29.3 29.2 0.711

400 0.8425 1.045 220.4 26.16 32.7 37.1 0.704

450 0.7485 1.050 239.6 32.01 35.8 45.6 0.703

500 0.6739 1.056 257.7 38.24 38.9 54.7 0.700

550 0.6124 1.065 274.7 44.86 41.7 63.9 0.702(continued)


Table B.6 Oxygen (O2) at 1 atm (Bergman and Lavine 2017)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

100 3.9450 0.9620 76.4 1.94 9.25 2.44 0.796

150 2.5850 0.9210 114.8 4.44 13.8 5.80 0.766

200 1.9300 0.9150 147.5 7.64 18.3 10.4 0.737

250 1.5420 0.9150 178.6 11.58 22.6 16.0 0.723

300 1.2840 0.9200 207.2 16.14 26.8 22.7 0.711

350 1.1000 0.9290 233.5 21.23 29.6 29.0 0.733

400 0.9620 0.9420 258.2 26.84 33.0 36.4 0.737

450 0.8554 0.9560 281.4 32.90 36.3 44.4 0.741

500 0.7698 0.9720 303.3 39.40 41.2 55.1 0.716

550 0.6998 0.9880 324.0 46.30 44.1 63.8 0.726

600 0.6414 1.0030 343.7 53.59 47.3 73.5 0.729

700 0.5498 1.0310 380.8 69.26 52.8 93.1 0.744

800 0.4810 1.0540 415.2 86.32 58.9 116 0.743

900 0.4275 1.0740 447.2 104.6 64.9 141 0.740

1000 0.3848 1.0900 477.0 124.0 71.0 169 0.733

1100 0.3498 1.1030 505.5 144.5 75.8 196 0.736

1200 0.3206 1.1150 532.5 166.1 81.9 229 0.725

1300 0.2960 1.1250 588.4 188.6 87.1 262 0.721

Table B.5 (continued)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

600 0.5615 1.075 290.8 51.79 44.6 73.9 0.701

700 0.4812 1.098 321.0 66.71 49.9 94.4 0.706

800 0.4211 1.220 349.1 82.9 54.8 116 0.715

900 0.3743 1.146 375.3 100.3 59.7 139 0.721

1000 0.3368 1.167 399.9 118.7 64.7 165 0.721

1100 0.3062 1.187 423.2 138.2 70.0 193 0.718

1200 0.2807 1.204 445.3 158.6 75.8 224 0.707

1300 0.2591 1.219 466.2 179.9 81.0 256 0.701


Table B.7 Water (H2O) vapor at 1 atm (Bergman and Lavine 2017)

TTemp. (K)

qDensity(kg/m3)






PrPrandtlnumber

380 0.5863 2.060 127.1 21.68 24.6 20.4 1.060

400 0.5542 2.014 134.4 24.25 26.1 23.4 1.040

450 0.4902 1.980 152.5 31.11 29.9 30.8 1.010

500 0.4405 1.985 170.4 38.68 33.9 38.8 0.998

550 0.4005 1.997 188.4 47.04 37.9 47.4 0.993

600 0.3652 2.026 206.7 56.60 42.2 57.0 0.993

650 0.3380 2.056 224.7 66.48 46.4 66.8 0.996

700 0.3140 2.085 242.6 77.26 50.5 77.1 1.000

750 0.2931 2.119 260.4 88.84 54.9 88.4 1.000

800 0.2739 2.152 278.6 101.7 59.2 100.0 1.010

850 0.2579 2.186 296.9 115.1 63.7 113.0 1.020

Table B.8 Volume expansion coefficients for liquids (Mills and Coimbra 2015)

Liquid T (K) b � 103 (1/K) Liquid T (K) b � 103 (1/K)

Ammonia 293 2.45 Hydrogen 20.3 15.1

Engine oil (SAE 50) 273 0.70 Mercury 273 0.18

430 0.70 550 0.18

Ethylene glycol C2H4(OH)2 273 0.65 Nitrogen 70 4.9

373 0.65 77.4 5.7

Refrigerant-22 250 2.27 80 5.9

260 2.41 90 7.2

270 2.58 100 9.0

280 2.78 110 12

290 3.03 120 24

300 3.35 Oxygen 89 2.0

310 3.75 Sodium 366 0.27

320 4.30 Therminol® 60 230 0.79

330 5.09 250 0.75

340 6.34 300 0.70

350 8.64 350 0.70

Refrigerant-134a 230 2.00 400 0.76

240 2.09 450 0.84

250 2.20 500 0.96

260 2.32 550 1.1

270 2.47

280 2.65

290 2.86

300 3.13

310 3.48

320 3.95

330 4.61

340 5.60

350 7.32

Glycerin C3H5(OH)3 280 0.47

300 0.48

320 0.50


Table B.9 Density and volume expansion coefficients of water (Mills and Coimbra 2015)

T (K) q (kg/m3) b � 106 (1/K) T (K) q (kg/m3) b � 106 (1/K)

273.15 999.8679 −68.05 320.00 989.12 436.7

274.00 999.9190 −51.30 330.00 984.25 504.0

275.00 999.9628 −32.74 340.00 979.43 566.0

276.00 999.9896 −15.30 350.00 973.71 624.4

277.00 999.9999 1.16 360.00 967.12 697.9

278.00 999.9941 16.78 370.00 960.61 728.7

279.00 999.9727 31.69 373.15 957.85 750.1

280.00 999.9362 46.04 380.00 953.29 788

285.00 999.5417 114.1 390.00 945.17 841

290.00 998.8281 174.0 400.00 937.21 896

295.00 997.8332 227.5 450.00 890.47 1129

300.00 996.5833 276.1 500.00 831.26 1432

310.00 993.4103 361.9

Table B.10 Aluminum

Aluminum, Al, Tm = 933 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)

cSpecific heat (kJ/kg K)

kThermal conductivity (W/m K)

100 2732 0.481 300

150 2726 0.683 250

200 2719 0.797 237

250 2710 0.859 235

300 2701 0.902 237

400 2681 0.949 240

600 2639 1.042 231

800 2591 1.134 218

Table B.11 Aluminum alloy, 2024-T6

Aluminum Alloy, 2024-T6, Tm = 775 K (Bergman and Lavine 2017) (4.5% Cu, 1.5% Mg, 0.6% Mn)

TTemp. (K)

qDensity (kg/m3)



100 0.473 65

200 0.787 163

300 2770 0.875 177

400 0.925 186

600 1.042 186


Table B.12 Cartridge brass

Cartridge brass, Tm = 1188 K (Bergman and Lavine 2017)

TTemp. (K)

qDensity (kg/m3)



100 75

200 0.360 95

300 8530 0.380 110

400 0.395 137

600 0.425 149

Table B.13 Copper

Copper, Cu, Tm = 1358 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 9009 0.254 480

150 8992 0.323 429

200 8973 0.357 413

250 8951 0.377 406

300 8930 0.386 401

400 8884 0.396 393

600 8787 0.431 379

800 8642 0.448 366

1000 8568 0.446 352

1200 8458 0.480 339

Table B.14 Fused silica

Silicon dioxide, SiO, Tm = 1883 K (Bergman and Lavine 2017)

TTemp. (K)

qDensity (kg/m3)



100 0.69

200 1.14

300 2220 0.745 1.38

400 0.905 1.51

600 1.040 1.75

800 1.105 2.17

1000 1.155 2.87

1200 1.195 4.00


Table B.15 Inconel® X-750

Inconel X-750, Tm = 1665 K (Bergman and Lavine 2017)(73% Ni, 15% Cr, 6.7% Fe)

TTemp. (K)

qDensity (kg/m3)



100 8.7

200 0.372 10.3

300 8510 0.439 11.7

400 0.473 13.5

600 0.510 17.0

800 0.546 20.5

1000 0.626 24.0

1200 27.6

1500 33.0

Table B.16 Iron

Iron, Fe, Tm = 1810 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 7900 0.216 134

150 7890 0.324 104

200 7880 0.384 94

250 7870 0.422 87

300 7860 0.450 80

400 7830 0.491 70

600 7760 0.555 55

800 7690 0.692 43

1000 7650 1.034 32

1200 7620 28

1400 7520 31

1600 7420

1800 7420

Table B.17 Molybdenum

Molybdenum, Mo, Tm = 2892 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 10,260 0.140 180

150 10,250 0.196 149

200 10,250 0.223 143

250 10,250 0.241 140

300 10,240 0.248 138

400 10,220 0.261 134

500 10,210 0.268 130

600 10,190 0.274 126

800 10,160 0.280 118

1000 10,120 0.292 112

1200 10,080 105

1400 10,040 100


Table B.18 Nickel

Nickel, Ni, Tm = 1728 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 8960 0.323 165

150 8940 0.329 120

200 8930 0.383 105

250 8910 0.416 98

300 8900 0.444 91

400 8860 0.490 80

600 8780 0.590 66

800 8690 0.530 68

1000 8610 0.556 72

1200 8510 0.582 76

1400 8410 80

1600 8320

Table B.19 Niobium

Niobium, Nb, Tm = 2740 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 8600 0.202 55

150 8590 0.238 53

200 8580 0.254 53

250 8570 0.263 53

300 8570 0.268 54

400 8550 0.272 55

500 8530 0.277 57

600 8510 0.281 58

800 8470 0.290 61

1000 8430 0.298 64

1200 8380 0.307 68

1400 8340 71

Table B.20 Plain carbon steel

Plain Carbon Steel, Tm = 1480 °C (Bergman and Lavine 2017)

TTemp. (K)

qDensity (kg/m3)



300 7854 0.434 60.5

400 0.487 56.7

600 0.559 48.0

800 0.685 39.2

1000 1.169 30.0


Table B.21 Stainless steel 304

Stainless Steel 304, Tm = 1670 K (Bergman and Lavine 2017)

TTemp. (K)

qDensity (kg/m3)



100 0.272 9.2

200 0.402 12.6

300 7900 0.477 14.9

400 0.515 16.6

600 0.557 19.8

800 0.582 22.6

1000 0.611 25.4

1200 0.640 28.0

1500 0.682 31.7

Table B.22 Tantalum

Tantalum, Ta, Tm = 3252 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 16,490 0.108 59

150 16,480 0.125 58

200 16,460 0.132 58

250 16,450 0.137 57

300 16,440 0.141 58

400 16,410 0.145 58

500 16,370 0.148 59

600 16,340 0.149 59

800 16,270 0.152 59

1000 16,200 0.160 60

1200 16,130 61

1400 16,060 62


Table B.23 Titanium

Titanium, Ti, Tm = 1953 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 4510 0.295 31

150 4515 0.406 27

200 4520 0.464 25

250 4515 0.501 23

300 4510 0.525 21

400 4490 0.555 20

600 4470 0.597 19

800 4440 0.627 19

1000 4410 0.652 21

1200 4380 22

1400 4350 24

1600 4320

Table B.24 Tungsten

Tungsten, W, Tm = 3660 K (Rohsenow et al. 1998)

TTemp. (K)

qDensity (kg/m3)



100 19,310 0.089 208

150 19,300 0.113 192

200 19,290 0.125 185

250 19,280 0.131 180

300 19,270 0.135 174

400 19,240 0.137 159

500 19,220 0.139 146

600 19,190 0.140 137

800 19,130 0.144 125

1000 19,080 0.148 118

1200 19,020 112

1400 18,950 108


Table

B.25

Phasechange

materials(PCMs)

PCMs

Chemical

form

ula

T m meltin

gpo

int

(°C)

h s‘

latent

heat

(kJ/kg

)

qs Solid

density

(kg/m

3 )

q ‘ Liquid

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

3N

s/m

2 )

k s Solid

thermal

cond

uctiv

ity(W

/mK)

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

c p,s

Solid

specific

heat

(kJ/kg

K)

c p,‘

Liquid

specific

heat

(kJ/kg

-K)

b Liquidthermal

expansion

coefficient

(10−

4 1/K)

n-Tetradecane

aC14H30

5.5

226

825

771

0.15

n-Hexadecaneb

C16H34

18.2

228.9

833

774

0.15

051.80

2.31

n-Octadecanec

C18H38

27.5

244

814a

774a

3.9

0.35

80.15

22.15

2.18

8.5

n-Eicosaneb

C20H42

36.40

247.3

815

780

0.15

01.92

2.46

8.5

Galliu

md

Ga

29.78

80.16

6095

6093

1.81

33.5

32.0

0.34

0c0.38

151.2

Aluminum

cAl

660.4

395

2702

2380

e1.3

238

94.03

1.07

61.08

1.2

Water

fH2O

033

3.7g

920

1000

1.75

1.88

0.56

92.04

4.23

−0.68

05

Acetic

acid

aCH3C

OOH

16.7

187

1214

1050

1.31

0.18

2040

1960

Sodium

hydrog

enph

osph

ate

dodecahy

dratea

Na 2HPO

4�12

H2O

3628

015

2014

460.51

40.47

616

9019

404.35

a Haleet

al.(19

71),

b Hum

phries

andGrigg

s(197

7),cBenno

nandIncrop

era(198

8);dBrent

etal.(19

88),

e IidaandGuthrie

(198

8),fBergm

anandLavine(201

7),gCengele

tal.

(201

9)


Table

B.26

Therm

ophy

sicalprop

ertiesat

saturatio

nforaceton

e

Acetone,(CH3)2C

O,Molecular

mass:58

.1,(T

sat=56

.25°C

;T m

=−93

.15°C

;Reayet

al.20

14;Fagh

ri20

16)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(kg/m

3 )

q v Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

-K)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heatb

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

−40

0.01

660.0

860.0

0.03

0.80

068

.00.20

031

.02.04

1.10

9

−20

0.03

615.6

845.0

0.10

0.50

073

.00.18

90.00

8227

.62.07

1.16

0

00.10

564.0

812.0

0.26

0.39

578

.00.18

30.00

9626

.22.11

1.21

5

200.27

552.0

790.0

0.64

0.32

382

.00.18

10.01

1023

.72.16

1.27

1

400.60

536.0

768.0

1.05

0.26

986

.00.17

50.01

2621

.22.22

1.32

8

601.15

517.0

744.0

2.37

0.22

690

.00.16

80.01

4318

.62.29

1.38

6

802.15

495.0

719.0

4.30

0.19

295

.00.16

00.01

6116

.22.39

1.44

4

100

4.43

472.0

689.6

6.94

0.17

098

.00.14

80.01

7813

.42.49

1.50

2

120

6.70

426.1

660.3

11.02

0.14

899

.00.13

50.01

9510

.72.61

1.56

0

140

10.49

394.4

631.8

18.61

0.13

210

3.0

0.12

60.02

158.1

2.77

1.61

6a Interpo

latio

nfrom

Roh

seno

wet

al.(199

8),b Interpo

latio

nfrom

Vargaftik

(197

5)


Table

B.27

Therm

ophy

sicalprop

ertiesat

saturatio

nforam

mon

ia

Ammon

ia,NH3,Molecular

mass:17

.0,(T

sat=23

9.9K;T m

=19

5.5K;ASH

RAE,20

09;Lem

mon

etal.20

16)

