CHEN 2311 Heat Transfer
FORMULA LISTS
Q̇ cond = kA
ΔT
L
Q̇ = ṁcp ∆T
𝑄̇ = 𝑈𝐴𝑎 ∆𝑇𝑙𝑚
Q̇ conv = hA(T∞ − TS )
∆𝑇𝑙𝑚 =
4
Q̇ rad = εσA(Tsurr
− TS4 )
q̇ =
Q̇
A
∆𝑇1 − ∆𝑇2
∆𝑇
ln ( 1⁄∆𝑇 )
2
Stefan − Boltzmann Constant, σ
= 5.67 × 10−8 W⁄m2 ∙ K 4
where the constant Cfilm = 0.62 for horizontal cylinders and
0.67 for spheres.
Tf = (Tsat + Ts )⁄2
5
CHEN 2311 Heat Transfer
CD =
FD
1
ρV 2 A
2
Re =
Tf =
VD
ν
Ts + T∞
2
Nu =
hL
k
6
CHEN 2311 Heat Transfer
Fully develop flow
Developing laminar flow in entrance region (Ts
constant)
Fully develop turbulent with smooth surface
Reciprocity rule
Summation Rule
Superposition Rule
7
542
NATURAL CONVECTION
TABLE 9–1
Empirical correlations for the average Nusselt number for natural convection over surfaces
Characteristic
length Lc
Geometry
Vertical plate
Ts
L
L
Range of Ra
Nu
104–109
1010–1013
Nu 5 0.59Ra1/4
L
Nu 5 0.1Ra1/3
L
Entire range
Nu 5 e 0.825 1
(9–19)
(9–20)
0.387Ra 1/6
L
[1 1 (0.492/Pr)
2
9/16 8/27
]
f
(9–21)
(complex but more accurate)
Inclined plate
Use vertical plate equations for the upper
surface of a cold plate and the lower
surface of a hot plate
L
L
u
Replace g by g cosu
Horizontal plate
(Surface area A and perimeter p)
(a) Upper surface of a hot plate
(or lower surface of a cold plate)
for
0 , u , 608
104–107
107–1011
Nu 5 0.59Ra1/4
L
Nu 5 0.1Ra1/3
L
(9–22)
(9–23)
105–1011
Nu 5 0.27Ra1/4
L
(9–24)
Ts
Hot surface
A s /p
(b) Lower surface of a hot plate
(or upper surface of a cold plate)
Ts
Hot surface
A vertical cylinder can be treated as a
vertical plate when
Ts
Vertical cylinder
L
L
D$
Horizontal cylinder
D
Ts
35L
Gr1/4
L
RaD # 1012
Nu 5 e 0.6 1
RaD # 1011
Nu 5 2 1
0.387Ra1/6
D
[1 1 (0.559/Pr)9/16] 8/27
2
f
(9–25)
D
Sphere
D
D
0.589Ra1/4
D
[1 1 (0.469/Pr)9/16] 4/9
(9–26)
(Pr $ 0.7)
8
773
CHAPTER 13
1.0
0.9
0.8
0.7
0.6
0.5
`
L2
L1
A2
D
0.4
R
A1
oL
ati
10 5
43
/D
2
1
1.5
1 0.9
0.8
0.7
0.6
0.5
0.3
0.2
`
10
0.4
F1→2
0.1
0.09
0.08
0.07
0.06
0.05
0.3
0.25
0.2
0.18
0.16
0.14
0.12
0.5
0.4
0.3
0.04
0.03
0.1
0.2
0.02
0.1
0.01
0.1
0.2
0.3
0.4 0.5 0.6 0.8 1
2
3
4
5 6
8
10
20
A2
L2
W
A1
Asymptote
Ratio L2/D
L1
0.1
0.15
0.2
0.4
FIGURE 13–5
View factor between two aligned
parallel rectangles of equal size.
