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Appendix C
Appendix C
THERMOPHYSICAL PROPERTIES Table C.1 Thermophysical Properties of Pure Water at Atmospheric Pressure T (°C)
ρ (kg/m3)
μ × 103 (kg/m s)
ν × 106 (m2/s)
k (W/m K)
β × 105 (1/K)
cp (J/kg K)
Pr
0 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100
999.84 999.96 999.70 999.10 998.20 997.07 995.65 994.30 992.21 990.22 988.04 983.19 977.76 971.79 965.31 958.35
1.7531 1.5012 1.2995 1.1360 1.0017 0.8904 0.7972 0.7185 0.6517 0.5939 0.5442 0.4631 0.4004 0.3509 0.3113 0.2789
1.7533 1.5013 1.2999 1.1370 1.0035 0.8930 0.8007 0.7228 0.6565 0.5997 0.5507 0.4710 0.4095 0.3611 0.3225 0.2911
0.5687 0.5780 0.5869 0.5953 0.6034 0.6110 0.6182 0.6251 0.6351 0.6376 0.6432 0.6535 0.6623 0.6698 0.6759 0.6807
6.8140 1.5980 8.7900 15.073 20.661 20.570 30.314 34.571 38.530 42.260 45.780 52.330 58.400 64.130 69.620 75.000
4209.3 4201.0 4194.1 4188.5 4184.1 4180.9 4178.8 4177.7 4177.6 4178.3 4179.7 4184.8 4192.0 4200.1 4210.7 4221.0
12.976 10.911 9.2860 7.9910 6.9460 6.0930 5.3880 4.8020 4.3090 3.8920 3.5350 2.9650 2.5340 2.2010 1.9390 1.7290
Source: Kukulka, D.J., 1981. Thermodynamic and Transport Properties of Pure and Saline Water (M.Sc. thesis). State University of New York at Buffalo.
373
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Appendix C
Table C.2 Thermophysical Properties of Air at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950
1.7458 1.3947 1.1614 0.9950 0.8711 0.7740 0.6964 0.6329 0.5804 0.5356 0.4975 0.4643 0.4354 0.4097 0.3868 0.3666
1.007 1.006 1.007 1.009 1.014 1.021 1.030 1.040 1.051 1.063 1.075 1.087 1.099 1.110 1.121 1.131
132.5 159.6 184.6 208.2 230.1 250.7 270.1 288.4 305.8 322.5 338.8 354.6 369.8 384.3 398.1 411.3
7.59 11.44 15.89 20.92 26.41 32.39 38.79 45.57 52.69 60.21 68.10 76.37 84.93 93.80 102.90 112.20
18.10 22.30 26.30 30.00 33.80 37.30 40.70 43.90 46.90 49.70 52.40 54.90 57.30 59.60 62.00 64.30
10.30 15.90 22.50 29.90 38.30 47.20 56.70 66.70 76.90 87.30 98.00 109.00 120.00 131.00 143.00 155.00
0.737 0.720 0.707 0.700 0.690 0.686 0.684 0.683 0.685 0.690 0.695 0.702 0.709 0.716 0.720 0.723
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; and Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.3 Thermophysical Properties of Ammonia (NH3) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
300 320 340 360 380 400 420 440 460 480 500 520 540 560 580
0.6994 0.6468 0.6059 0.5716 0.5410 0.5136 0.4888 0.4664 0.4460 0.4273 0.4101 0.3942 0.3795 0.3708 0.3533
2.158 2.170 2.192 2.221 2.254 2.287 2.322 2.357 2.393 2.430 2.467 2.504 2.540 2.577 2.613
101.5 109.0 116.5 124.0 131.0 138.0 145.0 152.5 159.0 166.5 173.0 180.0 186.5 193.5 199.5
14.70 16.90 19.20 21.70 24.20 26.90 29.70 32.70 35.70 39.00 42.20 45.70 49.10 52.00 56.50
24.70 27.20 29.30 31.60 34.00 37.00 40.40 43.50 46.30 49.20 52.50 54.50 57.50 60.60 63.68