T Tem

p.(°C)

p v Saturatio

npressure

(106

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(kg/m

3 )

q v Vapor

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

5N

s/m

2 )

lv Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tensiona

(N/m

)

c p,‘

Liquid

specificheat

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

200

0.00

8646

1477

728.9

0.08

899

50.728

69.5

0.80

30.01

970.06

044.22

72.07

6

210

0.01

7746

1451

717.5

0.17

4641

.498

72.1

0.76

80.01

990.05

634.28

52.11

2

220

0.03

3811

1425

705.8

0.31

9034

.668

74.8

0.73

30.02

010.05

234.34

22.16

0

230

0.06

0439

1398

693.7

0.54

8929

.494

77.7

0.69

90.02

050.04

854.39

72.22

2

240

0.10

226

1369

681.4

0.89

7225

.485

80.6

0.66

50.02

100.04

474.44

92.29

8

250

0.16

496

1339

668.9

1.40

422

.308

83.6

0.63

20.02

160.04

104.49

82.39

2

260

0.25

529

1307

656.1

2.11

519

.734

86.6

0.60

00.02

230.03

744.54

82.50

3

270

0.38

100

1273

642.9

3.08

617

.606

89.6

0.56

90.02

310.03

404.59

92.63

4

280

0.55

077

1237

629.2

4.38

015

.812

92.7

0.53

90.02

400.03

064.65

62.78

8

290

0.77

413

1198

615.0

6.07

114

.274

95.8

0.50

90.02

510.02

744.72

22.96

7

300

1.06

1411

5960

0.2

8.24

712

.933

98.9

0.48

00.02

640.02

424.80

03.17

7

310

1.42

3511

1358

4.6

11.01

11.749

102

0.45

20.02

790.02

124.89

73.42

3

320

1.87

2110

6656

8.2

14.51

10.691

106

0.42

50.02

960.01

835.01

83.71

8

330

2.41

9610

1455

0.9

18.89

9.73

109

0.39

80.03

160.01

555.17

64.07

8

340

3.07

8995

853

2.4

24.40

8.86

113

0.37

20.03

390.01

295.38

54.53

0

350

3.86

4189

551

2.3

31.34

8.04

118

0.34

50.03

690.01

045.67

15.12

5

360

4.79

0282

549

0.3

40.18

7.28

123

0.31

90.04

080.00

806.08

25.95

5

370

5.87

4074

546

5.5

51.65

6.55

131

0.29

30.04

610.00

586.71

57.21

4

380

7.13

5264

943

6.5

67.16

5.83

140

0.26

70.05

460.00

387.81

89.39

5

390

8.59

7752

940

0.2

89.85

5.09

155

0.24

00.07

010.00

2010

.31

14.19


Table

B.28

Therm

ophy

sicalprop

ertiesat

saturatio

nforcesium

Cesium,Cs,Molecular

mass:13

2.9,

(Tsat=94

3K;T m

=20

1.6K;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(10−

3kg

/m3 )

l ‘ Liquid

viscosity

(10−

4N

s/m

2 )

l v Vapor

viscosity

(10−

5N

s/m

2 )

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

500

0.00

0354

4.30

1.72

39.91

3.18

11.46

018

.79

61.9

0.23

20.19

82

600

0.00

5653

4.20

1.66

615

.50

2.55

81.66

819

.02

0.00

530

57.1

0.22

40.23

44

700

0.04

3752

3.30

1.60

910

5.20

2.16

31.89

318

.79

0.00

631

52.3

0.21

90.26

45

800

0.20

2651

1.60

1.55

243

3.60

1.89

02.12

418

.33

0.00

724

47.5

0.21

70.28

21

900

0.65

8049

9.50

1.49

512

75.90

1.69

02.33

617

.51

0.00

807

42.7

0.22

20.28

78

1000

1.68

0048

6.50

1.43

829

90.40

1.53

62.56

716

.47

0.00

878

37.9

0.23

10.28

50

1100

3.60

0047

2.60

1.37

759

24.10

1.41

52.78

215

.49

0.00

942

33.1

0.23

90.27

76

1200

6.77

0045

8.80

1.31

110

,364

.80

1.31

62.99

513

.57

0.01

000

28.3

0.24

80.26

81

1300

11.510

044

4.60

1.24

316

,520

.70

1.23

43.19

811

.60

0.01

060

23.5

0.25

60.25

82

1400

18.020

042

9.98

1.17

424

,307

.20

1.16

43.39

89.39

0.01

110

18.0

1500

26.720

041

5.40

1.10

234

,048

.30

1.10

43.58

97.50

0.01

150

14.0

a Vargaftik

(197

5)


Table

B.29

Therm

ophy

sicalprop

ertiesat

saturatio

nforDow

therm

®

Dipheny

lmixture

(Dow

therm

a ),Molecular

mass:16

6.0,

(Tsat=25

8°C

;T m

=12

°C;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

5N

s/m

2 )

lv Vapor

viscosity

(10−

5N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specificheat

(kJ/kg

K)

c p,v

Vapor

specificheat

(kJ/kg

K)

100

0.00

634

599

50.03

510

1.0

0.68

0.12

631

.61.88

150

0.05

132

995

30.24

60.3

0.77

0.11

926

.52.14

200

0.24

531

491

20.99

40.7

0.87

0.11

021

.82.34

250

0.84

329

187

13.20

29.7

0.97

0.10

417

.32.60

300

2.33

026

482

58.70

22.7

1.07

0.09

612

.92.76

350

5.20

023

577

220

.018

.21.17

0.09

08.9

2.89

400

10.43

207

709

42.0

14.9

1.26

0.08

35.0

3.01

a Dow

therm

isan

eutectic

mixture

of73

.5%

phenuletherand26

.5%

diph

enyl


Table

B.30

Therm

ophy

sicalprop

ertiesat

saturatio

nforethane

Ethane,

C2H

6,Molecular

mass:30

.1,(T

sat=−88

.6°C

;T m

=−18

3.3°C

;Ivanov

skiiet

al.,19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

q v Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

7N

s/m

2 )

lv Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specificheat

(kJ/kg

K)

c p,v

Vapor

specificheat

(kJ/kg

K)

−12

00.09

653

058

20.23

025

8049

.00.14

921

.23

2.82

1.29

7

−10

00.60

050

656

20.92

118

0055

.00.13

717

.93

2.94

1.34

9

−80

1.70

048

054

02.60

013

6061

.00.12

514

.60

3.05

1.40

1

−60

3.70

045

051

66.20

011

0067

.00.11

30.01

1611

.30

3.16

1.45

9

−40

7.20

041

448

812

.700

900

73.0

0.10

00.01

388.00

3.26

1.52

1

−20

14.000

368

454

25.500

760

79.0

0.08

80.01

604.60

3.38

1.58

5

025

.000

304

414

46.000

660

85.5

0.07

70.01

851.20

3.48

1.66

0

2038

.000

200

360

85.000

600

91.0

0.06

60.02

090.08

1.73

6a Interpo

latio

n(Roh

seno

wet

al.19

98)


Table

B.31

Therm

ophy

sicalprop

ertiesat

saturatio

nforethano

l

Ethanol,C2H

5OH,Molecular

mass:46

.0,(T

sat=78

.3°C

;T m

=−11

4.5°C

;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

lv Vapor

viscosity

(10−

5N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heatb

(kJ/kg

K)

c p,v

Vapor

specific

heatc

(kJ/kg

K)

00.01

210

48.4

0.90

10.03

61.79

900.77

40.18

30.01

1724

.42.27

1.34

200.05

810

30.0

0.80

00.08

51.19

800.83

50.17

90.01

3922

.82.40

1.40

400.18

010

11.9

0.78

90.31

60.81

900.90

00.17

50.01

6021

.02.57

1.48

600.47

298

8.9

0.77

00.74

80.58

800.95

90.17

10.01

7919

.22.78

1.54

801.08

696

0.0

0.75

71.43

00.43

201.03

00.16

90.01

9917

.33.03

1.61

100

2.26

092

7.0

0.73

03.41

00.31

801.09

20.16

70.02

1915

.53.30

1.68

120

4.29

088

5.5

0.71

06.01

00.24

301.15

70.16

50.02

3813

.43.61

1.75

140

7.53

083

4.0

0.68

010

.670

0.19

001.21

90.16

30.02

5611

.23.96

160

12.756

772.9

0.65

017

.450

0.15

001.29

30.16

10.02

729.0

180

19.600

698.8

0.61

027

.650

0.12

001.36

90.15

90.02

886.7

200

29.400

598.3

0.56

444

.480

0.09

501.46

40.15

70.03

954.3

220

42.800

468.5

0.51

074

.350

0.07

251.61

80.15

50.03

212.2

240

60.200

280.5

0.41

513

5.50

00.04

881.94

80.15

30.1

a Interpo

latio

nfrom

Roh

seno

wet

al.(199

8),b Interpo

latio

nfrom

Vargaftik

(197

5),c Reayet

al.(201

4)


Table

B.32

Therm

ophy

sicalprop

ertiesat

saturatio

nforFreon®

-113

Freon-11

3,C2F

3Cl 3,Molecular

mass:18

7.4,

(Tsat=47

.68°C

;T m

=−36

.6°C

;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

itya

(W/m

K)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

−30

0.02

8316

6.88

1.68

70.26

391.67

089

.40.08

8925

.30.85

50.58

7

−20

0.09

0516

1.48

1.64

30.78

001.13

094

.20.08

6722

.80.88

20.59

7

00.15

0015

8.68

1.62

11.25

100.94

896

.70.08

2221

.50.92

10.62

1

100.23

8715

5.83

1.59

81.93

000.78

099

.00.07

9920

.60.93

70.62

7

300.54

2014

9.93

1.55

44.15

000.59

010

4.0

0.07

5418

.10.96

20.64

7

501.09

4314

3.82

1.50

88.00

000.47

510

8.5

0.07

090.00

866

16.0

0.98

60.66

7

702.01

2013

7.46

1.45

514

.300

00.40

111

3.0

0.06

6413

.91.00

40.68

9a A

SHRAE(200

1)


Table

B.33

Therm

ophy

sicalprop

ertiesat

saturatio

nforFreon®

-123

Freon-12

3,CHCl 2CF 3,Molecular

mass:15

2.9,

(Tsat=27

.8°C

;T m

=−10

7°C

;ASH

RAE20

01)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

−60

0.00

8120

4.20

1.66

50.07

01.38

375

.00.10

200.00

435

25.78

0.93

20.55

3

−40

0.03

5819

6.63

1.62

00.28

30.98

683

.10.09

610.00

549

23.19

0.94

80.58

5

−20

0.12

0018

9.11

1.57

40.88

00.73

590

.90.08

980.00

661

20.66

0.96

80.61

7

00.32

6518

1.44

1.52

62.24

20.56

598

.40.08

370.00

774

18.18

0.99

00.65

1

200.75

6117

3.44

1.47

74.90

50.44

310

5.6

0.07

780.00

889

15.77

1.01

40.68

6

401.54

4716

4.95

1.42

59.62

90.35

211

2.6

0.07

240.01

008

13.43

1.03

80.72

4

602.85

8915

5.73

1.37

017

.331

0.28

411

9.4

0.06

730.01

134

11.16

1.06

60.76

7

804.89

0914

5.54

1.31

129

.189

0.23

112

6.3

0.06

260.01

273

8.97

1.10

00.81

6


Table

B.34

Therm

ophy

sicalprop

ertiesat

saturatio

nforFreon®

-134

a

Freon-13

4a,CF 3CH2F,Molecular

mass:10

2.0,

(Tsat=−26

.4°C

;T m

=−10

1°C

;ASH

RAE20

09)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

−60

0.15

9123

7.95

1.47

40.92

680.66

383

.00.12

10.00

656

20.80

1.22

30.69

2

−40

0.51

2122

5.86

1.41

82.76

90.47

291

.20.11

10.00

817

17.60

1.25

50.74

9

−20

1.32

7321

2.91

1.35

86.78

50.35

399

.20.10

10.00

982

14.51

1.29

30.81

6

02.92

8019

8.60

1.29

514

.428

0.27

110

7.3

0.09

200.01

151

11.56

1.34

10.89

7

205.71

7118

2.28

1.22

527

.778

0.21

111

5.81

0.08

330.01

333

8.76

1.40

51.00

1

4010

.166

163.02

1.14

750

.075

0.16

312

5.5

0.07

470.01

544

6.13

1.49

81.14

5

6016

.818

139.13

1.05

381

.413

0.12

413

7.9

0.06

610.01

831

3.72

1.66

01.38

7


Table

B.35

Therm

ophy

sicalprop

ertiesat

saturatio

nforFreon®

-21

Freon-21

,CHFC

l 2,Molecular

mass:10

2.9,

(Tsat=8.90

°C;T m

=−13

5°C

)(V

argaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(103

kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

−60

0.02

5326

91.55

40.14

70.84

989

0.13

229

.81

0.50

1

−40

0.09

5426

21.51

00.51

00.59

795

0.12

326

.99

0.52

3

−20

0.28

4725

31.47

01.41

00.44

410

00.11

624

.17

0.99

40.54

5

00.70

8524

31.42

03.31

00.34

510

60.10

921

.35

1.01

50.56

6

201.53

0023

21.38

06.81

00.27

211

20.10

218

.35

1.04

80.58

8

402.95

522

01.33

012

.690

0.22

911

80.09

50.00

9415

.71

1.09

30.60

6

605.21

620

61.28

021

.930

0.20

012

40.08

70.01

0412

.89

1.14

90.62

3

808.56

719

11.22

035

.710

0.19

513

00.08

00.01

1310

.07

0.64

1

100

13.283

174

1.16

055

.860

0.18

013

60.07

20.01

227.25

0.65

9

120

19.666

155

1.08

085

.470

0.17

014

20.06

00.01

324.43

0.67

7a Interpo

latio

nfrom

Roh

seno

wet

al.(199

8)


Table

B.36

Therm

ophy

sicalprop

ertiesat

saturatio

nforFreon®

-22

Freon-22

,CHF 2Cl,Molecular

mass:86

.5,(T

sat=−40

.8°C

;T m

=−16

0°C

;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

4N

s/m

2 )

lv Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tensiona

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

−10

00.01

9926

9.29

1.55

70.11

966.00

80.0

0.14

870.00

446

28.1

1.07

50.49

7

−80

0.10

3425

7.43

1.51

40.56

15.00

87.5

0.13

850.00

525

24.8

1.08

30.52

8

−60

0.37

5224

5.42

1.46

51.86

54.14

95.0

0.12

830.00

612

21.5

1.09

10.56

4

−40

1.05

4023

2.92

1.41

24.88

53.49

101.7

0.11

810.00

831

18.5

1.10

50.61

1

−20

2.45

6021

9.40

1.35

110

.821

3.02

110.4

0.10

790.00

929

15.0

1.13

00.65

4

04.98

3020

4.28

1.28

521

.285

2.67

118.7

0.09

770.01

026

11.7

1.17

10.74

1

209.09

7018

6.89

1.21

438

.550

2.40

126.8

0.08

750.01

123

8.7

1.23

20.85

4

4015

.315

016

6.22

1.13

266

.225

2.19

134.5

0.07

720.01

221

5.8

1.31

90.99

4

6024

.236

013

9.94

1.03

011

1.65

2.00

142.1

0.06

460.01

318

3.3

1.52

61.24

3a Ivano

vskiiet

al.(198

2)


Table

B.37

Therm

ophy

sicalprop

ertiesat

saturatio

nforheliu

m

Helium,He,

Molecular

mass:4.0,

(Tsat=−26

8°C

;T m

=−27

1°C

;Reayet

al.20

14;Fagh

ri20

16)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

7N

s/m

2 )

l v Vapor

viscosity

(10−

8N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heatb

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

−27

10.06

22.8

148.3

26.0

390

200.01

810.00

393

0.26

5.18

2.04

5

−27

00.32

23.6

140.7

17.0

370

300.02

240.00

607

0.19

2.49

2.69

9

−26

91.00

20.9

128.0

10.0

290

600.02

770.00

803

0.09

3.99

4.61

9

−26

82.29

4.0

113.8

8.5

134

900.03

500.00

962

0.01

11.5

6.64

2a Tou

louk

ianet

al.(197

0),b V

argaftik

(197

5)


Table

B.38

Therm

ophy

sicalprop

ertiesat

saturatio

nforheptane

Heptane,C7H

16,Molecular

mass:10

0.2,

(Tsat=98

.43°C

;T m

=−90

.59°C

;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(103

kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tensiona

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heatb

(kJ/kg

K)

−20

0.00

3866

383.1

0.71

720.68

900.14

00.00

842.10

0.83

00.01

5237

5.6

0.70

050.00

0070

0.52

600.13

40.00

992.16

0.87

200.04

7236

6.0

0.68

360.00

0200

0.41

400.12

90.01

1520

.86

2.23

0.92

400.12

3035

4.7

0.66

650.00

0500

0.33

800.12

30.01

3218

.47

2.30

0.97

600.28

0034

2.6

0.64

910.00

1100

0.28

100.11

80.01

5116

.39

2.39

1.02

800.57

0033

0.1

0.63

110.00

2000

0.23

900.11

30.01

7014

.35

2.47

1.05

100

1.06

0631

6.7

0.61

240.00

3597

0.19

8073

.60.01

8912

.47

2.57

1.09

120

1.83

3030

2.9

0.59

260.00

6075

0.16

7278

.20.02

0710

.63

2.67

1.16

140

2.97

9028

7.4

0.57

110.00

9785

0.14

2783

.40.02

288.87

2.78

160

4.59

9026

9.5

0.54

810.01

5110

0.12

1789

.70.02

517.19

2.89

a Interpo

latio

nfrom

Roh

seno

wet

al.(199

8),b R

eayet

al.(201

4)