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3
1 /W
0.3
Ra
tio
L
F1→2
0.2
0.5
0.1
4
5
6
8
10
20
1
2
0
0.1
5
10
0.2
0.3 0.4 0.5 0.6
0.8 1
2
Ratio L2/W
3
4
5 6
8
10
20
FIGURE 13–6
View factor between two perpendicular
rectangles with a common edge.
9
774
RADIATION HEAT TRANSFER
1.0
0.9
r2
r2 /L = 8
6
2
5
4
0.8
r1
3
0.7
L
1
2
1.5
0.6
1.25
F1→2 0.5
1.0
0.4
0.3
0.8
0.2
0.6
0.5
0.4
0.1
FIGURE 13–7
View factor between two coaxial
parallel disks.
0
0.1
0.2
0.3 0.4
0.6
1.0
L /r1
r2/L = 0.3
2
3
4
5 6
8 10
1.0
A2
L
r1
0.8
r2
A1
1.0
0.9
`
0.6
=
0.8
L/
r2
F2→1
2
0.7
L/
r2
0.6
5
1
0.4
0.
F2→2 0.5
0.
25
1
0.5
0.25
0.1
0.2
0.4
0.6
r1/r2
`
0.3
0.2
0
=
2
0.4
0.
1
0.2
4
0.8
1.0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
r1/r2
FIGURE 13–8
View factors for two concentric cylinders of finite length: (a) outer cylinder to inner cylinder; (b) outer cylinder to itself.
10
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878
APPENDIX 1
TABLE A–9
Properties of saturated water
Temp.
T, ⬚C
0.01
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
220
240
260
280
300
320
340
360
374.14
Saturation
Pressure
Psat, kPa
0.6113
0.8721
1.2276
1.7051
2.339
3.169
4.246
5.628
7.384
9.593
12.35
15.76
19.94
25.03
31.19
38.58
47.39
57.83
70.14
84.55
101.33
143.27
198.53
270.1
361.3
475.8
617.8
791.7
1,002.1
1,254.4
1,553.8
2,318
3,344
4,688
6,412
8,581
11,274
14,586
18,651
22,090
Density
r, kg/m3
Enthalpy
of
Vaporization
Specific
Heat
cp, J/kg·K
Thermal
Conductivity
k, W/m·K
Liquid
Vapor
hfg, kJ/kg
Liquid
Vapor
999.8
0.0048
999.9
0.0068
999.7
0.0094
999.1
0.0128
998.0
0.0173
997.0
0.0231
996.0
0.0304
994.0
0.0397
992.1
0.0512
990.1
0.0655
988.1
0.0831
985.2
0.1045
983.3
0.1304
980.4
0.1614
977.5
0.1983
974.7
0.2421
971.8
0.2935
968.1
0.3536
965.3
0.4235
961.5
0.5045
957.9
0.5978
950.6
0.8263
943.4
1.121
934.6
1.496
921.7
1.965
916.6
2.546
907.4
3.256
897.7
4.119
887.3
5.153
876.4
6.388
864.3
7.852
840.3 11.60
813.7 16.73
783.7 23.69
750.8 33.15
713.8 46.15
667.1 64.57
610.5 92.62