16.66 19.40 22.10 24.90 27.90 31.50 35.60 39.60 43.40 47.40 51.90 55.20 59.70 63.40 69.10
0.887 0.870 0.872 0.870 0.869 0.853 0.833 0.826 0.822 0.822 0.813 0.827 0.824 0.827 0.817
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Appendix C
Table C.4 Thermophysical Properties of Carbon Dioxide (CO2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
280 300 320 340 360 380 400 450 500 550 600 650 700 750 800
1.9022 1.7730 1.6609 1.5618 1.4743 1.3961 1.3257 1.1782 1.0594 0.9625 0.8826 0.8143 0.7564 0.7057 0.6614
0.830 0.851 0.872 0.891 0.908 0.926 0.942 0.981 1.020 1.050 1.080 1.100 1.130 1.150 1.170
140.0 149.0 156.0 165.0 173.0 181.0 190.0 210.0 231.0 251.0 270.0 288.0 305.0 321.0 337.0
7.36 8.40 9.39 10.60 11.70 13.00 14.30 17.80 21.80 26.10 30.60 35.40 40.30 45.50 51.00
15.20 16.55 18.05 19.70 21.20 22.75 24.30 28.20 32.50 36.60 40.70 44.50 48.10 51.70 55.10
9.63 11.00 12.50 14.20 15.80 17.60 19.50 24.50 30.10 36.20 42.70 49.70 56.30 63.70 71.20
0.765 0.766 0.754 0.746 0.741 0.737 0.737 0.728 0.725 0.721 0.717 0.712 0.717 0.714 0.716
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.5 Thermophysical Properties of Hydrogen (H2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
100 150 200 250 300 350 400 450 500 550 600 700 800 900
0.2425 0.1615 0.1211 0.0969 0.0808 0.0692 0.0606 0.0538 0.0485 0.0440 0.0404 0.0346 0.0303 0.0269
11.23 12.60 13.54 14.06 14.31 14.43 14.48 14.50 14.52 14.53 14.55 14.61 14.70 14.83
42.1 56.0 68.1 78.9 89.6 98.8 108.2 117.2 126.4 134.3 142.4 157.8 172.4 186.5
17.40 34.70 56.20 81.40 111.00 143.00 179.00 218.00 261.00 305.00 352.00 456.00 569.00 692.00
67.00 101.00 131.00 157.00 183.00 204.00 226.00 247.00 266.00 285.00 305.00 342.00 378.00 412.00
24.60 49.60 79.90 115.00 158.00 204.00 258.00 316.00 378.00 445.00 519.00 676.00 849.00 1030.00
0.707 0.699 0.704 0.707 0.701 0.700 0.695 0.689 0.691 0.685 0.678 0.675 0.670 0.671
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
375
376
Appendix C
Table C.6 Thermophysical Properties of Oxygen (O2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
100 150 200 250 300 350 400 450 500 550 600 700 800 900
3.9450 2.5850 1.9300 1.5420 1.2840 1.1000 0.9620 0.8554 0.7698 0.6998 0.6414 0.5498 0.4810 0.4275
0.962 0.921 0.915 0.915 0.920 0.929 0.942 0.956 0.972 0.988 1.003 1.031 1.054 1.074
76.4 114.8 147.5 178.6 207.2 233.5 258.2 281.4 303.3 324.0 343.7 380.8 415.2 447.2
1.94 4.44 7.64 11.58 16.14 21.23 26.84 32.90 39.40 46.30 53.59 69.26 86.32 104.60
9.25 13.80 18.30 22.60 26.80 29.60 33.00 36.30 41.20 44.10 47.30 52.80 58.90 64.90
2.44 5.80 10.40 16.00 22.70 29.00 36.40 44.40 55.10 63.80 73.50 93.10 116.00 141.00
0.796 0.766 0.737 0.723 0.711 0.733 0.737 0.741 0.716 0.726 0.729 0.744 0.743 0.740
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.7 Thermophysical Properties of Water Vapor (Steam) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