Table

B.39

Therm

ophy

sicalprop

ertiesat

saturatio

nforlead

Lead,

Pb,Molecular

mass:20

7.2,

(Tsat=17

40°C

;T m

=32

7.5°C

;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(102

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(103

kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

1400

0.09

8692

09.27

0.14

70.91

227.46

347.28

1500

0.21

0892

09.14

0.29

60.88

477.90

335.88

1600

0.42

0092

09.01

0.55

90.85

868.34

324.48

1700

0.80

1092

08.89

1.01

10.83

528.78

313.08

1800

1.36

2092

08.76

1.63

50.81

439.21

301.68

1900

2.31

0092

08.63

2.64

80.79

589.66

290.28

2000

3.74

1092

08.51

4.10

60.77

9410

.10

278.88

2100

5.55

0092

08.37

5.81

70.75

9010

.54

260.00

2200

8.20

0092

08.25

8.25

60.74

1010

.98

248.00

2300

11.850

092

08.12

11.480

0.72

3011

.42

237.00

2400

16.750

092

07.99

15.600

0.70

5011

.86

225.00

2500

22.600

092

07.86

20.280

0.68

7012

.30

214.00

a Reayet

al.(201

4)


Table

B.40

Therm

ophy

sicalprop

ertiesat

saturatio

nforlithium

Lith

ium,Li,Molecular

mass:6.9,

(Tsat=16

15K;T m

=45

3.7K;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(102

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

q v Vapor

density

(103

kg/m

3 )

l‘ Liquid

viscosity

(10−

4N

s/m

2 )

l v Vapor

viscosity

(10−

8N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

900

0.12

5621

712

472.8

0.01

22.78

489

0.1

52.75

335.8

4.16

6.95

6

1000

0.96

8021

400

462.6

0.08

52.47

297

5.2

55.10

321.8

4.16

8.17

1

1100

5.12

0021

000

452.4

0.41

52.25

210

55.0

57.42

0.12

030

7.8

4.15

9.11

4

1200

20.500

020

740

442.2

1.54

02.07

211

28.0

59.62

0.13

829

3.8

4.14

9.72

3

1300

65.860

020

380

432.0

4.65

01.92

212

13.0

61.94

0.15

627

9.8

4.16

10.019

1400

179.40

0020

020

421.7

11.960

1.79

512

89.0

64.00

0.17

226

6.0

4.19

10.049

1500

426.50

0019

670

411.5

26.900

1.68

513

68.0

66.50

0.18

325

2.0

4.20

9.89

1

1600

908.40

0019

330

401.3

54.610

1.59

014

42.0

68.50

0.19

223

8.0

4.23

9.61

1

1700

1769

.300

018

990

391.1

101.50

01.50

615

18.0

71.00

0.19

822

6.0

4.25

9.25

9

1800

3190

.000

018

670

380.9

175.10

01.43

215

87.0

73.00

0.20

221

2.0

4.27

8.87

1

1900

5397

.000

018

370

370.0

283.90

01.38

016

66.0

75.50

0.20

719

8.0

4.30

8.48

1

2000

8640

.400

018

080

360.0

436.30

01.30

017

46.0

77.00

0.20

918

2.0

4.32

8.09

8a V

argaftik

(197

5)


Table

B.41

Therm

ophy

sicalprop

ertiesat

saturatio

nformercury

Mercury,Hg,

Molecular

mass:20

0.6,

(Tsat=63

0.1K;T m

=23

4.3K;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

lv Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

100

0.00

0374

530

3.31

713

351.42

0.00

242

1.24

136

09.47

50.46

000.13

711.04

200

0.02

315

300.05

613

111.97

0.11

800

1.03

946

410

.64

0.43

600.13

551.04

300

0.33

015

296.82

412

873.50

1.39

100

0.92

656

211

.69

0.00

430.40

500.13

531.04

400

2.10

240

293.31

412

632.60

7.57

200

0.85

366

212

.60

0.00

580.37

700.13

641.04

500

8.22

2028

9.11

612

386.00

26.000

000.80

476

213

.39

0.00

730.32

900.13

891.04

600

23.460

0028

3.76

912

130.00

66.660

000.76

786

214

.04

0.00

900.29

890.14

271.04

700

54.030

0027

6.84

511

863.00

140.75

000

0.73

996

114

.58

0.01

070.26

870.14

781.04

a Kakac

etal.(198

7)


Table

B.42

Therm

ophy

sicalprop

ertiesat

saturatio

nformethano

l

Methano

l,CH4O

,Molecular

mass:32

.0,(T

sat=64

.7°C

;T m

=−98

°C;Lem

mon

etal.20

16;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(103

kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

00.04

1112

10.0

0.80

970.00

0058

00.81

7088

0.20

524

.52.40

2.99

200.10

311

91.1

0.79

090.00

0175

10.57

8095

0.20

422

.62.50

3.50

400.35

811

63.9

0.77

210.00

0452

10.44

6010

10.20

30.00

157

20.9

2.63

3.96

600.86

111

30.4

0.75

280.00

1029

90.34

7010

80.20

20.00

178

19.3

2.79

4.35

801.81

910

84.4

0.73

260.00

2122

90.27

1011

50.20

00.00

199

17.5

2.97

4.72

100

3.73

110

30.0

0.71

100.00

4042

10.21

4012

30.19

80.00

220

15.7

3.17

5.14

120

6.55

197

1.3

0.68

730.00

7235

90.17

0013

00.19

60.00

241

13.6

3.40

5.69

140

10.810

904.3

0.66

080.01

2378

00.13

6013

60.19

40.00

262

11.5

3.68

6.51

160

17.609

828.0

0.63

040.02

0529

00.10

9014

30.00

283

9.3

4.02

7.61

180

16.869

741.1

0.59

430.03

3184

00.08

8315

00.00

303

6.9

4.49

8.29

200

38.434

636.4

0.54

920.05

2124

00.07

1615

70.00

324

4.5

5.27

8.06

220

56.728

473.1

0.48

490.08

8140

00.05

8316

60.00

344

2.1

7.54


Table

B.43

Therm

ophy

sicalprop

ertiesat

saturatio

nfornitrog

en

Nitrog

en,N2,Molecular

mass:28

.0,(T

sat=−19

5.65

°C;T m

=20

9.85

°C;Vargaftik,19

75)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(103

kg/m

3 )

q v Vapor

density

(103

kg/m

3 )

l‘ Liquid

viscosity

(10−

5N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heata

(kJ/kg

K)

700.38

5920

5.7

0.83

80.00

1920

1048

.00

0.14

200.00

6610

.53

1.93

51.08

801.36

9019

4.5

0.79

00.00

6013

9055

.20

0.12

800.00

778.27

1.96

41.14

903.60

0018

0.5

0.74

60.01

5011

6062

.00

0.11

200.00

916.16

2.02

81.26

100

7.77

5016

2.2

0.69

10.03

2081

068

.80

0.09

550.01

114.00

2.17

61.47

110

14.670

013

7.0

0.62

60.06

2074

075

.60

0.08

020.01

382.00

2.56

61.97

120

25.150

095

.70.52

80.12

4564

082

.10

0.06

280.01

950.20

4.14

a ASH

RAE(200

1)


Table

B.44

Therm

ophy

sicalprop

ertiesat

saturatio

nforpo

tassium

Potassium,K,Molecular

mass:39

.1,(T

sat=10

32.2

K;T m

=33

6.4K;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(10−

3kg

/m3 )

l ‘ Liquid

viscosity

(10−

4N

s/m

2 )

lv Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(10−

1kJ/kgK)

600

0.00

0925

821

4376

6.9

0.69

2.38

043

.85

98.2

0.77

10.81

94

700

0.01

022

2108

743.3

6.68

1.98

140

.72

0.01

4292

.20.76

20.96

46

800

0.06

116

2068

719.6

36.44

1.70

713

437

.58

0.01

7586

.20.76

11.06

6

900

0.24

4120

2369

5.7

134.80

1.50

714

834

.45

0.02

0580

.20.76

91.11

6

1000

0.73

2219

7067

1.6

380.20

1.35

416

331

.32

0.02

2874

.20.79

21.12

1

1100

1.86

419

2464

7.3

871.90

1.23

317

828

.19

0.02

4868

.20.81

91.10

0

1200

3.91

318

7262

2.9

1703

.00

1.13

519

625

.05

0.02

6662

.20.84

61.06

4

1300

7.30

418

2059

8.4

2969

.10

1.05

321

222

.00

0.02

8056

.20.87

31.02

2

1400

12.44

1765

573.6

4768

.70

0.98

422

819

.00

0.02

9353

.00.89

90.97

96

1500

20.0

1711

548.8

7062

.10

0.92

524

216

.00

0.03

0347

.00.92

4


Table

B.45

Therm

ophy

sicalprop

ertiesat

saturatio

nforrubidium

Rub

idium,Rb,

Molecular

mass:85

.5,(T

sat=95

9.2K;T m

=31

2.7K;Vargaftik

1975

)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

q v Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

4N

s/m

2 )

l v Vapor

viscosity

(10−

4N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heat

(kJ/kg

K)

c p,v

Vapor

specific

heat

(kJ/kg

K)

500

0.00

0173

388

9.6

1386

0.00

0358

53.23

29.8

81.6

0.36

90.33

53

600

0.00

3664

870.9

1340

0.00

6386

2.58

0.11

227

.80.00

7375

.70.36

20.41

00

700

0.03

174

849.7

1294

0.04

819

2.18

0.13

525

.90.00

8969

.80.35

70.46

79

800

0.15

8482

7.3

1248

0.21

451.89

0.15

824

.10.01

0363

.90.35

30.49

79

900

0.54

7680

4.6

1202

0.67

261.69

0.18

322

.20.01

1558

.00.35

30.50

35

1000

1.46

778

2.2

1156

1.65

81.53

0.20

820

.30.01

2551

.30.36

00.49

37

1100

3.29

575

9.6

1110

3.43

71.40

0.24

418

.50.01

3344

.50.37

30.47

62

1200

6.46

673

7.0

1064

6.27

41.30

0.26

816

.70.01

4137

.70.38

50.45

58

1300

11.43

714.5

1018

10.36

1.21

0.28

915

.00.01

4930

.90.39

90.43

54

1400

18.6

694.0

972

12.35

1.14

0.31

413

.60.01

5626

.00.40

80.41

30

1500

28.5

674.0

926

22.22

1.08

0.33

612

.00.01

6019

.00.41

80.39

00


Table

B.46

Therm

ophy

sicalprop

ertiesat

saturatio

nforsilver

Silver,Ag,

Molecular

mass:10

7.9,

(Tsat=22

12°C

;T m

=96

0.5°C

;Ivanov

skiiet

al.19

82)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(kg/m

3 )

l‘ Liquid

viscosity

(10−

3N

s/m

2 )

lv Vapor

viscosity

(10−

6N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

itya

(W/m

K)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specificheat

(kJ/kg

K)

c p,v

Vapor

specificheat

(kJ/kg

K)

1500

0.01

008

298

8782

0.00

762.88

61.69

191.3

827.5

1600

0.02

420

298

8683

0.01

698

2.47

64.69

192.7

810.1

1700

0.05

300

298

8585

0.03

548

2.08

67.69

194.1

792.1

1800

0.10

800

298

8485

0.06

823

1.75

70.69

195.5

775.3

1900

0.20

600

298

8385

0.12

300

1.44

73.69

196.9

757.9

2000

0.38

300

298

8289

0.21

880

1.17

76.69

198.3

740.5

2100

0.63

500

298

8190

0.35

480

0.90

79.69

199.7

723.1

2200

0.86

000

298

8092

0.57

540

0.67

82.69

705.7

2300

1.36

000

298

8000

0.87

100

0.44

85.69

638.0

2400

2.53

000

298

7894

1.23

000

0.24

88.69

680.0

2500

3.84

000

298

7796

1.82

000

0.05

91.69

665.0

a Brenn

anandKroliczek(197

9)


Table

B.47

Therm

ophy

sicalprop

ertiesat

saturatio

nforsodium

Sodium

,Na,

Molecular

mass:23

.0,(T

sat=11

51.2

K;T m

=37

1.0K;Ivanov

skiiet

al.19

82;ANL19

95)

T Tem

p.(°C)

p v Saturatio

npressure

(102

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q ‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(10−

3kg

/m3 )

l‘ Liquid

viscosity

(10−

4N

s/m

2 )

lv Vapor

viscosity

(10−

8N

s/m

2 )

k ‘ Liquid

thermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

itya

(W/m

K)

r Liquid

surface

tension

(10−

3N/m

)

c p,‘

Liquid

specific

heata

(kJ/kg

K)

c p,v

Vapor

specific

heat

(10−

1kJ/kgK)

600

0.04

744

2987

3.2

0.02

23.27

614

8075

.17

172.1

1.30

11.80

700

0.95

143

4184

9.4

0.39

62.69

016

6070

.53

0.02

7716

2.1

1.27

72.28

800

8.76

042

3782

5.6

3.27

02.29

818

2765

.88

0.03

4315

2.1

1.26

02.59

900

48.760

4131

801.8

16.500

2.01

820

1061

.25

0.04

0614

2.1

1.25

22.72

1000

192.20

040

2677

8.0

59.980

1.80

922

1156

.60

0.04

5513

2.1

1.25

22.70

1100

584.28

039

2575

4.2

168.10

01.64

523

9851

.96

0.04

9212

2.1

1.26

12.62

1200

1465

.400

3829

730.4

396.60

01.51

425

7747

.00

0.05

2211

2.1

1.27

92.51

1300

3165

.000

3742

706.6

804.50

01.40

727

6342

.50

0.05

4710

2.1

1.30

52.43

1400

6097

.400

3656

682.8

1459

.200

1.31

729

3837

.50

0.05

7092

.11.34

02.39

1500

1071

6.60

035

7765

8.0

2424

.800

1.24

031

1733

.00

0.05

9282

.01.38

42.36

1600

1749

5.90

035

0063

5.2

3750

.900

1.17

632

8128

.50

72.0

1.43

72.34

1700

2691

9.90

034

2561

1.4

5482

.400

1.11

734

4924

.00

62.0

1.50

02.41

1800

3935

0.00

033

5358

7.6

7627

.700

1.06

736

2019

.00

52.0

1.57

42.46

a Vargaftik

(197

5)


Table

B.48

Therm

ophy

sicalprop

ertiesat

saturatio

nforwater

Water,H2O

,Molecular

mass:18

.0,(T

sat=10

0°C

;T m

=0.0°C

;Lem

mon

etal.20

16)

T Tem

p.(°C)

p v Saturatio

npressure

(105

Pa)

h ‘v

Latent

heat

(kJ/kg

)

q‘ Liquid

density

(kg/m

3 )

qv Vapor

density

(kg/m

3 )

l ‘ Liquid

viscosity

(10−

7N

s/m

2 )

l v Vapor

viscosity

(10−

7N

s/m

2 )

k ‘ Liquidthermal

cond

uctiv

ity(W

/mK)

k v Vapor

thermal

cond

uctiv

ity(W

/mK)

r Liquidsurface

tension

(10−

3N/m

)

c p,‘

Liquid

specificheat

(kJ/kg

K)

c p,v

Vapor

specificheat

(kJ/kg

K)

200.02

3368

2453

.899

9.0

0.01

729

1001

697

.30.59

80.01

8272

.88

4.18

41.90

6

400.07

3749

2406

.599

3.05

0.05

110

6530

103.1

0.63

10.01

9669

.48

4.18

01.93

1

600.19

9190

2358

.498

3.28

0.13

020

4664

109.4

0.65

40.02

1266

.07

4.18

51.96

5

800.47

3590

2308

.997

1.82

0.29

320

3543

115.9

0.67

00.02

3062

.69

4.19

72.01

2

100

1.01

3250

2251

.295

8.77

0.59

740

2817

122.7

0.67

90.02

5158

.91

4.21

62.08

0

120

1.98

5400

2202

.994

3.39

1.12

100

2321

129.6

0.68

30.02

7554

.96

4.24

42.17

7

140

3.61

3600

2144

.992

5.93

1.96

560

1965

136.5

0.68

30.03

0150

.79

4.28

32.31

1

160

6.18

0400

2082

.290

7.44

3.25

890

1702

143.4

0.68

00.03

3146

.51

4.33

52.48

8

180

10.027

0020

14.0

887.31

5.15

970

1501

150.3

0.67

30.03

6442

.19

4.40

52.71

3

200

15.551

0019

39.0

865.05

7.86

530

1343

157.2

0.66

30.04

0137

.77

4.49

62.99

0


Table B.49 Binary diffusion coefficients at 1 atma (Bergman and Lavine 2017)