528.3 144.0
317.0 317.0
2501
2490
2478
2466
2454
2442
2431
2419
2407
2395
2383
2371
2359
2346
2334
2321
2309
2296
2283
2270
2257
2230
2203
2174
2145
2114
2083
2050
2015
1979
1941
1859
1767
1663
1544
1405
1239
1028
720
0
4217
4205
4194
4185
4182
4180
4178
4178
4179
4180
4181
4183
4185
4187
4190
4193
4197
4201
4206
4212
4217
4229
4244
4263
4286
4311
4340
4370
4410
4460
4500
4610
4760
4970
5280
5750
6540
8240
14,690
—
1854
1857
1862
1863
1867
1870
1875
1880
1885
1892
1900
1908
1916
1926
1936
1948
1962
1977
1993
2010
2029
2071
2120
2177
2244
2314
2420
2490
2590
2710
2840
3110
3520
4070
4835
5980
7900
11,870
25,800
—
Liquid
Vapor
0.561 0.0171
0.571 0.0173
0.580 0.0176
0.589 0.0179
0.598 0.0182
0.607 0.0186
0.615 0.0189
0.623 0.0192
0.631 0.0196
0.637 0.0200
0.644 0.0204
0.649 0.0208
0.654 0.0212
0.659 0.0216
0.663 0.0221
0.667 0.0225
0.670 0.0230
0.673 0.0235
0.675 0.0240
0.677 0.0246
0.679 0.0251
0.682 0.0262
0.683 0.0275
0.684 0.0288
0.683 0.0301
0.682 0.0316
0.680 0.0331
0.677 0.0347
0.673 0.0364
0.669 0.0382
0.663 0.0401
0.650 0.0442
0.632 0.0487
0.609 0.0540
0.581 0.0605
0.548 0.0695
0.509 0.0836
0.469 0.110
0.427 0.178
—
—
Dynamic Viscosity
m, kg/m·s
Prandtl
Number
Pr
Volume
Expansion
Coefficient
b, 1/K
Liquid
Vapor
Liquid
Vapor
1.792 ⫻ 10⫺3
1.519 ⫻ 10⫺3
1.307 ⫻ 10⫺3
1.138 ⫻ 10⫺3
1.002 ⫻ 10⫺3
0.891 ⫻ 10⫺3
0.798 ⫻ 10⫺3
0.720 ⫻ 10⫺3
0.653 ⫻ 10⫺3
0.596 ⫻ 10⫺3
0.547 ⫻ 10⫺3
0.504 ⫻ 10⫺3
0.467 ⫻ 10⫺3
0.433 ⫻ 10⫺3
0.404 ⫻ 10⫺3
0.378 ⫻ 10⫺3
0.355 ⫻ 10⫺3
0.333 ⫻ 10⫺3
0.315 ⫻ 10⫺3
0.297 ⫻ 10⫺3
0.282 ⫻ 10⫺3
0.255 ⫻ 10⫺3
0.232 ⫻ 10⫺3
0.213 ⫻ 10⫺3
0.197 ⫻ 10⫺3
0.183 ⫻ 10⫺3
0.170 ⫻ 10⫺3
0.160 ⫻ 10⫺3
0.150 ⫻ 10⫺3
0.142 ⫻ 10⫺3
0.134 ⫻ 10⫺3
0.122 ⫻ 10⫺3
0.111 ⫻ 10⫺3
0.102 ⫻ 10⫺3
0.094 ⫻ 10⫺3
0.086 ⫻ 10⫺3
0.078 ⫻ 10⫺3
0.070 ⫻ 10⫺3
0.060 ⫻ 10⫺3
0.043 ⫻ 10⫺3
0.922 ⫻ 10⫺5
0.934 ⫻ 10⫺5
0.946 ⫻ 10⫺5
0.959 ⫻ 10⫺5
0.973 ⫻ 10⫺5
0.987 ⫻ 10⫺5
1.001 ⫻ 10⫺5
1.016 ⫻ 10⫺5
1.031 ⫻ 10⫺5
1.046 ⫻ 10⫺5
1.062 ⫻ 10⫺5
1.077 ⫻ 10⫺5
1.093 ⫻ 10⫺5
1.110 ⫻ 10⫺5
1.126 ⫻ 10⫺5
1.142 ⫻ 10⫺5
1.159 ⫻ 10⫺5