380 400 450 500 550 600 650 700 750 800 850
0.5863 0.5542 0.4902 0.4405 0.4005 0.3652 0.3380 0.3140 0.2931 0.2739 0.2579
2.060 2.014 1.980 1.985 1.997 2.026 2.056 2.085 2.119 2.152 2.186
127.1 134.4 152.5 170.4 188.4 206.7 224.7 242.6 260.4 278.6 296.9
21.68 24.25 31.11 38.68 47.04 56.60 66.48 77.26 88.84 101.70 115.10
24.60 26.10 29.90 33.90 37.90 42.20 46.40 50.50 54.90 59.20 63.70
20.40 23.40 30.80 38.80 47.40 57.00 66.80 77.10 88.40 100.00 113.00
1.060 1.040 1.010 0.998 0.993 0.993 0.996 1.000 1.000 1.010 1.020
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Appendix C
Table C.8 Thermophysical Properties of Some Solid Materials Composition
T (K)
ρ (kg/m3)
k (W/m K)
cp (J/kg K)
Aluminum Asphalt Bakelite Brass (70% Cu + 30% Zn) Carborundum Chrome brick
273-673 300 300 373-573 872 473 823 478 478 922 273-373 300 300 300 273-373 273-873 300
2720 2115 1300 8520 – 3010 – – 2645 – 8670 1460 1350 2300 8920 8950 80
204-250 0.0662 1.4 104-147 18.5 2.3 2.5 0.25 1.0 1.5 26.0 1.3 0.26 1.4 22-26 385-350 0.06
895 920 1465 380 – 835 – – 960 – 340 880 1260 880 420 380 1300
300 300 253 273 273-1273 273-1273 273-573 300 273-573 273-573 273-1273 273-673 300 300 273-1273
2500 2225 – 920 7260 7850 – 998 1750 13,400 10,220 8900 930 900 21,400
1.4 1.4 2.03 1.88 52-35 59-35 – 0.159 171-157 8-10 125-99 93-59 0.18 0.24 70-75
750 835 1945 2040 420 460 – – 1010 125 251 450 1340 2890 240
300 300 300
2630 2320 2680
2.79 2.15 2.80
775 810 830
300
1100
0.13
2010
Diatomaceous silica, fired Fire clay brick Bronze (75% Cu + 25% Sn) Clay Coal (anthracite) Concrete (stone mix) Constantan (60% Cu + 40% Ni) Copper Cotton Glass Plate (soda lime) Pyrex Ice Iron (C 4% cast) Iron (C 0.5% wrought) Lead Leather (sole) Magnesium Mercury Molybdenum Nickel Paper Paraffin Platinum Rock Granite, Barre Limestone, Salem Marble, Halston Rubber, vulcanized Soft
Continued
377
378
Appendix C
Table C.8 Thermophysical Properties of Some Solid Materials Continued Composition
T (K)
ρ (kg/m3)
k (W/m K)
cp (J/kg K)
Sandstone, Berea Hard Sand Silver Soil Steel (C 1%) Steel (Cr 1%) Steel (18% Cr + 8% Ni) Snow Teflon Tin Tissue, human Skin Fat layer (adipose) Muscle Tungsten Wood, cross grain Fir Oak Yellow pine White pine Wood, radial Fir Oak Zinc
300 300 300 273-673 300 273-1273 273-1273 273-1273 273 300 273-473
2150 1190 1515 10,520 2050 7800 7860 7810 110 2200 7300
2.90 0.16 0.27 410-360 0.52 43-28 62-33 16-26 0.049 0.35 65-57
745 – 800 230 1840 470 460 460 – – 230
300 300 300 273-1273
– – – 19,350
0.37 0.2 0.41 166-76
– – – 130
300 300 300 300
415 545 640 435
0.11 0.17 0.15 0.11
2720 2385 2805 –
300 300 273-673
420 545 7140
0.14 0.19 112-93
2720 2385 380
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Incropera, F.P., DeWitt, D.P., 1998. Fundamentals of Heat and Mass Transfer. Wiley, New York.