Substance A Substance B T (K) DAB (m2/s)

Gases NH3 Air 298 0.28 � 10−4

H2O Air 298 0.26 � 10−4

CO2 Air 298 0.16 � 10−4

H2 Air 298 0.41 � 10−4

O2 Air 298 0.21 � 10−4

Acetone Air 273 0.11 � 10−4

Benzene Air 298 0.88 � 10−5

Naphthalene Air 300 0.62 � 10−5

Ar N2 293 0.19 � 10−4

H2 O2 273 0.70 � 10−4

H2 N2 273 0.68 � 10−4

H2 CO2 273 0.55 � 10−4

CO2 N2 293 0.16 � 10−4

CO2 O2 273 0.14 � 10−4

O2 N2 273 0.18 � 10−4

Dilute solutions Caffeine H2O 298 0.63 � 10−9

Ethanol H2O 298 0.12 � 10−8

Glucose H2O 298 0.69 � 10−9

Glycerol H2O 298 0.94 � 10−9

Acetone H2O 298 0.13 � 10−8

CO2 H2O 298 0.20 � 10−8

O2 H2O 298 0.24 � 10−8

H2 H2O 298 0.63 � 10−8

N2 H2O 298 0.26 � 10−8

Solids O2 Rubber 298 0.21 � 10−9

N2 Rubber 298 0.15 � 10−9

CO2 Rubber 298 0.11 � 10−9

He SiO2 293 0.4 � 10−13

H2 Fe 293 0.26 � 10−12

Cd Cu 293 0.27 � 10−18

Al Cu 293 0.13 � 10−33

aAssuming ideal gas behavior, the pressure and temperature dependence of the diffusion coefficient for a binary mixtureof gases may be estimated form the relation DAB / p−1 T 3/2


Table B.50 Diffusion coefficients in air at 1 atm (1.013 � 105 Pa)a (Mills and Coimbra 2015)

T [K] Binary diffusion coefficient (m2/s � 104)

O2 CO2 CO C7H16 H2 NO SO2 He

200 0.095 0.074 0.098 0.036 0.375 0.088 0.058 0.363

300 0.188 0.157 0.202 0.075 0.777 0.180 0.126 0.713

400 0.325 0.263 0.332 0.128 1.25 0.303 0.214 1.14

500 0.475 0.385 0.485 0.194 1.71 0.443 0.326 1.66

600 0.646 0.537 0.659 0.270 2.44 0.603 0.440 2.26

700 0.838 0.684 0.854 0.354 3.17 0.782 0.576 2.91

800 1.05 0.857 1.06 0.442 3.93 0.978 0.724 3.64

900 1.26 1.05 1.28 0.538 4.77 1.18 0.887 4.42

1000 1.52 1.24 1.54 0.641 5.69 1.41 1.06 5.26

1200 2.06 1.69 2.09 0.881 7.77 1.92 1.44 7.12

1400 2.66 2.17 2.70 1.13 9.90 2.45 1.87 9.20

1600 3.32 2.75 3.37 1.41 12.5 3.04 2.34 11.5

1800 4.03 3.28 4.10 1.72 15.2 3.70 2.85 13.9

2000 4.80 3.94 4.87 2.06 18.0 4.48 3.36 16.6aOwing to the practical importance of water vapor-air mixtures, engineers have used convenient empirical formulas forDH2Oair. A formula that has been widely used is

DH2O;air ¼ 1:97� 10�5 p0p

� �TT0

� �1:685m2=s; 273 K\T\373 K

where p0 ¼ 1 atm; T0 ¼ 256 K. The following formula has also found increasing use (Marrero and Mason 1972)

DH2Oair ¼ 1:87� 10�10 T2:072

p; 280 K\T\450 K

¼ 2:75� 10�9 T1:632

p; 450 K\T\1070 K

for p in atmospheres and T in Kelvins. Over the temperature range 290–330 K, the discrepancy between the twoformulas is less than 2.5%. For small concentrations of water vapor in air, the older formula gives a constant value ofScH2Oair = 0.61 over the temperature range 273–373 K. On the other hand, the Marrero and Mason (1972) formula givevalues of ScH2Oair that vary from 0.63 at 280 K to 0.57 at 373 K

Table B.51 Diffusion coefficients in solids, D ¼ D0 exp �Ea=RuTð Þ (Mills and Coimbra 2015)

System D0 m2/s Ea

a (kJ/kmol)

Oxygen-Pyrex glass 6:19� 10�8 4:69� 104

Oxygen-fused silica glass 2:61� 10�9 3:77� 104

Oxygen-titanium 5:0� 10�3 2:13� 105

Oxygen-titanium alloy (Ti-6Al-4 V) 5:82� 10�2 2:59� 105

Oxygen-zirconium 4:68� 10�5 7:06� 105

Hydrogen-iron 7:60� 10�8 5:60� 103

Hydrogen-a-titanium 1:80� 10�6 5:18� 104

Hydrogen-b-titanium 1:95� 10�7 2:78� 104

Hydrogen-zirconium 1:09� 10�7 4:81� 104

Hydrogen-Zircaloy-4 1:27� 10�5 6:05� 105

Deuterium-Pyrex glass 6:19� 10�8 4:69� 104

Deuterium-fused silica glass 2:61� 10�9 3:77� 104

(continued)


Table B.52 Schmidt number for vapors in dilute mixture in air at normal temperature, enthalpy of vaporization andboiling point at 1 atma (Mills and Coimbra 2015)

Vapor Chemical formula Scb h‘v J/kg � 10−6 Boiling point temperature K

Acetone CH3COCH3 1.42 0.527 329

Ammonia NH3 0.61 1.370 240

Benzene C6H6 1.79 0.395 354

Carbon dioxide CO2 1.00 0.398 194

Carbon monoxide CO 0.77 0.217 81

Chlorine Cl2 1.42 0.288 238

Ethanol CH3CH2OH 1.32 0.854 352

Helium He 0.22 4.3

Heptane C7H16 2.0 0.340 372

Hydrogen H2 0.20 0.454 20.3

Hydrogen sulfide H2S 0.94 0.548 213

Methanol CH3OH 0.98 1.100 338

Napthalenec C10H8 2.35 0.567 491

Nitric oxide NO 0.87 0.465 121

Octane C8H18 2.66 0.303 399

Oxygen O2 0.83 0.214 90.6

Pentane C5H12 1.49 0.357 309

Sulfur dioxide SO2 1.24 0.398 263

Water vapor H2O 0.61 2.257 373aWith the Clausius–Clapeyron relation, one may estimate vapor pressure as

psat ’ exp �Mh‘vRu

1T � 1

TBP

� �n oatm; for T � TBP

bThe Schmidt number is defined as Sc ¼ l=qD ¼ v=D. Since the vapors are in small concentrations, values for l, q andv can be taken as pure air valuescCho et al. (1992); h‘v ¼ 0:567� 106 J/K is at 300 K


System D0 m2/s Ea

a (kJ/kmol)

Helium-Pyrex glass 4:76� 10�8 2:72� 104

Helium-fused silica glass 5:29� 10�8 2:55� 104

Helium-borosilicate 1:94� 10�8 2:34� 104

Neon-borosilicate 1:02� 10�10 3:77� 104

Carbon-FCC iron 2:3� 10�5 1:378� 105

Carbon-BCC iron 1:1� 10�6 8:75� 104

aActivation energy


Table B.53 Schmidt numbers for dilute solution in water at 300 Ka (Mills and Coimbra 2015)

Solute Schmidt number, Sc Molecular mass, M (kg/kmol)

Helium 120 4.003

Hydrogen 190 2.016

Nitrogen 280 28.02

Water 340 18.016

Nitric Oxide 350 30.01

Carbon monoxide 360 28.01

Oxygen 400 32.00

Ammonia 410 17.03

Carbon dioxide 420 44.01

Hydrogen sulfide 430 34.08

Ethylene 450 28.05

Methane 490 16.04

Nitrous oxide 490 44.02

Sulfur dioxide 520 64.06

Sodium chloride 540 58.45

Sodium hydroxide 490 40.00

Acetic acid 620 60.05

Acetone 630 58.08

Methanol 640 32.04

Ethanol 640 46.07

Chlorine 670 70.90

Benzene 720 78.11

Ethylene glycol 720 62.07

n-Propanol 730 60.09

i-Propanol 730 60.09

Propane 750 44.09

Aniline 800 93.13

Benzoic acid 830 122.12

Glycerol 1040 92.09

Sucrose 1670 342.3aFor other temperatures use Sc=Sc300 K ’ ðl2=qTÞ=ðl2=qTÞ300 K, where l and q are for water, and T isabsolute temperature. For chemically similar solutes of different molecular weights useSc2=Sc1 ’ ðM2=M1Þ0:4. A table of ðl2=qTÞ=ðl2=qTÞ300 K for water follows

T [K] ðl2=qTÞ=ðl2=qTÞ300 K T [K] ðl2=qTÞ=ðl2=qTÞ300 K

290 1.66 340 0.221

300 1.00 350 0.167

310 0.623 360 0.123

320 0.429 370 0.097

330 0.296

Spalding (1963)


Table B.54 Solubility and permeability of gases in solids (Mills and Coimbra 2015)

Gas Solid T (K) S0 [m3 (STP)/m3 atm]or S′a

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

H2 Vulcanized rubber 300 S0 ¼ 0:040 0.34 � 10−10

Vulcanized neoprene 290 S0 ¼ 0:051 0.053 � 10−10

Silicone rubber 300 4.2 � 10−10

Natural rubber 300 0.37 � 10−10

Polyethylene 300 0.065 � 10−10

Polycarbonate 300 0.091 � 10−10

Fused silica 400 S00 ffi 0:035

Nickel 800 S00 ffi 0:030

360 S00 ffi 0:202

440 S00 ffi 0:192

He Silicone rubber 300 2.3 � 10−10



Nylon 66 300 0.0076 � 10−10

Teflon 300 0.047 � 10−10

Fused silica 300 S00 ffi 0:018

800 S00 ffi 0:026

Pyrex glass 300 S00 ffi 0:006

800 S00 ffi 0:024

7740 glass(94% SiO2 + B2O3 + P2O5

5% Na2O + Li2 + K2O1% other oxides)

470 S0 ¼ 0:0084 4.6 � 10−13

580 S0 ¼ 0:0038 1.6 � 10−12

720 S0 ¼ 0:0046 6.4 � 10−12

7056 glass(90% SiO2 + B2O3 + P2O5

8% Na2O + Li2 + K2O1% PbO, 0.5% other oxides)

390 S0 ¼ 0:0039 1.2 � 10−14

680 S0 ¼ 0:0059 1.0 � 10−12

O2 Vulcanized rubber 300 S0 ¼ 0:070 0.15 � 10−10



Polyethylene 300 4.2 � 10−12


Silicone-polycarbonate copolymer(57% silicone)

300 1.2 � 10−10

Ethyl cellulose 300 0.09 � 10−10

N2 Vulcanized rubber 300 S0 ¼ 0:035 0.054 � 10−10




300 0.53 � 10−10

Teflon® 300 0.019 � 10−10

(continued)



Gas Solid T (K) S0 [m3 (STP)/m3 atm]or S′a

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

CO2 Vulcanized rubber 300 S0 ¼ 0:90 1.0 � 10−10

Silicone rubber 300 21 � 10−10



300 7.4 � 10−10

Nylon 66 300 0.0013 � 10−10

H2O Cellophane 310 0.91–1.8 � 10−10

Ne Fused silica 300–1200

S00 ffi 0:002

Ar Fused silica 900–1200

S00 ffi 0:01

aSolubility S0 = Volume of solute gas (0 °C, 1 atm) dissolved in unit volume of solid when the gas is at 1 atm partialpressure. Solubility coefficient S00 ¼ c1;g=c2bPermeability K ¼ DABS0

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

Table B.55 Henry’s constant for selected gases in water at moderate pressurea

H ¼ pA;i=xA;i (bars)

T (K) NH3 Cl2 H2S SO2 CO2 CH4 O2 H2

273 21 265 260 165 710 22,880 25,500 58,000

280 23 365 335 210 960 27,800 30,500 61,500

290 26 480 450 315 1300 35,200 37,600 66,500

300 30 615 570 440 1730 42,800 45,700 71,600

310 – 755 700 600 2175 50,000 52,500 76,000

320 – 860 835 800 2650 56,300 56,800 78,600

323 – 890 870 850 2870 58,000 58,000 79,000aBergman and Lavine (2017) and Spalding (1963)

Table B.56 Solubility of selected gases and solids (Bergman and Lavine 2017)

Gas Solid T (K) S ¼ cA;s=pA;g (k mol/m3 bar)

O2 Rubber 298 3.12 � 10−3

N2 Rubber 298 1.56 � 10−3

CO2 Rubber 298 40.15 � 10−3

He SiO2 293 0.45 � 10−3

H2 Ni 358 9.01 � 10−3


Table

B.57

Solubilityof

inorganiccompo

unds

inwater

a(M

illsandCoimbra20

15)

Solute

Form

ula

Solid

Phase

T(K

)

273.15

280

290

300

310

320

330

340

350

360

370

373.15

Aluminum

sulfate

Al 2(SO4)3

18H2O

31.2

32.8

35.5

39.1

44.3

50.3

57.0

63.9

70.8

78.3

84.6

89.0

Calcium

bicarbon

ate

Ca(HCO3)2

–16

.15

16.30

16.53

16.75

16.98

17.20

17.43

17.65

17.88

18.10

18.33

18.40

Calcium

chloride

CaC

l 26H

2O59

.563

.371

.593

.313

7.2

––

––

––

–

CaC

l 22H

2O–

––

––

–13

4.6

140.2

145.3

150.9

157.0

159.0

Calcium

hydrox

ide

Ca(OH) 2

–0.18

50.17

90.16

80.15

70.14

50.13

20.12

00.10

90.09

80.08

80.08

00.07

7

Potassium

chloride

KCl

–27

.629

.933

.136

.139

.141

.844

.647

.450

.253

.155

.856

.7

Potassium

nitrate

KNO3

–13

.318

.528

.241

.358

.278

.710

2.3

129.2

159.2

191.6

232.1

246.0

Potassium

sulfate

K2SO4

–7.35

8.63

10.51

12.38

14.20

15.95

17.64

19.25

20.88

22.36

23.69

24.1

Sodium

bicarbon

ate

NaH

CO3

–6.9

7.76

9.14

10.63

12.20

13.90

15.79

––

––

–

Sodium

carbon

ate

Na 2O3

10H2O

710

.818

.733

.4–

––

––

––

–

Na 2CO3

1H2O

––

––

49.1

47.8

46.7

46.2

45.9

45.7

45.55

45.5

Sodium

chloride

NaC

l–

35.7

35.8

35.9

36.2

36.5

36.9

37.2

37.6

38.2

38.8

39.5

39.8

Sodium

nitrate

NaN

O2

–73

7885

9310

111

112

113

214

415

917

518

0

Sodium

sulfate

Na 2SO

410

H2O

5.0

7.7

16.1

34.1

––

––

––

––

Na 2SO

47H

2O19

.526

.739

.6–

––

––

––

––

Na 2SO

4–

––

––

49.6

47.4

45.7

43.7

44.0

43.3

42.7

42.5

a Solub

ility

expressedin

kilogram

sof

anhy

drou

ssubstancethat

issolublein

100kg

water


Table B.58 Equilibrium compositions for the NH3-water system (Mills and Coimbra 2015)

pA;g (atm) xA;‘290 K 300 K 310 K 320 K 330 K

0.02 0.030 0.019 0.012 0.008 0.006

0.04 0.056 0.036 0.024 0.016 0.012

0.06 0.078 0.052 0.035 0.024 0.017

0.08 0.096 0.064 0.046 0.032 0.023

0.1 0.11 0.079 0.056 0.040 0.029

0.2 0.18 0.14 0.099 0.057 0.052

0.4 0.26 0.21 0.16 0.12 0.092

0.6 0.31 0.26 0.20 0.16 0.13

0.8 0.35 0.29 0.23 0.19 0.15

1.0 – 0.32 0.27 0.22 0.17

Table B.59 Equilibrium compositions for the SO2-water systema (Mills and Coimbra 2015)

pA;g (atm) xA;‘ � 103

290 K 300 K 310 K 320 K

0.001 0.12 0.084 0.059 0.042

0.003 0.25 0.18 0.13 0.093

0.01 0.62 0.42 0.31 0.22

0.03 1.4 1.1 0.73 0.51

0.1 4.1 2.9 2.0 1.4

0.3 11.0 7.9 5.6 3.9

1.0 33.0 24.0 18.0 12.0aNotice that Henry’s law is invalid for the SO2-water system, even at very dilute concentrations

Table B.60 Thermodynamic properties of water vapor-air mixtures at 1 atm (Mills and Coimbra 2015)

Temp.(°C)

Saturation mass fraction Specific volume (m3/kg) Enthalpya, b (KJ/kg)

Dry air Saturated air Liquid water Dry air Saturated air

10 0.007608 0.8018 0.8054 42.13 10.059 29.145

11 0.008136 0.8046 0.8086 46.32 11.065 31.481

12 0.008696 0.8075 0.8117 50.52 12.071 33.898

13 0.009289 0.8103 0.8148 54.71 13.077 36.401

14 0.009918 0.8131 0.8180 58.90 14.083 38.995

15 0.01058 0.8160 0.8212 63.08 15.089 41.684

16 0.01129 0.8188 0.8244 67.27 16.095 44.473

17 0.01204 0.8217 0.8276 71.45 17.101 47.367

18 0.01283 0.8245 0.8309 75.64 18.107 50.372

19 0.01366 0.8273 0.8341 79.82 19.113 53.493

20 0.01455 0.8302 0.8374 83.99 20.120 56.736

21 0.01548 0.8330 0.8408 88.17 21.128 60.107

22 0.01647 0.8359 0.8441 92.35 22.134 63.612

23 0.01751 0.8387 0.8475 96.53 23.140 67.259(continued)


References

Altemose, V. O. (1961). Helium diffusion through glass. Journal of Applied Physics, 32, 1309–1316.American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE). (2009). ASHRAE handbook of

fundamentals. New York, NY: ASHRAE.Argonne National Laboratory (ANL). (1995). Thermodynamic and transport properties of the sodium liquid and vapor.