1.176 ⫻ 10⫺5
1.193 ⫻ 10⫺5
1.210 ⫻ 10⫺5
1.227 ⫻ 10⫺5
1.261 ⫻ 10⫺5
1.296 ⫻ 10⫺5
1.330 ⫻ 10⫺5
1.365 ⫻ 10⫺5
1.399 ⫻ 10⫺5
1.434 ⫻ 10⫺5
1.468 ⫻ 10⫺5
1.502 ⫻ 10⫺5
1.537 ⫻ 10⫺5
1.571 ⫻ 10⫺5
1.641 ⫻ 10⫺5
1.712 ⫻ 10⫺5
1.788 ⫻ 10⫺5
1.870 ⫻ 10⫺5
1.965 ⫻ 10⫺5
2.084 ⫻ 10⫺5
2.255 ⫻ 10⫺5
2.571 ⫻ 10⫺5
4.313 ⫻ 10⫺5
13.5
11.2
9.45
8.09
7.01
6.14
5.42
4.83
4.32
3.91
3.55
3.25
2.99
2.75
2.55
2.38
2.22
2.08
1.96
1.85
1.75
1.58
1.44
1.33
1.24
1.16
1.09
1.03
0.983
0.947
0.910
0.865
0.836
0.832
0.854
0.902
1.00
1.23
2.06
1.00 ⫺0.068 ⫻ 10⫺3
1.00 0.015 ⫻ 10⫺3
1.00 0.733 ⫻ 10⫺3
1.00 0.138 ⫻ 10⫺3
1.00 0.195 ⫻ 10⫺3
1.00 0.247 ⫻ 10⫺3
1.00 0.294 ⫻ 10⫺3
1.00 0.337 ⫻ 10⫺3
1.00 0.377 ⫻ 10⫺3
1.00 0.415 ⫻ 10⫺3
1.00 0.451 ⫻ 10⫺3
1.00 0.484 ⫻ 10⫺3
1.00 0.517 ⫻ 10⫺3
1.00 0.548 ⫻ 10⫺3
1.00 0.578 ⫻ 10⫺3
1.00 0.607 ⫻ 10⫺3
1.00 0.653 ⫻ 10⫺3
1.00 0.670 ⫻ 10⫺3
1.00 0.702 ⫻ 10⫺3
1.00 0.716 ⫻ 10⫺3
1.00 0.750 ⫻ 10⫺3
1.00 0.798 ⫻ 10⫺3
1.00 0.858 ⫻ 10⫺3
1.01 0.913 ⫻ 10⫺3
1.02 0.970 ⫻ 10⫺3
1.02 1.025 ⫻ 10⫺3
1.05 1.145 ⫻ 10⫺3
1.05 1.178 ⫻ 10⫺3
1.07 1.210 ⫻ 10⫺3
1.09 1.280 ⫻ 10⫺3
1.11 1.350 ⫻ 10⫺3
1.15 1.520 ⫻ 10⫺3
1.24 1.720 ⫻ 10⫺3
1.35 2.000 ⫻ 10⫺3
1.49 2.380 ⫻ 10⫺3
1.69 2.950 ⫻ 10⫺3
1.97
2.43
3.73
Liquid
Note 1: Kinematic viscosity n and thermal diffusivity a can be calculated from their definitions, n ⫽ m/r and a ⫽ k/rcp ⫽ n/Pr. The temperatures 0.01⬚C, 100⬚C,
and 374.14⬚C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can be used at
any pressure with negligible error except at temperatures near the critical-point value.
Note 2: The unit kJ/kg·⬚C for specific heat is equivalent to kJ/kg·K, and the unit W/m·⬚C for thermal conductivity is equivalent to W/m·K.
Source: Viscosity and thermal conductivity data are from J. V. Sengers and J. T. R. Watson, Journal of Physical and Chemical Reference Data 15 (1986),
pp. 1291–1322. Other data are obtained from various sources or calculated.
11
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Page 882
882
APPENDIX 1
TABLE A–13
Properties of liquids
Temp.