THERMOPHYSICAL PROPERTIES Table C.1 Thermophysical Properties of Pure Water at Atmospheric Pressure T (°C)
ρ (kg/m3)
μ × 103 (kg/m s)
ν × 106 (m2/s)
k (W/m K)
β × 105 (1/K)
cp (J/kg K)
Pr
0 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100
999.84 999.96 999.70 999.10 998.20 997.07 995.65 994.30 992.21 990.22 988.04 983.19 977.76 971.79 965.31 958.35
1.7531 1.5012 1.2995 1.1360 1.0017 0.8904 0.7972 0.7185 0.6517 0.5939 0.5442 0.4631 0.4004 0.3509 0.3113 0.2789
1.7533 1.5013 1.2999 1.1370 1.0035 0.8930 0.8007 0.7228 0.6565 0.5997 0.5507 0.4710 0.4095 0.3611 0.3225 0.2911
0.5687 0.5780 0.5869 0.5953 0.6034 0.6110 0.6182 0.6251 0.6351 0.6376 0.6432 0.6535 0.6623 0.6698 0.6759 0.6807
6.8140 1.5980 8.7900 15.073 20.661 20.570 30.314 34.571 38.530 42.260 45.780 52.330 58.400 64.130 69.620 75.000
4209.3 4201.0 4194.1 4188.5 4184.1 4180.9 4178.8 4177.7 4177.6 4178.3 4179.7 4184.8 4192.0 4200.1 4210.7 4221.0
12.976 10.911 9.2860 7.9910 6.9460 6.0930 5.3880 4.8020 4.3090 3.8920 3.5350 2.9650 2.5340 2.2010 1.9390 1.7290
Source: Kukulka, D.J., 1981. Thermodynamic and Transport Properties of Pure and Saline Water (M.Sc. thesis). State University of New York at Buffalo.
373
374
Appendix C
Table C.2 Thermophysical Properties of Air at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950
1.7458 1.3947 1.1614 0.9950 0.8711 0.7740 0.6964 0.6329 0.5804 0.5356 0.4975 0.4643 0.4354 0.4097 0.3868 0.3666
1.007 1.006 1.007 1.009 1.014 1.021 1.030 1.040 1.051 1.063 1.075 1.087 1.099 1.110 1.121 1.131
132.5 159.6 184.6 208.2 230.1 250.7 270.1 288.4 305.8 322.5 338.8 354.6 369.8 384.3 398.1 411.3
7.59 11.44 15.89 20.92 26.41 32.39 38.79 45.57 52.69 60.21 68.10 76.37 84.93 93.80 102.90 112.20
18.10 22.30 26.30 30.00 33.80 37.30 40.70 43.90 46.90 49.70 52.40 54.90 57.30 59.60 62.00 64.30
10.30 15.90 22.50 29.90 38.30 47.20 56.70 66.70 76.90 87.30 98.00 109.00 120.00 131.00 143.00 155.00
0.737 0.720 0.707 0.700 0.690 0.686 0.684 0.683 0.685 0.690 0.695 0.702 0.709 0.716 0.720 0.723
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; and Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.3 Thermophysical Properties of Ammonia (NH3) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
300 320 340 360 380 400 420 440 460 480 500 520 540 560 580
0.6994 0.6468 0.6059 0.5716 0.5410 0.5136 0.4888 0.4664 0.4460 0.4273 0.4101 0.3942 0.3795 0.3708 0.3533
2.158 2.170 2.192 2.221 2.254 2.287 2.322 2.357 2.393 2.430 2.467 2.504 2.540 2.577 2.613
101.5 109.0 116.5 124.0 131.0 138.0 145.0 152.5 159.0 166.5 173.0 180.0 186.5 193.5 199.5
14.70 16.90 19.20 21.70 24.20 26.90 29.70 32.70 35.70 39.00 42.20 45.70 49.10 52.00 56.50
24.70 27.20 29.30 31.60 34.00 37.00 40.40 43.50 46.30 49.20 52.50 54.50 57.50 60.60 63.68
16.66 19.40 22.10 24.90 27.90 31.50 35.60 39.60 43.40 47.40 51.90 55.20 59.70 63.40 69.10
0.887 0.870 0.872 0.870 0.869 0.853 0.833 0.826 0.822 0.822 0.813 0.827 0.824 0.827 0.817
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Appendix C
Table C.4 Thermophysical Properties of Carbon Dioxide (CO2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
280 300 320 340 360 380 400 450 500 550 600 650 700 750 800