ANL/RE-95/2, https://www.ne.anl.gov/eda/ANL-RE-95-2.pdf. Accessed on September 17, 2018.Bejan, A. (2013). Convection heat transfer (4th ed.). New York, NY: Wiley.Bennon, W. D., & Incropera, F. P. (1988). Developing laminar mixed convection with solidification in a vertical

channel. Journal of Heat Transfer, 110, 410–415.Bergman, T. L., & Lavine, A. S. (2017). Fundamentals of heat and mass transfer (8th ed.). Hoboken, NJ: Wiley.Brennan, P. J., & Kroliczek, E. J. (1979). Heat pipe design handbook (Vol. 2). Towson, MD: NASA Goddard by B&K

Engineering, Inc., Suite 825, One Investment Place.Cengel, Y. A., Boles, M. A., & Kanoglu, M. (2019). Thermodynamics—An engineering approach (9th ed.). New York,

NY: McGraw-Hill.Cho, C., Irvine, T. F., Jr., & Karni, J. (1992). Measurement of the diffusion coefficient of naphthalene into air.

International Journal of Heat and Mass Transfer, 35, 957–966.


Temp.(°C)

Saturation mass fraction Specific volume (m3/kg) Enthalpya, b (KJ/kg)

Dry air Saturated air Liquid water Dry air Saturated air

24 0.01861 0.8415 0.8510 100.71 24.147 71.054

25 0.01978 0.8444 0.8544 104.89 25.153 75.004

26 0.02100 0.8472 0.8579 109.07 26.159 79.116

27 0.02229 0.8500 0.8615 113.25 27.166 83.400

28 0.02366 0.8529 0.8650 117.43 28.172 87.862

29 0.02509 0.8557 0.8686 121.61 29.178 92.511

30 0.02660 0.8586 0.8723 125.79 30.185 97.357

31 0.02820 0.8614 0.8760 129.97 31.191 102.408

32 0.02987 0.8642 0.8798 134.15 32.198 107.674

33 0.03164 0.8671 0.8836 138.32 33.204 113.166

34 0.03350 0.8699 0.8874 142.50 34.211 118.893

35 0.03545 0.8728 0.8914 146.68 35.218 124.868

36 0.03751 0.8756 0.8953 150.86 36.224 131.100

37 0.03967 0.8784 0.8994 155.04 37.231 137.604

38 0.04194 0.8813 0.9035 159.22 38.238 144.389

39 0.04432 0.8841 0.9077 163.40 39.245 151.471

40 0.04683 0.8870 0.9119 167.58 40.252 158.862

41 0.04946 0.8898 0.9162 171.76 41.259 166.577

42 0.05222 0.8926 0.9206 175.94 42.266 174.630

43 0.05512 0.8955 0.9251 180.12 43.273 183.037

44 0.05817 0.8983 0.9297 184.29 44.280 191.815

45 0.06137 0.9012 0.9343 188.47 45.287 200.980

46 0.06472 0.9040 0.9391 192.65 46.294 210.550

47 0.06842 0.9068 0.9439 196.83 47.301 220.543

48 0.07193 0.9097 0.9489 201.01 48.308 230.980

49 0.07580 0.9125 0.9539 205.19 49.316 241.881aThe enthalpies of dry air and liquid water are set equal to zero at a datum temperature of 0 °CbThe enthalpy of an unsaturated water vapor-air mixture can be calculated as h ¼ hdryair þðm1=m1;satÞðhsat � hdryairÞ


https://www.ne.anl.gov/eda/ANL-RE-95-2.pdf

Doremus, R. H. (1973). Glass science. New York: Wiley.Faghri, A. (2016). Heat pipe science and technology (2nd ed.). Columbia, MO: Global Digital Press.Geankoplis, C. J. (1993). Transport processes and unit operations (3rd ed.). Englewood Cliffs, NJ: Prentice-Hall.Hale, D. V., Hoovers, M. J., & O’Nell, M. J. (1971). Phase change materials handbook. NASA-CR-61363.Humphries, W. R., & Griggs, E. I. (1977). A design handbook for phase change thermal control and energy storage

devices. NASA-TP-1074.Iida, T., & Guthrie, R. I. L. (1988). The physical properties of liquid metals. Oxford, UK: Oxford University Press.Ivanovskii, M.N., Sorokin, V.P., and Yagodkin, I.V., 1982, The Physical Principles of Heat Pipes, Clarendon Press,

Oxford, UK.Kakac, S., Shah, R. K., & Aung, W. (Eds.). (1987). Handbook of single-phase convective heat transfer. New York, NY:

Wiley.Lemmon, E. W., McLinden, M. O., & Friend, D. G. (2016). Thermophysical properties offluid systems. In P. I. Linstrom

& W. G. Mallard (Eds.), NIST chemistry WebBook, NIST Standard Reference Database Number 69. Gaithersburg,MD: National Institute of Standards and Technology, 20899. http://webbook.nist.gov.

Marrero, T. R., & Mason, E. A. (1972). Gaseous diffusion coefficients. Journal of Physical and Chemical ReferenceData, 1, 3–118.

Mills, A. F., & Coimbra, C. F. M. (2015). Basic heat and mass transfer (3rd ed.). San Diego, CA: Temporal Publishing,LLC.

Reay, D. A., Kew, P. A., & McGlen, R. J. (2014). Heat pipes—Theory, design, and applications (6th ed.). New York:Elsevier.

Rohsenow, W. N., Hartnett, J. P., & Ganic, E. N. (Eds.). (1998). Handbook of heat transfer fundamentals (3rd ed.).New York, NY: McGraw-Hill.

Spalding, D. B. (1963). Convective mass transfer. New York, NY: McGraw-Hill.Touloukian, Y. S., Liley, P. E., & Saxena, S. C., (Eds.). (1970). Thermophysical properties of matter (Vol. 3). New

York, NY: Plenum.Vargaftik, N. B. (1975). Handbook of physical properties of liquids and gases. New York, NY: Hemisphere.


http://webbook.nist.gov

Appendix C: Vectors and Tensors

C.1 Vectors

The term scalar refers to a single real number used to describe the magnitude of a quantity. Pressure,temperature, and internal energy are all scalar. A vector is defined as an entity that possesses bothmagnitude and direction or as a directed line segment subject to the parallelogram law of addition. Inthree-dimensional space, a vector may be specified by three vector components. A unit vector is avector whose magnitude is unity. A vector in a three-dimensional Cartesian coordinate system can beexpressed as

A ¼ iAx þ jAy þ kAz ðC:1Þ

where i, j, and k are unit vectors in the x-, y-, and z-directions. The vector components in the x-, y-,and z-directions are Ax, Ay, and Az, respectively. A vector in a Cartesian coordinate system is shown inFig. C.1. It can be seen that the magnitude of the vector is

Aj j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2x þA2

y þA2z

qðC:2Þ

and that its three components are the projections of the vector on the x, y, and z-axes.A vector can also be represented in matrix form:

A ¼Ax

Ay

Az

24

35 ðC:3Þ

The dot product (also referred to as the scalar or inner product) of two vectors A and B is a scalar;it is obtained by summation of the product of each of their corresponding components, i.e.,

A � B ¼ AxBx þAyBy þAzBz ðC:4Þ

The cross product (or vector product) of two vectors A and B is a vector, i.e.,

A� B ¼i j k

Ax Ay Az

Bx By Bz

��

¼ i AyBz � AzBy

� �þ j AzBx � AxBzð Þþ k AxBy � AyBx

� � ðC:5Þ


799

https://doi.org/10.1007/978-3-030-22137-9

C.2 Operations with the $ Operator

C.2.1 Cartesian Coordinate System

An important vector for fluid mechanics and heat transfer is the r operator (pronounced Del ornabla), which is defined as

r ¼ i@

@xþ j

@

@yþ k

@

@zðC:6Þ

in a three-dimensional Cartesian coordinate system. It can be applied to a scalar function, /, to obtainits gradient,

grad/ ¼ r/ ¼ i@/@x

þ j@/@y

þ k@/@z

ðC:7Þ

which is a vector.The r operator can also be applied to a vector function such as velocity,

V ¼ iuþ jvþ kw ðC:8Þ

to get its divergence:

divV ¼ r � V ¼ @u

@xþ @v

@yþ @w

@zðC:9Þ

or its curl:

curlV ¼ r� V ¼ i@w

@y� @v

@z

� þ j

@u

@z� @w

@x

� þ k

@v

@x� @u

@y

� ðC:10Þ

Another related operator that is very useful in fluid mechanics and heat transfer is Laplacianoperator, defined as

Figure C.1 Vector and its components

800 Appendix C: Vectors and Tensors

r2 ¼ r � r ¼ @2

@x2þ @2

@y2þ @2

@z2ðC:11Þ

Application of the Laplace operator to a scalar function / results in

r2/ ¼ @2/@x2

þ @2/@y2

þ @2/@z2

ðC:12Þ

Forming the dot product of the velocity and the gradient of a scalar / results in a scalar:

V � r/ ¼ u@/@x

þ v@/@y

þw@/@z

ðC:13Þ

which is used to describe the advection of the property /.The operation

r � ðar/Þ ¼ @

@xa@/@x

� þ @

@ya@/@y

� þ @

@za@/@z

� ðC:14Þ

results in a scalar that describe the diffusion of the property /.Application of the Laplace operator to a velocity vector, V, results in a vector:

r2V ¼ ir2uþ jr2vþ kr2w ðC:15Þ

C.2.2 Cylindrical Coordinate System

The cylindrical coordinate system (r, u, z) shown in Fig. C.2 is related to Cartesian coordinates (x, y, z)by

x ¼ r cosu y ¼ r sinu z ¼ z ðC:16Þ

The velocity vector, V, in a cylindrical coordinate system has three components, i.e.,

V ¼ krVr þ kuVu þ kzVz ðC:17Þ

where kr; ku and kz are the unit vectors in r-, u-, and z-directions, respectively.The operations involving the r operator and either the general scalar function / or the vector V in

a cylindrical coordinate system is summarized below:

grad/ ¼ r/ ¼ kr@/@r

þ ku1r

@/@u

þ kz@/@z

ðC:18Þ

divV ¼ r � V ¼ 1r

@ðrVrÞ@r

þ 1r

@Vu

@uþ @Vz

@zðC:19Þ

Appendix C: Vectors and Tensors 801

r2/ ¼ 1r

@

@rr@/@r

� þ 1

r2@2/@u2

þ @2/@z2

ðC:20Þ

V � r/ ¼ Vr@/@r

þ Vu

r

@/@u

þVz@/@z

ðC:21Þ

r � ar/ ¼ 1r

@

@rra

@/@r

� þ 1

r

@

@uar

@/@u

� þ @

@za@/@z

� ðC:22Þ

r2V ¼ kr@

@r

1r

@

@rrVrð Þ

�þ 1

r2@2Vr

@u2� 2r2@Vu

@uþ @2Vr

@z2

�

þ ku@

@r

1r

@

@rrVu� � �

þ 1r2@2Vu

@u2þ 2

r2@Vr

@uþ @2Vu

@z2

�

þ kz1r

@

@rr@Vz

@r

� þ 1

r2@2Vz

@u2þ @2Vz

@z2

� ðC:23Þ

C.2.3 Spherical Coordinate System

The spherical coordinate system (r, h, u) shown in Fig. C.3 is related to the Cartesian coordinatesystem by

x ¼ r sin h cosu y ¼ r sin h sinu z ¼ r cos h ðC:24Þ

A velocity vector, V, has three components, i.e.,

V ¼ krVr þ khVh þ kuVu ðC:25Þ

where kr; kh; and ku are the unit vectors in r, h, and u directions, respectively.The operations involving the r operator and either the general scalar function / or the vector V in

a spherical coordinate system are summarized below:

Figure C.2 Relationship between cylindrical and Cartesian coordinates


grad/ ¼ r/ ¼ kr@/@r

þ kh1r

@/@h

þ ku1

r sin h@/@u

ðC:26Þ

divV ¼ r � V ¼ 1r2@ðr2VrÞ

@rþ 1

r sin h@ðVh sin hÞ

@hþ 1

r sin h@Vu

@uðC:27Þ

r2/ ¼ 1r2

@

@rr2@/@r

� þ 1

r2 sin h@

@hsin h

@/@h

� þ 1

r2 sin2 h

@2/@u2

ðC:28Þ

V � r/ ¼ Vr@/@r

þ Vh

r

@/@h

þ Vu

r sin h@/@u

ðC:29Þ

r � ðar/Þ ¼ 1r2

@

@rr2a

@/@r

� þ 1

r2 sin h@

@hsin hð Þa @/

@h

�

þ 1

r2 sin2 h

@

@ua@/@u

� ðC:30Þ

r2V ¼ kr r2Vr � 2Vr

r2� 2r2@Vh

@h� 2Vh cot h

r2� 2r2 sin h

@Vu

@u

�

þ kh r2Vh þ 2r2@Vr

@h� Vh

r2 sin h� 2 cos h

r2 sin2 h

@Vu

@u

�

þ kz r2V/ � Vu

r2 sin2 hþ 2

r2 sin h@Vr

@uþ 2 cos h

r2 sin2 h

@Vh

@u

� ðC:31Þ

C.3 Tensors

A tensor of rank n in the Cartesian coordinate system has 3n components. A scalar can be consideredas a tensor of rank 0 because it has only one component. A vector is a tensor of rank 1 since it hasthree components. As was demonstrated in Sect. 1.3.2, the normal and shear stresses in a fluid can be

Figure C.3 Relationship between spherical and Cartesian coordinates


http://dx.doi.org/10.1007/978-3-030-22137-9_1

described by a tensor of rank 2. The defining characteristics of a tensor are the manner in which itscomponents transform under a rotation of the coordinate system where the components are defined.The transformation law for the components of tensor of a rank two is given as

s0ij ¼ aikajlskl ðC:32Þ

where the prime denotes the tensor components in the rotated coordinate, and aik and ajl represent,respectively, the cosines of the angles between the ith rotated axis and the kth original axis, andbetween the jth rotated axis and the lth original axis. It should be noted that it is not the tensor itselfthat transforms under this change in the reference coordinate system but, rather, the coordinates thatdescribe the tensor.

Application of the r operator to each component of the velocity vector V ¼ iuþ jvþ kw alsoyields a tensor of rank two:

rV ¼

@u

@x

@u

@y

@u

@z@v

@x

@v

@y

@v

@z@w

@x

@w

@y

@w

@z

26666664

37777775

ðC:33Þ

which is a dyadic product of two vectors r and V, and it can be used to determine the strain ratetensor.