1.9022 1.7730 1.6609 1.5618 1.4743 1.3961 1.3257 1.1782 1.0594 0.9625 0.8826 0.8143 0.7564 0.7057 0.6614
0.830 0.851 0.872 0.891 0.908 0.926 0.942 0.981 1.020 1.050 1.080 1.100 1.130 1.150 1.170
140.0 149.0 156.0 165.0 173.0 181.0 190.0 210.0 231.0 251.0 270.0 288.0 305.0 321.0 337.0
7.36 8.40 9.39 10.60 11.70 13.00 14.30 17.80 21.80 26.10 30.60 35.40 40.30 45.50 51.00
15.20 16.55 18.05 19.70 21.20 22.75 24.30 28.20 32.50 36.60 40.70 44.50 48.10 51.70 55.10
9.63 11.00 12.50 14.20 15.80 17.60 19.50 24.50 30.10 36.20 42.70 49.70 56.30 63.70 71.20
0.765 0.766 0.754 0.746 0.741 0.737 0.737 0.728 0.725 0.721 0.717 0.712 0.717 0.714 0.716
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.5 Thermophysical Properties of Hydrogen (H2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
100 150 200 250 300 350 400 450 500 550 600 700 800 900
0.2425 0.1615 0.1211 0.0969 0.0808 0.0692 0.0606 0.0538 0.0485 0.0440 0.0404 0.0346 0.0303 0.0269
11.23 12.60 13.54 14.06 14.31 14.43 14.48 14.50 14.52 14.53 14.55 14.61 14.70 14.83
42.1 56.0 68.1 78.9 89.6 98.8 108.2 117.2 126.4 134.3 142.4 157.8 172.4 186.5
17.40 34.70 56.20 81.40 111.00 143.00 179.00 218.00 261.00 305.00 352.00 456.00 569.00 692.00
67.00 101.00 131.00 157.00 183.00 204.00 226.00 247.00 266.00 285.00 305.00 342.00 378.00 412.00
24.60 49.60 79.90 115.00 158.00 204.00 258.00 316.00 378.00 445.00 519.00 676.00 849.00 1030.00
0.707 0.699 0.704 0.707 0.701 0.700 0.695 0.689 0.691 0.685 0.678 0.675 0.670 0.671
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
375
376
Appendix C
Table C.6 Thermophysical Properties of Oxygen (O2) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
100 150 200 250 300 350 400 450 500 550 600 700 800 900
3.9450 2.5850 1.9300 1.5420 1.2840 1.1000 0.9620 0.8554 0.7698 0.6998 0.6414 0.5498 0.4810 0.4275
0.962 0.921 0.915 0.915 0.920 0.929 0.942 0.956 0.972 0.988 1.003 1.031 1.054 1.074
76.4 114.8 147.5 178.6 207.2 233.5 258.2 281.4 303.3 324.0 343.7 380.8 415.2 447.2
1.94 4.44 7.64 11.58 16.14 21.23 26.84 32.90 39.40 46.30 53.59 69.26 86.32 104.60
9.25 13.80 18.30 22.60 26.80 29.60 33.00 36.30 41.20 44.10 47.30 52.80 58.90 64.90
2.44 5.80 10.40 16.00 22.70 29.00 36.40 44.40 55.10 63.80 73.50 93.10 116.00 141.00
0.796 0.766 0.737 0.723 0.711 0.733 0.737 0.741 0.716 0.726 0.729 0.744 0.743 0.740
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Table C.7 Thermophysical Properties of Water Vapor (Steam) Gas at Atmospheric Pressure T (K)
ρ (kg/m3)
cp (J/kg K)
μ × 107 (kg/m s)
ν × 106 (m2/s)
k × 103 (W/m K)
a × 106 (m2/s)
Pr
380 400 450 500 550 600 650 700 750 800 850
0.5863 0.5542 0.4902 0.4405 0.4005 0.3652 0.3380 0.3140 0.2931 0.2739 0.2579
2.060 2.014 1.980 1.985 1.997 2.026 2.056 2.085 2.119 2.152 2.186
127.1 134.4 152.5 170.4 188.4 206.7 224.7 242.6 260.4 278.6 296.9
21.68 24.25 31.11 38.68 47.04 56.60 66.48 77.26 88.84 101.70 115.10
24.60 26.10 29.90 33.90 37.90 42.20 46.40 50.50 54.90 59.20 63.70
20.40 23.40 30.80 38.80 47.40 57.00 66.80 77.10 88.40 100.00 113.00
1.060 1.040 1.010 0.998 0.993 0.993 0.996 1.000 1.000 1.010 1.020
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Borgnakke, C., Sonntag, R.E., 1997. Thermodynamic and Transport Properties. Wiley, New York.