The dot product of a vector and a tensor of rank 2 is a vector. For example, the dot product of ther operator and a stress tensor is

r � s ¼ s � r ¼

@

@x@

@y@

@z

2666664

3777775

sxx sxy sxzsyx syy syzszx szy szz

24

35 ¼

@sxx@x

þ @sxy@y

þ @sxz@z

@syx@x

þ @syy@y

þ @syz@z

@szx@x

þ @szy@y

þ @szz@z

26666664

37777775

ðC:34Þ

where r � s ¼ s � r is valid because the stress tensor is a symmetric tensor. For the case that thetensor is not symmetric, the order of vector and tensor cannot be switched in their dot product.

The contraction of two tensors of rank two a and b is obtained by summing the products of thecorresponding components from both tensors:

a:b ¼ axxbxx þ axybxy þ axzbxz þ ayxbyx þ ayybyy þ ayzbyzþ azxbzx þ azybzy þ azzbzz

ðC:35Þ

which can also be written as

a:b ¼ aijbij ðC:36Þ

using the summation convention of tensors. According to the summation convention, the repetition ofan index in a term denotes a summation with respect to that index over its range (i, j = x, y, z). The


definitions and operations of the vectors and tensors reviewed here provide foundations for thegoverning equations for multiphase systems. Additional information about tensors and their associ-ated operations can be found in a continuum mechanics textbook, such as Fung (1994).

Reference

Fung, Y. C. (1994). First course in continuum mechanics (3rd ed.). New York: Prentice Hall.


Appendix D: Convective Heat TransferCorrelations

See Table D.1.

Table D.1 Convective heat transfer correlations for various heat and mass transfer modes and geometries

Heattransfermode

Geometry Nusselt number Comments andrestrictions

Dimensionlessnumbers

Forcedconvection

Flow parallel to aflat plate

Nux ¼ 0:332Re1=2x Pr1=3

ðPr[ 0:6ÞNux ¼ 0:565Re1=2x Pr1=2

ðPr� 0:05Þ

Isothermal surface

Rex\5� 105

(laminar)

Nux ¼ hx

k

Rex ¼ u1x

m

Nu ¼0:037ðRe0:8L � 871ÞPr0:33ð0:6�Pr� 60Þ

5� 105\ReL\108

(turbulent)Nu ¼

�hL

k

ReL ¼ u1L

m

Flow in a pipe(conventional size)

Nu ¼ 3:66

þ 0:0668ðD=LÞRePr1þ 0:04½ðD=LÞRePr�2=3

Isothermal surfaceRe� 2300

Thermal entry region

Nu ¼�hD

k

Re ¼ �uD

m�u is mean velocityNu ¼ 0:027Re0:8

� Pr0:33 l=lwð Þ0:14ð0:7�Pr� 16;700Þ

L=D 10

Re[ 10; 000

(Fully developedturbulent)lw is viscosityevaluated at Tw

Flow in a pipe(miniature)

Nu ¼ ð1þFÞ

� ðf =8ÞðRe� 1000ÞPr1þ 12:7ðf =8Þ0:5ðPr2=3 � 1Þ

f ¼ ½1:82 logReÞ � 1:64��2

F ¼ 7:6� 10�5Re

� ½1� ðD=D0Þ2�

D0 = 1.164 mm isreferencediameterCorrelation wasobtained for waterat D = 0.102, 0.76and 1.09 mm

Nu ¼�hD

k

Re ¼ �uD

m

Flow between parallelplates

Nu ¼ 7:54

þ 0:03ðDh=LÞRePr1þ 0:016½ðDh=LÞRePr�2=3

Isothermal surfaceRe� 2800

(laminar)

Nu ¼�hDh

k

Re ¼ �uDh

mNu ¼ 0:023Re0:8Pr0:33

ðPr[ 0:5ÞRe[ 10;000

(Turbulent)

(continued)


807

https://doi.org/10.1007/978-3-030-22137-9

Table D.1 (continued)

Heattransfermode



Flow across a circularcylinder

Nu ¼ 0:3

þ 0:62Re1=2Pr1=3

½1þð0:4=Pr=Þ2=3�1=4

� 1þ Re

282000

� 5=8" #4=5

RePr[ 0:2

(both laminar andturbulent)

Nu ¼�hD

k

Re ¼ u1D

m

Flow across a sphere Nu ¼ 2þð0:4Re0:5

þ 0:06Re2=3ÞPr0:4ðl=lwÞ14

3:5\Re

\76;000

0:71�Pr� 380

lw is viscosityevaluated at Tw

Flow through a packedbed of spheres

Nu ¼ 1:625Re1=2Pr1=3 15�Re� 120

D—diameter ofsphereA—bed cross-sectional area

Nu ¼�hD

k

Re ¼ _mD

Al

Freeconvection

On a vertical surface Nu1=2 ¼ 0:825

þ 0:387Ra1=6

½1þð0:492=PrÞ9=16�8=27

DT ¼ Tw � T1j jApplicable to bothlaminar andturbulent

Nu ¼�hL

k

Ra ¼ gbDTL3

ma

On a horizontal heatedsquare facing up

Nu ¼ 0:54ðGr PrÞ1=4 Isothermal surface

105 �Gr� 7� 107

For rectangle, useshorter side of L

Nu ¼�hL

k

Gr ¼ gbDTL3

m2

(continued)

808 Appendix D: Convective Heat Transfer Correlations


Heattransfermode



On a horizontal heatedsquare facing down

Nu ¼ 0:27ðGr PrÞ1=4Isothermal surface3� 105 �Gr

� 3� 1010

For rectangle, useshorter side of L

Nu ¼�hL

k

Gr ¼ gbDTL3

m2

On a horizontal cylinder Nu1=2 ¼ 0:60þ

0:387Ra1=6

½1þð0:559=PrÞ9=16�8=27

Ra\1012Nu ¼

�hD

k

Ra ¼ gbDTD3

ma

On a sphere Nu ¼ 2

þ 0:589Ra1=4

½1þð0:469=PrÞ9=16�4=9

DT ¼ Tw � T1Ra\1011

Pr 0:7

Nu ¼�hD

k

Ra ¼ gbDTD3

ma

Evaporation Falling filmevaporation

Laminar

Nu ¼ 1:10Re�1=3d

ðRed � 30Þ

Nu—local NusseltnumberC—mass flow rateper unit width ofthe vertical surface

Nu ¼ hðm2‘ =gÞ13

k

Red ¼ 4Cl

Wavy laminar

Nu ¼ 0:828Re�0:22d

ð30�Red � 1800ÞTurbulent

Nu ¼ 0:0038Re0:4d Pr0:65

ðRed [ 1800Þ

Condensation On a vertical surface Laminar (Nusselt)

Nu ¼ 1:10Re�1=3d

ðRed � 30Þ

Nu—local NusseltnumberC—mass flowrate per unit widthof the verticalsurface

Nu ¼ hðm2‘ =gÞ13

k

Red ¼ 4Cl

Wavy laminar

Nu ¼ RedRe1:22d � 5:22

ð30�Red � 1800ÞTurbulent

Nu ¼ 0:023Re0:25d Pr�0:5

(continued)

Appendix D: Convective Heat Transfer Correlations 809


Heattransfermode



On tubes Nu ¼ 0:729

� D3h‘vg q‘ � qvð Þnk‘m‘DT

�14

DT ¼ Tsat � Twn—number oftubes

Nu ¼ �hDk‘

In microscale channel(Dh\1:5 mm)

Nu ¼ We�JaRe PrY Y ¼ 1:3

for Re� 65

Y ¼ ð0:5Dh � 1Þ=ð2DhÞ

for Re[ 65

We ¼ q‘V2L

r

Ja ¼ cp‘ðTsat�TwÞhlv

Re ¼ GDhl‘

G—mass flux (kg/s m2)

Boiling Nucleate, saturated poolboiling

Nu ¼ Ja2‘

C3Prm‘

m = 2 for waterm = 4.1 for otherfluidsC = 0.013 water-copper or stainlesssteelC = 0.006 for water-nickel or brass

Nu ¼�hLck‘

Lc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r‘gðq‘ � qvÞ

r

Ja‘ ¼ cp;‘DTh‘v

DT ¼ Tw � Tsat

Film boiling on ahorizontal plate

Nu ¼ 0:425

� GrPrv1þ 0:4 Jav

Jav

� �14

Term in parenthesesaccounts forsensible heatingeffect in vapor film

Nu ¼�hLckv

Lc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r‘gðq‘ � qvÞ

r

Gr ¼ g½ðq‘ � qvÞ=qv�L3cm2v

Jav ¼ cp;vDTh‘v

Film boiling on ahorizontal cylinder

Nu ¼ 0:62

� Gr Prv1þ 0:4 Jav

Jav

� �14

D film thicknessNu ¼

�hD

kv

Gr ¼ g½ðq‘ � qvÞ=qv�D3

m2v

Jav ¼ cp;vDTh‘v

Film boiling on a sphere Nu ¼ 0:4

� GrPrv1þ 0:4 Jav

Jav

� �13

D filmthickness

(continued)

810 Appendix D: Convective Heat Transfer Correlations


Heattransfermode



Boiling in microchannel(D = 1.39–1.69 mm)

Nu ¼ 30Re0:857

� Bo0:714ð1� xÞ�0:143

Correlationobtained by usingFreon® 141x is quality

Nu ¼ �hDk‘

Bo ¼ q00h‘vG

G—mass flux (kg/s m2)

Melting Melting in a rectangularcavity

Nu ¼ ð2sÞ�1=2

þ ½c1Ra1=4 � ð2sÞ�1=2�� ½1þðc2Ra3=4s3=2Þn�1=n

c1 ¼ 0:35; c2 ¼ 0:175

Nusselt number isfunction of time

Nu ¼�hH

k

Ra ¼ gbDTH3

mas ¼ SteFo

Fo ¼ a‘ tH2

Solidification Solidification around ahorizontal tube

Nu ¼ 0:52Ra1=4 D is transientequivalent outerdiameter of the

solid Ra� 109

Nu ¼�hD

k

Ra ¼ gbDTD3

ma

Sublimation Nux ¼ 0:458Re1=2x Pr1=3

Shx ¼ 0:459Re1=2x Sc1=3

Uniform heat fluxsurface

Rex\5� 105

Nux ¼ hx

k

Shx ¼ hmx

D

Appendix D: Convective Heat Transfer Correlations 811

Index

AAblation, 283–286, 315, 316, 660Accumulative distribution, 626, 627, 681Activation energy, 325, 338, 661, 790Adhesion, 284, 405Adiabatic tube, sublimation, 329, 333Adiabatic wall evaporation, 154Adsorption, 203, 204, 207Anisotropic materials, 17, 25Annular condensation heat transfer, 411Annular-dispersed flow, 543, 564Annular flow, 3–7, 185, 388, 409, 540, 541, 562–567,

584, 589, 601, 610, 611Archimedes number, 303, 381, 382, 645, 646Area-averaged homogeneous model, 169, 170, 173Area-averaged models, 168Arrhenius equation, 661Atmospheric reduced pressure (APCVD), 338Average kinetic energy, 145Avogadro’s number, 79, 82, 145Axisymmetric film condensation, 597

BBarrel reactors, 338Bernard cellular flow, 197, 198Binary diffusion coefficients, 788, 789Binary solidification, 292Binary vapor mixtures, 326, 356, 357, 372, 374Bingham plastic fluids, 668Biot number, 199, 200, 270, 289, 349Boilers, 569Boiling, 4, 6, 11, 18, 26, 62, 67, 68, 87, 91, 199, 344, 357,

373, 415, 469–473, 487–489, 492, 493, 499–501,506–511, 515, 519, 521, 529–531, 535, 569 –573,578–581, 583, 600, 603, 608–613, 689, 714–716,718–720, 807

Boiling point line, 357Boltzmann constant, 133, 670, 747Boltzmann equation, 12, 145Boltzmann statistical averaging, xiiiBounds on two-phase flow, 554Boussinesq assumption, 112Brinkman’s equation, 691, 695–697Bubble detachment, 472

Bubble dynamics, 469, 497Bubble-free bed expansion, 648Bubble growth, 1, 87, 469, 475, 478, 480–489, 491, 493,

497, 500, 528, 573, 576, 584Bubble lift-off, 573, 575, 577, 578Bubble point line, 357Bubbling fluidization, 648, 682Bubbly flow, 4, 6, 7, 539, 563, 564, 569, 584, 585, 610Buckingham’s theorem, 233, 319, 530, 668Burnout point, 472

CCaloric, 8Capillary action, 617, 703Capillary depression, 205, 366, 367, 369Capillary phenomenon, 205, 589Capillary pressure, 84, 190, 192, 193, 204, 206, 207, 209,

210, 226, 246, 491, 603, 608, 609, 701, 702, 709,712, 714, 728

Carbon dioxide, 9, 52, 59, 135, 502, 791Centrifugal field via rotating disk, 413CFD, 680CFD-DEM, 680Chemical equilibrium, 39, 45, 53–56Chemical reactions, 52, 53, 106, 119, 186, 325, 337, 338,

341, 415, 649, 706, 712Chemical reaction sublimation, 325, 333, 334Chemical stability, 50, 51Chemical Vapor Deposition (CVD), 120, 324, 325, 337–

344Chimney effect, 427, 432Churn flow, 539–542Clapeyron equation, 39, 60, 62, 63, 91, 366, 474, 495Clausius-Clapeyron equation, 12, 63, 91, 480, 594, 717Cohesion, 147Cohesive force, 639–641Collisions, 11, 33, 144, 145, 623, 630, 633, 638, 644, 680Combustion, 3, 7, 8, 52, 53, 56, 96, 133–138, 140, 184,

189, 333, 334, 336, 417, 660Combustors, 7Completely wetting, 203Condensation, 4, 7, 11, 18, 26, 66–68, 76, 79, 83, 85, 88,

92, 129–131, 210, 212, 214, 224, 225, 231, 236,248–250, 323, 355–360, 366, 368, 369, 371–373,


813

https://doi.org/10.1007/978-3-030-22137-9

814 Index

376, 378, 379, 381, 383–385, 387, 388, 391, 392,396–398, 403, 405, 407–411, 440, 459, 469, 483,514, 530, 535, 541, 544, 547, 550, 562–566, 573,583–590, 592, 595–597, 617, 623, 689, 701, 704,708, 724, 727, 730, 743, 807

Condensers, 231, 372, 562Conduction-controlled melting, 309Contact angles, 190, 202–204, 207, 223, 246, 405, 475,

488, 507, 575Contact melting, 27–30, 259, 298–300, 303Continuous size distributions, 627Continuum flow, 30Continuum regime, 12, 13Continuum surface force (CSF) model, 240, 241Convection-controlled melting, 319, 732Convective cooling, 289, 405, 408, 590Convective heat transfer coefficient, 17, 24, 27, 35, 36,

151, 199, 245, 261, 268, 290, 315, 323, 395, 406,463, 465, 516, 595, 599, 643, 651, 652

Convective heat transfer correlation, 184, 471, 500, 501Convective mass transfer, 20, 24, 26, 27Conversion factors, 748Cool evaporation, 421Coordination number, 631–633, 636, 637, 681Couette flow, 13, 120, 181Counter-current condensation, 248Coupling factor, 643, 671–673Creep flow, 111Crispation number, 199, 201Critical droplet radius, 361Critical Heat Flux (CHF), 503, 504, 506, 509, 581, 582,

603, 612, 613Critical Helmholtz velocity, 504, 505Critical velocity for turbulent fluidization, 650Cryopreservation, 732Cumulative distribution function, 629Cyclic dryout, 610Cylindrical coordinate systems, 286

DDamping coefficient, 633–636Damping functions, 430Darcian velocity, 728Darcy’s law, 689–691, 695–697, 704, 721, 722, 725, 728,

732, 733, 735, 740, 741Deformation tensor, 211Dense phase conveying system, 654, 660, 683Dense Suspension Up-flow (DSU), 650Deposition, 4, 5, 11, 323, 324, 337, 338, 340, 346, 347,

349, 350, 506, 639Dew point, 37, 133, 136, 356–358, 371Dew point line, 357Diffusion coefficients, 220Diffusive mass fluxes, 24Dilute phase conveying system, 654Dilute Pneumatic Conveying (DPC), 650Dimensional analysis, 26, 28, 36, 233, 319, 504, 526,

527, 530, 572, 589

Dimensionless numbers, 26, 199, 387, 388, 807Direct contact condensation, 323Direct contact evaporation, 418–421, 456Direct Methanol Fuel Cells (DMFCs), 205Direct numerical simulation, 519Discrete Element Method (DEM), 630, 633, 635, 636,