Appendix C
Table C.8 Thermophysical Properties of Some Solid Materials Composition
T (K)
ρ (kg/m3)
k (W/m K)
cp (J/kg K)
Aluminum Asphalt Bakelite Brass (70% Cu + 30% Zn) Carborundum Chrome brick
273-673 300 300 373-573 872 473 823 478 478 922 273-373 300 300 300 273-373 273-873 300
2720 2115 1300 8520 – 3010 – – 2645 – 8670 1460 1350 2300 8920 8950 80
204-250 0.0662 1.4 104-147 18.5 2.3 2.5 0.25 1.0 1.5 26.0 1.3 0.26 1.4 22-26 385-350 0.06
895 920 1465 380 – 835 – – 960 – 340 880 1260 880 420 380 1300
300 300 253 273 273-1273 273-1273 273-573 300 273-573 273-573 273-1273 273-673 300 300 273-1273
2500 2225 – 920 7260 7850 – 998 1750 13,400 10,220 8900 930 900 21,400
1.4 1.4 2.03 1.88 52-35 59-35 – 0.159 171-157 8-10 125-99 93-59 0.18 0.24 70-75
750 835 1945 2040 420 460 – – 1010 125 251 450 1340 2890 240
300 300 300
2630 2320 2680
2.79 2.15 2.80
775 810 830
300
1100
0.13
2010
Diatomaceous silica, fired Fire clay brick Bronze (75% Cu + 25% Sn) Clay Coal (anthracite) Concrete (stone mix) Constantan (60% Cu + 40% Ni) Copper Cotton Glass Plate (soda lime) Pyrex Ice Iron (C 4% cast) Iron (C 0.5% wrought) Lead Leather (sole) Magnesium Mercury Molybdenum Nickel Paper Paraffin Platinum Rock Granite, Barre Limestone, Salem Marble, Halston Rubber, vulcanized Soft
Continued
377
378
Appendix C
Table C.8 Thermophysical Properties of Some Solid Materials Continued Composition
T (K)
ρ (kg/m3)
k (W/m K)
cp (J/kg K)
Sandstone, Berea Hard Sand Silver Soil Steel (C 1%) Steel (Cr 1%) Steel (18% Cr + 8% Ni) Snow Teflon Tin Tissue, human Skin Fat layer (adipose) Muscle Tungsten Wood, cross grain Fir Oak Yellow pine White pine Wood, radial Fir Oak Zinc
300 300 300 273-673 300 273-1273 273-1273 273-1273 273 300 273-473
2150 1190 1515 10,520 2050 7800 7860 7810 110 2200 7300
2.90 0.16 0.27 410-360 0.52 43-28 62-33 16-26 0.049 0.35 65-57
745 – 800 230 1840 470 460 460 – – 230
300 300 300 273-1273
– – – 19,350
0.37 0.2 0.41 166-76
– – – 130
300 300 300 300
415 545 640 435
0.11 0.17 0.15 0.11
2720 2385 2805 –
300 300 273-673
420 545 7140
0.14 0.19 112-93
2720 2385 380
Source: Dincer, I., 1997. Heat Transfer in Food Cooling Applications. Taylor & Francis, Washington, DC; Incropera, F.P., DeWitt, D.P., 1998. Fundamentals of Heat and Mass Transfer. Wiley, New York.