680Discrete number frequency, 625, 626, 628, 681Discrete particles, 4, 176, 623Discrete size distributions, 624Disjoining pressure, 40, 80, 81, 83, 84, 127, 190,

206–210, 213, 219, 226, 227, 234, 249, 251, 495,590, 593

Dispersed bubble flow, 543Dispersed flow, 33, 623, 624, 638Dispersed phases, 4, 7, 30, 164, 177Dispersion forces, 74Distribution functions, 145, 273, 274, 287, 315, 370, 405,

628, 629, 637, 638, 681Disturbance amplification, 236Disturbance wavelength, 230Dittus-Boelter/McAdams equation, 565, 579Drag coefficient, 148, 149, 184, 490, 639, 640, 642, 682Drag force, 161, 165, 489, 490, 512, 574–577, 624, 639,

641, 642, 661, 662, 677Drift velocity, 164, 165Dropwise condensation, 355, 359, 360, 366–368, 370,

371, 405Dune flow, 653Dynamic behaviors of interface, 227, 661Dynamic viscosity, 14, 376, 676, 689, 691, 703

EEffective thermal conductivity, 140, 671, 674, 676, 677,

699, 707, 712, 737EHD-induced flow, 573EHD number, 572Electro-Discharge Machining (EDM), 603, 608Electronics cooling, 1, 585Electrophoretic force, 572Elongated bubbles, 610Embryo droplets, 88, 363Emissive power, 18, 19Energy flux, conversion factor, 159, 335, 440, 748Enthalpy Method, 259, 304, 308, 319Equations of state, 67, 91Equilibrium, 34, 39–43, 46, 49–51, 53–57, 60, 62–70,

74–80, 84–86, 89–91, 161, 164, 165, 169, 189,190, 193, 195, 196, 201–204, 206–208, 216, 224,253, 293, 355, 357, 358, 360, 362–367, 369, 374,405, 420, 421, 435, 473–475, 484, 598, 672, 682,688, 698, 699, 701, 703, 707, 716, 732, 736

Equilibrium bubble radius, 77Equilibrium criteria, 39, 40, 42, 46, 65Equilibrium radius, 359, 361, 363–366Equivalent diameter, 624, 682Equivalent heat capacity method, 259, 304, 309Ergun equation, 645

Eulerian approach, 95, 96, 176, 238Eulerian averaging, 140, 141, 144Evaporating film, 226, 445Evaporation, 4, 5, 10, 11, 18, 34, 35, 76, 79, 140, 153,

161, 182, 184, 185, 199, 207, 212, 214–216, 219,221, 223–225, 231, 236, 247–249, 251, 325, 383,409, 415–421, 425–428, 430, 431, 433, 434,436–438, 440, 442, 445, 448–450, 452–454,456–463, 465, 466, 469, 473, 476, 477, 483, 489,494, 498–500, 503, 511, 521, 524–528, 535, 544,547, 550, 603, 608–610, 614, 617, 623, 680, 701,703, 704, 714, 718, 739, 807

Extrinsic average velocity, 688, 694Extrinsic phase average, 142

FFalling film evaporation, 438, 441, 442, 452, 465, 807Fick’s law, 22–25, 35, 118, 215Fictitious density, 385Film boiling, 5, 186, 469, 470, 472, 484, 503, 507–512,

514–520, 529, 530, 603, 689, 715, 719–722, 807Film condensation, 4, 5, 26, 95, 360, 377, 382–384,

388–390, 397, 402, 404, 406, 407, 409, 566, 567,589, 590, 597, 723, 724

Film evaporation, 4, 6, 7, 83, 95, 210, 417, 421, 431,463–465

Film evaporators, 415, 427, 438Film thickness, 132, 182, 186, 206–208, 226, 227, 233,

234, 236, 248, 249, 251, 303, 325, 352, 367, 372,378, 379, 386–388, 391, 392, 407–411, 439,443–445, 449, 477, 495, 517, 524, 525, 529, 530,590, 591, 595–597, 610, 723, 726, 727, 807

Filmwise condensation, 355, 359, 360, 366, 367, 370,371, 592

Fixed melting, 298, 299Flat miniature evaporator, 601Flow boiling, 569, 573, 579, 601, 608, 610, 611, 613, 615Flow condensation, 372, 564, 565, 588Flow evaporation, 325, 521, 601Flow maps, 540, 541, 543, 544, 665Flow pattern regime map for slurry flow, 665Flow patterns, 470, 535, 536, 539, 542, 544, 554, 559,

562, 563, 569, 584, 589, 610, 648, 653, 663, 676Flow regimes, 2, 3, 12, 177, 234, 390, 535, 536, 539–541,

543, 544, 562–564, 566, 569, 571, 573, 578, 584,586, 587, 611, 649, 667

Fluidization, 3, 645, 648–651, 683, 743Fluidized bed, 7, 623, 624, 644–652, 682, 683, 743Fluid-particle flow, 638Fluid-particle interactions, 624Fluxes, 21–25, 35, 128, 133, 189, 213, 214, 224, 260,

341, 376, 402, 404, 506, 541, 601, 603, 606, 609,676, 728

Forced convection, 18, 26, 27, 36, 368, 402, 423, 460,469, 470, 473, 500, 515, 565, 569, 573, 606, 807

Forced convective boiling, 4, 469, 544, 569, 571, 573,582

Forced convective condensation, 403, 535

Forchheimer inertia coefficient, 737Fourier’s law, 1, 16, 25, 130, 180, 213, 260, 366, 370,

379, 386, 690, 699, 712Free convection, 18, 219, 469, 470, 498, 515, 807Free energy approach, 49, 51Free liquid surface curvature, 193Free molecular flow regime, 12Free surfaces, numerical simulation, 127Freezing, 5, 6, 268, 269, 291, 292, 297, 316, 318, 323,

732Frequency function, 625–627, 681Frictional, 179, 181, 550–553, 559, 590, 592, 603, 617,

633, 634, 657, 660, 667, 693–695Frictional coefficient, 37, 181Frictional factor, 552, 659, 660Frictional pressure drop, 550, 558, 658Frictional pressure gradients, 551, 556, 557Front tracking methods, 519Froude number, 26, 36, 581, 587, 654, 656, 660Fuel burning rate, 138, 139Fuel cell, 187, 205, 706, 742

GGas Diffusion Layers (GDLs), 706–708, 742Gas dynamic model, 352, 633Gas-particle systems, 624, 644Gaussian error function, 224Generalized Fick equation, 24Generalized Maxwell-Stefan Equations, 25, 35Gibbs-Duhem equation, 83, 208Gibbs free energy, 42, 44, 45, 50, 51, 54, 55, 61, 62, 64,

73, 76, 78, 91, 92, 361, 362, 364, 365Gibbs phase rule, 65Gran-Hertz-History, 640Granular flow, 3, 177, 623Grashof numbers, 26, 36, 319, 521, 530, 573, 720Gravity-dominated condensation, 724, 727Griffith’s correlation, 371

HHamaker constant, 82, 635, 636, 682Heat pipes, 1, 11, 12, 37, 80, 83, 198, 207, 388, 472, 530,

583, 603, 606, 687, 692, 714, 715, 741, 744Heat sinks, 606, 676Heaviside function, 243, 520Hedstrom number, 669Helium properties, 754, 776, 790Helmholtz free energy, 41, 42, 44, 45, 49, 54, 71, 75, 92,

477Helmholtz instability, 504Henry’s constant, 217Heterogeneous bubble growth, 483Heterogeneous condensation, 355, 356Heterogeneous evaporation, 418, 420, 438Heterogeneous flow, 664, 665Heterogeneous nucleation, 68, 355, 473Heterogeneous reaction, 120

Index 815

Holdup void fraction, 169, 536Homogeneous bubble growth, 87, 478Homogeneous condensation, 356Homogeneous flow, 177, 538, 545, 551, 610, 653, 664Homogeneous flow model, 545, 616Homogeneous fluidization, 648Homogeneous model, 143, 144, 158, 160, 164, 165, 167,

173, 184, 185, 544–547, 550, 551, 559, 561, 614,664

Homogeneous nucleation, 68, 88, 89, 355, 473, 479, 484,486, 487

Homogeneous reacting systems, 119Horizontal film evaporation, 421Horizontal reactors, 338Horizontal two-phase flow, 230, 542–544Hot evaporation, 420, 421Hot gas evaporation, 417–419, 456, 459, 460, 466Hot wall tubular LPCVD reactors, 338Hydrophobic materials, 205Hydrostatic pressure gradient, 385Hydrotransport, 177, 663Hyperbolic function, 127

IImmiscible fluids, 166Inclined microchannel evaporation, 3, 259Indirect contact condensation, 603Injection velocity, 327Inorganic compounds, solubility, 794Integral formulation, 99, 127Integral solution, 259, 271, 273–277, 281, 286, 294, 297,

298, 315, 316, 318, 352Interactive force, 147–149, 184, 187Interfaces, 1, 2, 4, 7, 80, 95, 96, 98–100, 107, 148, 151,

153, 159, 168, 189, 190, 193, 201, 203, 209, 228,242, 243, 258, 312, 351, 355, 357, 358, 360, 362,366–370, 373, 376, 380, 386, 394–396, 399, 404,407, 408, 471, 514, 535, 536, 564, 737

Interface shapes at equilibrium, 193Interface tracking, 7, 95, 223Interface velocity, 244, 263Interfacial phenomena, 189, 190, 236, 700, 702Interfacial resistance, 224, 226, 249, 357, 367, 590, 594,

684Interfacial temperature, 207, 210, 216, 226, 293, 323,

349, 404, 420, 421, 430, 592, 595Interfacial tension gradients, 190, 196, 203, 204, 487Interfacial velocity, 130, 143, 213, 242, 244, 264, 323,

478, 519Intermolecular forces, 70, 191, 203, 206Internal energy, 41, 44–48, 51, 52, 54, 56, 57, 69, 71, 72,

91, 92, 102, 104, 114, 131, 170, 179, 361, 743,799

Interphase forces, 159Interphase phase-change energy, 159Intrinsic phase average, 142, 154, 691, 705Isothermal compatibility, 184

Isotropic materials, 17, 25

JJakob number, 26, 398, 424, 425, 458, 461, 481, 482,

488, 530, 576, 578, 726, 727Joule, heat concept, 8, 9Jump conditions, 1, 2, 7, 95, 96, 107, 127, 168, 209, 247,

248, 519

KKapitza number, 26, 232, 448, 449Kapitza resistance, 674Kattan-Thome-Favrat flow pattern, 571Kelvin equation, 209, 226, 249Kelvin-Helmholtz instability, 228, 230Kinetic energy, 26, 130, 145, 170, 213, 672Kinetic theory, 12, 20, 23, 88, 133, 224Kucherov-Rikenglaz equation, 225Kutateladze correlation, 406

LLagrangian approach, 95, 96, 237, 238, 241, 242, 680Lagrangian averaging, 140, 144Lagrangian interface tracking technique, 236Laminar condensate flow, 15, 385, 440, 494, 512Laminar falling film, 448Laminar film condensation, 359, 372–374, 377, 379, 380,

384, 385, 396, 398, 407, 408, 411, 448Laplace operator, 165, 801Laplace-Young equation, 75–78, 473, 478, 590, 604, 608Laser Chemical Vapor Deposition (LCVD), 325, 338,

346– 348, 351Laser drilling, 257Latent heat, 1, 2, 8, 10, 11, 13, 26, 27, 35, 62, 91, 130,

140, 184, 213, 225, 240, 244, 257, 259, 260, 264,269, 277, 295, 303, 305, 309, 312, 315, 317, 319,323–325, 329, 330, 334–336, 351, 366, 371, 376,379, 381, 383, 384, 387, 397, 408, 418–421, 425,427, 430, 434, 445, 454, 456, 457, 460, 471, 478,510, 518, 530, 676, 678, 679, 703, 704, 712, 732,738

Lattice Boltzmann Equation (LBE), 12Lattice Boltzmann method (LBM), 12Leibniz’s rule, 108Leidenfrost drops, 523, 528Leidenfrost effect, 521Leidenfrost phenomena, 470Lennard-Jones potential, 133Leverett function, 709, 712Lewis number, 137, 333–335Limiting viscosity, 668, 683, 684Liquid droplets, 3, 6, 7, 40, 136, 148, 149, 161, 184, 245,

356, 360, 367, 369, 370, 405, 417, 484, 540, 603Liquid fuel droplets, 136–140, 184, 466Liquid jet, 4, 5, 418, 460, 461, 465

816 Index

Index 817

Liquid microlayer, 206Liquid-particle systems, 3, 663Liquid slugs, 610, 617Liquid-solid particle flow, 623Liquid-solid transport in ducts, 624Liquid-vapor flow patterns, 196, 470, 535, 536, 543, 559,

569, 617Liquid-vapor interface, 74, 83, 91, 133, 134, 137, 138,

183, 190, 191, 196, 197, 201, 204, 206, 208–210,212, 226, 227, 245–248, 255, 355, 357, 360, 368,369, 371, 374–376, 378, 379, 381, 385, 386, 391,395, 398–404, 407, 408, 411, 415, 417, 430, 438,439, 443, 472, 475, 477–480, 495, 496, 503, 504,510–513, 518–520, 530, 559, 563, 571, 590–595,597, 605, 617, 714, 715, 721, 722

Liquid-vapor meniscus, 246, 249, 603, 717Lockhart-Martinelli correlations, 553Lower bound, 554, 561Low pressure chemical vapor deposition (LPCVD), 338Lumped capacitance model, 643

MMacroscopic (integral) formulation, 96, 98Marangoni effect, 196–199, 210, 592Marangoni number, 199, 201, 245Mass-averaged velocity, 21, 22, 106, 123, 124, 158, 160,

165Mass species equation, 16, 215, 247Mass transfer, 1, 2, 4, 8, 13, 20, 24, 25, 27, 96, 105, 118,

123, 134, 144, 146, 153, 166, 189, 199, 208,214–218, 223, 228, 232, 236, 252, 324, 325,328–330, 333, 346, 347, 352, 366, 368, 398–400,404, 419, 423, 424, 426, 434, 438, 457, 459, 463,466, 486, 535, 536, 624, 639, 660, 669, 676, 689,698, 700, 701, 714, 718, 807

Maxwell equations, 347Maxwell relations, 44Maxwell-Stefan diffusivity, 347Mean-field potential energy, 81Mean film thickness, 232, 233, 381Mean free time, 638Mean number diameter, 628Mechanical energy balance equation, 113Mechanical stability, 48, 50, 67, 85, 86Melting, 4–7, 10, 11, 18, 27, 28, 37, 91, 95, 183, 218,

246, 257 –262, 264–266, 268, 270, 271, 274, 275,277–281, 284, 286–288, 298–300, 303–306, 309,312–319, 323, 472, 639, 661, 676, 677, 689,732–738, 764, 807

Meniscus, 204, 207, 219, 223, 246, 249, 251, 253, 596,603, 605, 716, 717

Metastable equilibrium, 66, 67, 77, 484Microchannel, 11, 12, 187, 251, 597–599, 610, 669, 673,

674, 743, 807Microchannel heat exchangers, 672, 743Micro-Electro-Mechanical Systems (MEMS), 11, 187,

585

Microfilm region, 207Micrometer-scale particle packing, 633Microscopic (differential) formulation, 96Miniature heat sinks, 601, 606Miniature/micro channels, 12, 205, 207, 249, 250, 252,

535, 565, 583–585, 587–590, 601, 606, 608, 609,614, 617, 807

Minimum bubbling velocity, 649Minimum contact angle, 476Minimum equilibrium size, 366Minimum fluidization velocity, 645–649, 651, 682Minimum slugging velocity, 649Mixture model, 144, 164–168, 176, 177, 186Molar-averaged velocity, 21, 118Molar fluxes, 376Molar fraction, 15, 20, 21, 23, 63, 64, 118, 197, 376, 708Molecular Dynamic Simulation (MDS), 145Molecular statistical averaging, 140, 144Momentum production rate, 159Momentum response time, 32, 33, 165, 638Morton number, 233Moving boundary problem, 258Multicomponent PCM, 258, 312Multi-fluid models, 145, 158, 545, 638, 639Multiphase flows, 2, 7, 164, 177Multiphase Mixture Model (MMM), 689, 701, 709–713Multiphase mixtures, 31, 32, 158, 159, 169, 689, 701Multiphase systems, 1, 2, 4, 5, 7, 13, 26, 56, 95, 96, 143,

805Mush zone, 257, 258, 293–289, 309, 310, 318

NNanoencapsulated Phase Change Material (NEPCM),

675–680Nanoscale, 127Naphthalene sublimation, 324Natural convection, 18, 26, 36, 112, 223, 258, 261, 262,

266, 277, 290–292, 295, 299, 304, 313–315, 340,346, 348, 352, 427, 469, 471, 499, 714, 732, 734,737–739

Navier-Stokes equation, 11, 12, 572Net surface reaction rate, 341Neumann problem, 270Neumann stability criterion, 308Newton-Raphson/secant method, 13Newton’s law of viscosity, 14, 25, 111, 667Noncondensable gas, 368, 377, 398–404, 411, 420, 473,

475Nonequilibrium Molecular Dynamics (NEMD), 672Nonspherical particle, 624, 681Nonwetting, 203, 355, 356, 506, 523Normal contact force, 634, 635, 640Nucleate boiling, 77, 415, 469–473, 475, 484, 489, 493,

497–501, 503, 504, 506–510, 529, 569, 578–581,597, 600, 603, 611, 612, 714, 715, 718

Nucleate site density, 492

818 Index

Nucleation, 6, 66, 68, 85, 87–89, 355, 360, 361, 367, 469,471, 473, 475–477, 483, 484, 486, 489, 492, 493,497, 500, 508, 521, 526, 573, 600, 611, 715, 716

Number-averaged particle diameter, 626, 681Number density, 81, 82, 88, 370, 492, 493, 499, 661Numerical simulation, 190, 214, 259, 319, 334, 347, 427,

469, 493, 630, 660Numerical solution, 214, 262, 289, 308, 312, 314, 319,

347, 485, 520, 526, 595, 597, 729Nusselt evaporation, 418Nusselt number, 17, 26, 27, 151, 181, 182, 318, 328, 332,

333, 350, 351, 377, 379, 380, 382, 388, 394, 396,423, 446–448, 459, 500, 515, 516, 518, 567, 568,588, 599, 672, 727, 730, 734, 807

OOhm’s law, 572One-region problem, 257, 265, 274, 275, 315OpenFOAM, 662Oscillating Heat Pipes (OHP), 671

PPacked bed, 297, 653, 664, 719, 720, 740, 807Packing density, 630–633, 681Partial Differential Equations (PDEs), 96, 127Partially wetting, 203Particle number density, 144, 637Particulate fluidization, 7Partition coefficient, 219Peclet number, 26, 30, 349, 488, 677Permeability, 688–690, 692, 693, 695, 703, 708, 719,

724, 728, 730, 737, 740, 741, 792Phase Change Materials (PCMs), 284, 293, 295, 319, 732,

764Phase diagrams, 218, 219, 292, 358Phase interface fitted grid, 237, 241Phases, 1–5, 7, 9, 31, 39, 56–58, 60–62, 65, 68, 70,

74–76, 78, 83, 91, 95, 96, 98–101, 103, 107,127–129, 141, 142, 144–155, 158–160, 164–169,173, 176, 177, 183–185, 189, 193, 194, 197, 201,203, 208, 212–215, 218, 228, 230, 236–243, 257,259–262, 266, 270, 271, 277, 280, 295, 304, 305,311, 314, 315, 317, 319, 324, 357, 358, 420, 431,474, 478, 495, 513, 529, 535–538, 541, 542, 544,545, 547–549, 551, 556–559, 566, 568, 580, 593,601, 623, 639, 699–703, 705–707, 709, 711–713,721, 725, 728, 735, 736

Physical constants, 747Physical Vapor Deposition (PVD), 324Pigment, 660, 661Planck’s constant, 18Plug flow, 5, 539, 543, 563Pneumatic conveying system, 649, 653, 654Pneumatic transport, 3, 177, 623, 624, 653, 654Poisson’s ratio, 634–636

Polyatomic gas, 344Pool boiling, 4, 230, 469, 470, 472, 473, 477, 483, 493,

498, 504, 506–511, 528, 529, 573, 579, 597, 598,715, 719, 807

Porosity, 636, 637, 681, 682, 687, 689–693, 695, 699,703, 705, 712, 719, 724, 727, 731

Porous media, 204, 259, 312, 359, 406, 470, 653, 671,687, 689–693, 695, 698–701, 703, 709, 712, 714,718–721, 723, 727, 728, 732, 735, 736, 740, 743

Porous media boiling, 470, 714, 718, 721Power, 1, 3, 289, 348, 349, 351, 498, 528, 530, 550, 668,

674, 675, 684, 748Power law equation, 498Prandtl number, 26, 152, 290, 291, 393, 395, 412, 424,

430, 446, 448, 451, 565, 576, 581, 753–757Precursors, 325, 337–340, 343, 351Preheating duration, 279Pressure drop, 1, 179, 411, 412, 415, 524, 535, 540,

544–546, 550, 552–556, 558, 570, 573, 587, 589,597, 601, 606, 614, 616, 644, 653, 657–659, 667,668, 675, 703–705

Pressure gradients, 24, 25, 161, 422, 544, 554, 604, 609,689

Proton Exchange Membrane Fuel Cell (PEMFC), 706Puddle thickness, 523, 524Pulsating Heat Pipes (PHP), 5, 251, 617Pulverized coal, 623, 624, 642, 646, 660, 682, 683Pure substance, 4, 56, 58, 60, 66, 86, 115, 180, 197

QQuality, 32, 148, 184, 187, 243, 356, 538, 540, 541, 543,

545, 547, 556, 562, 563, 568, 579, 588, 609, 611,612, 614–616, 807

RRadiation, 16, 18, 19, 102, 315, 352, 456, 472, 514, 516,

518, 529, 530, 643, 644, 706Raindrop algorithm, 623, 630Random packing, 629, 630, 682Rarefied vapor self-diffusion model, 96Rayleigh number, 26, 292, 572, 730, 734, 739Rayleigh-Taylor instability, 228, 523, 718Reference frame velocity, 340Reference velocity, 116Relative (slip) velocity, 164Response times, 32Rizk’s correlation, 654, 655, 657Rohsenow’s correlation, 488, 500, 501Rolling friction coefficient, 635, 636, 641Rotational energy, 18Runge-Kutta method, 253, 331, 729

SSaltation flow, 664

Index 819

Saltation velocity, 653–657, 683Saturated boiling, 469, 470, 506, 576Saturation pressure, 13, 63, 76–78, 84, 91, 92, 187, 216,

226, 357, 371, 420, 425, 434, 474, 580, 594, 595,609, 702, 708, 717

Saturation temperature, 63, 66–68, 85, 91, 130, 136, 137,140, 207, 249, 250, 355–357, 366, 367, 369, 371,378, 379, 383, 386, 397, 399, 404, 407, 408, 411,415, 418, 420–422, 425, 426, 438, 449, 455–457,460, 465, 469, 474–476, 482, 498, 507, 513, 521,562, 569, 572, 579, 598, 615, 702, 703, 718,721–725, 743

Scale analysis, 2, 26–28, 30, 36, 37, 263, 274, 302, 453,455, 530

Scaling, 2, 27, 30, 524, 690Scanning velocity, 348, 349Schmidt number, 26, 403, 424, 425, 430, 463, 791Sedimentation, 3, 166, 177, 623Selective Area Laser Deposition (SALD), 339, 346, 351Selective Laser Sintering (SLS), 630, 633, 682Self-assembly, 624, 680, 681Self-diffusion coefficient, 133Self-diffusion equation, 133Sensible heat, 9, 10, 26, 27, 35, 263, 264, 301, 309, 314,

315, 335, 336, 351, 427Separated flow model, 166–168, 173, 174, 177, 545, 547,

549, 550, 559Settling velocity, 641, 664–666, 683Sherwood number, 24, 27, 328, 332, 333, 350, 351, 424Size distribution of particles, 623, 624, 681Sliding friction coefficient, 634, 636Slip flow regime, 12Slip ratio, 2, 537, 538, 550, 558–560, 567, 614Sludge layer, 3, 623Slug flow, 3, 460, 540, 543, 564, 584, 648, 649, 653, 654,

660Slurry flow, 3, 7, 623, 663–666, 677Smooth-surface model, 418, 715Solidification, 4–7, 10, 11, 18, 27, 95, 183, 218, 257–

259, 261, 262, 264, 265, 268, 270, 271, 274, 286,288–298, 304, 309, 312–314, 318, 319, 639, 689,732, 735, 737, 807

Solid-liquid interface, 29, 183, 201, 203, 257–264, 266,268, 271, 275–277, 280–284, 288–293, 304, 305,307, 310, 311, 313–315, 362, 591, 595, 733, 738,739

Solid-liquid phase change, 4, 257–260, 262, 263, 286,292, 293, 295, 304, 310, 312, 735, 737

Solid loading, 3, 654, 659Solid-vapor phase change, 4Species equation, 118, 124, 153, 156, 162, 215, 220, 331,

700, 706, 710, 711, 713Specific heats, 9, 219, 310, 374, 422, 432Spherical coordinate system, 466, 478, 802Sphericity, 642, 645, 646, 682Stability, 1, 39, 40, 46, 55, 56, 86, 87, 198, 199, 227, 235,

308, 510, 606, 630Stable equilibrium, 46, 66, 86, 362

Stagnant vapor reservoir, 372, 382Standard deviation, 626, 628, 629, 633, 650, 681Standard reference state, 135Stationary grid approach, 237Stefan-Boltzmann constant, 19, 516, 747Stefan-Maxwell equation, 347Stefan number, 27, 263, 264, 266, 270, 276, 277, 301Sticking coefficient, 341, 347, 348Stokes drag force, 690Stokes flow, 682, 690Stokes number, 3, 27, 33, 176, 177Stratified flow, 168, 543, 563–565, 567, 584, 610, 614Stratified wavy flow, 543, 567Stream functions, 327, 423, 529, 725, 733Stress-strain rate relationships, 15Stress tensors, 14, 101, 110, 111, 116, 159, 210, 213, 340,

691Strong numerical solution, 304Subcooled boiling, 469, 470, 516, 530, 569, 573, 578,

597Subcooling, 280, 283, 285, 286, 378–381, 386, 387, 407,

408, 410, 503, 506, 515, 590, 591, 609, 723, 726,729

Subeutectic concentration, 293Sublimation, 4, 5, 11, 215, 216, 323–327, 329, 333–336,

349–351, 639, 807Supereutectic concentration, 293Superficial velocity, 31, 500, 537, 538, 587, 614, 645,

648, 649, 654, 683Superheat, 40, 66, 68, 85–89, 292, 297, 323, 381, 415,

421, 453, 461, 473, 475–478, 484–486, 488, 492,597, 598, 600, 603, 611, 715, 716, 718, 723

Superheated liquids, 85, 87Supersaturation, 79, 80, 92, 421Surface excess, 70Surface pressure, 203Surface roughness, 208, 501, 503, 506, 551, 667Surface tension, 26, 27, 40, 70–74, 77, 92, 102, 127, 168,

183, 185, 189, 190, 193, 196–198, 201–205, 207,209, 210, 213, 219, 221, 229, 234, 240–242, 244,245, 249, 250, 254, 358, 360–362, 366, 430, 448,478, 480, 483, 488–490, 495, 523, 530, 557, 574,575, 577, 584, 587, 590, 592, 595, 601, 603, 608,617, 703, 724, 727, 731, 732

Surface waves, 240, 427, 429

TTaitel-Dukler flow map, 556, 569Tangential contact force, 634, 635Taylor series, 47, 364Temperature-transforming model, 259, 304, 310–312Tensors, 114, 116, 804, 805Terminal velocity, 641–643, 646, 647, 650, 651,

655–657, 665, 666, 682Thermal energy, 8, 9, 16, 52, 72, 114, 150, 259, 264, 277,

286, 289, 303, 312, 313, 317, 351, 409, 472, 546,651, 732

820 Index

Thermal expansion coefficient, 36Thermal penetration depth, 27, 28, 272–275, 279,

281–283, 315Thermal radiation, 18Thermal resistances, 366, 367, 405, 456Thermal stability, 47–50Thermodynamic equilibrium, 1, 39, 40, 56, 65, 83, 85,

119, 293, 429, 711, 712Thermodynamic laws, 1, 40, 41, 52, 73Thermodynamic limit of superheat, 68, 86, 87Thermodynamic pressure, 14Thermodynamic relations, 115Thermodynamic surfaces, xiiiThermophysical properties, 1, 120, 300, 343, 417, 456,

460, 515, 556, 651, 669, 676Thermosyphon, 396, 410, 416, 464, 587Thin liquid films, 80, 381, 421, 443Todes’ correlation, 652Transfer driving force, 335, 336Transitional velocities, 666Transition boiling, 469, 470, 472, 507–511, 529, 720Transition regime, 12, 472, 508Transport velocity for fast fluidization, 650Tube, external heating, sublimation, 325, 329, 332, 333,

350, 470, 501, 514, 528Turbulence modeling, 127Turbulent condensate flow, 390Turbulent falling film, 452Turbulent film condensation, 359, 383, 390, 391, 406Turbulent film regime, 382Turbulent fluidization, 648, 649Two-component flows, 4Two-fluid model, 144, 173, 547Two-phase flow, 26, 37, 174, 250, 255, 470, 535–548,

550–553, 556–558, 560, 561, 563, 565, 569 –573,583, 584, 586, 587, 589, 597, 601, 608, 610, 613,614, 623, 624, 703, 743

Two-phase flow patterns, 584Two-phase single-component systems, 56Two-region problem, 257, 270, 278, 294, 735

UUltra-thin liquid films, 80, 190, 206Unstable equilibrium, 66, 87, 365, 366Upper bound, 555, 561Urethane-based paint, 660

VVan der Waals equation, 58–60, 67, 68, 86, 87, 90–92Van der Waals limit, 87Vapor bubbles, 4–6, 75, 77, 148, 199, 356, 415, 421, 469,

471, 473, 484, 493, 504, 510, 528, 539, 569, 578,587, 603, 613, 623, 648, 714, 718

Vapor deposition, 324, 325, 337, 346Vaporization, 11, 13, 35, 62, 66, 85, 88, 91, 213, 236,

283, 366, 371, 376, 383, 384, 397, 418, 421, 422,427, 430, 445, 460, 465, 478, 521, 530, 569, 573,703, 714, 718

Vapor pressure, 76, 78, 79, 81, 83, 84, 86, 89, 92, 132,156, 190, 204, 206–208, 216, 217, 223, 226, 253,420, 460, 464, 474, 475, 491, 594, 595, 597, 603,608, 716, 717

Vectors, 17, 109, 128, 446, 634, 799, 801, 802, 804, 805Verlet method, 635Vertical falling film evaporation, 418, 427Vertical reactors, 338Vibrational energy, 18Viscous dissipation, 26, 114, 116–118, 120, 123, 130,

134, 170, 180, 181, 185, 186, 240, 244, 340, 422,432, 698

Voidage, 645, 646, 649, 650, 652, 657, 682, 683Void fraction, 2, 31, 535–538, 545, 547, 550, 558–563,

566, 567, 569, 614–617, 687, 743Volume average, 142, 143, 145, 691, 695, 696, 723, 724Volume-averaged multifluid models, 145Volume-averaged velocity, 688, 693, 703, 704Volume-average pressure, 691Volume-averaging model, 185Volume flow rate, 614, 748Volume fractions, 30, 31, 166, 167, 177, 238, 675, 678,

679, 702Volume of Fluid (VOF) method , 168, 238, 239, 241, 242,

519Volumetric averaging, 141Volumetric condensation rate, 707, 708Volumetric heat generation rate, 706

WWall superheat, 464, 473, 475, 492, 600, 715Water droplets, 153, 160, 465, 521, 525Wave equation, 127Wave velocity, 233, 235Wavy condensate regime, 381Wavy film analysis, 446Wavy flows, 381, 443Weber number, 27, 430, 560, 601, 608, 609, 611, 613Wetting, 190, 193, 202–204, 207, 208, 355, 356, 503,

504, 508, 709Wicked surfaces, 715, 718Wicks, 687, 692, 714Wispy annular flow, 540

YYield stress, 668, 683, 684Young-Laplace equation, 193, 194, 208, 229, 234Young’s modulus, 634–636

Date post:	25-Nov-2023
Category:	Documents
Upload:	khangminh22
View:	0 times
Download:	0 times

Appendix A: Constants, Units, and Conversion Factors

Documents