T, ⬚C
Density
r, kg/m3
Specific
Heat
cp, J/kg·K
Thermal
Conductivity
k, W/m·K
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m·s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
Volume
Expansion
Coeff.
b, 1/K
2.699 ⫻ 10⫺7
2.264 ⫻ 10⫺7
1.942 ⫻ 10⫺7
1.694 ⫻ 10⫺7
1.496 ⫻ 10⫺7
1.331 ⫻ 10⫺7
1.188 ⫻ 10⫺7
1.055 ⫻ 10⫺7
2.126
1.927
1.803
1.738
1.732
1.810
2.063
3.082
0.00352
0.00391
0.00444
0.00520
0.00637
0.00841
0.01282
0.02922
7.429 ⫻ 10⫺7
6.531 ⫻ 10⫺7
5.795 ⫻ 10⫺7
5.185 ⫻ 10⫺7
4.677 ⫻ 10⫺7
4.250 ⫻ 10⫺7
7.414
6.622
5.980
5.453
5.018
4.655
0.00118
0.00120
0.00123
0.00127
0.00132
0.00137
1.360 ⫻ 10⫺6
8.531 ⫻ 10⫺7
5.942 ⫻ 10⫺7
4.420 ⫻ 10⫺7
3.432 ⫻ 10⫺7
2.743 ⫻ 10⫺7
2.233 ⫻ 10⫺7
1.836 ⫻ 10⫺7
1.509 ⫻ 10⫺7
12.65
8.167
6.079
4.963
4.304
3.880
3.582
3.363
3.256
0.00142
0.00150
0.00161
0.00177
0.00199
0.00232
0.00286
0.00385
0.00628
8.219 ⫻ 10⫺3
5.287 ⫻ 10⫺3
3.339 ⫻ 10⫺3
1.970 ⫻ 10⫺3
1.201 ⫻ 10⫺3
7.878 ⫻ 10⫺4
5.232 ⫻ 10⫺4
3.464 ⫻ 10⫺4
2.455 ⫻ 10⫺4
84,101
54,327
34,561
20,570
12,671
8,392
5,631
3,767
2,697
4.242 ⫻ 10⫺3
9.429 ⫻ 10⫺4
2.485 ⫻ 10⫺4
8.565 ⫻ 10⫺5
3.794 ⫻ 10⫺5
2.046 ⫻ 10⫺5
1.241 ⫻ 10⫺5
8.029 ⫻ 10⫺6
6.595 ⫻ 10⫺6
46,636
10,863
2,962
1,080
499.3
279.1
176.3
118.1
98.31
Methane [CH4]
⫺160
⫺150
⫺140
⫺130
⫺120
⫺110
⫺100
⫺90
420.2
405.0
388.8
371.1
351.4
328.8
301.0
261.7
3492
3580
3700
3875
4146
4611
5578
8902
0.1863
0.1703
0.1550
0.1402
0.1258
0.1115
0.0967
0.0797
1.270 ⫻ 10⫺7
1.174 ⫻ 10⫺7
1.077 ⫻ 10⫺7
9.749 ⫻ 10⫺8
8.634 ⫻ 10⫺8
7.356 ⫻ 10⫺8
5.761 ⫻ 10⫺8
3.423 ⫻ 10⫺8
1.133 ⫻ 10⫺4
9.169 ⫻ 10⫺5
7.551 ⫻ 10⫺5
6.288 ⫻ 10⫺5
5.257 ⫻ 10⫺5
4.377 ⫻ 10⫺5
3.577 ⫻ 10⫺5
2.761 ⫻ 10⫺5
Methanol [CH3(OH)]
20
30
40
50
60
70
788.4
779.1
769.6
760.1
750.4
740.4
2515
2577
2644
2718
2798
2885
0.1987
0.1980
0.1972
0.1965
0.1957
0.1950
1.002 ⫻ 10⫺7
9.862 ⫻ 10⫺8
9.690 ⫻ 10⫺8
9.509 ⫻ 10⫺8
9.320 ⫻ 10⫺8
9.128 ⫻ 10⫺8
⫺100
⫺75
⫺50
⫺25
0
25
50
75
100
683.8
659.3
634.3
608.2
580.6
550.7
517.3
478.5
429.6
1881
1970
2069
2180
2306
2455
2640
2896
3361
0.1383
0.1357
0.1283
0.1181
0.1068
0.0956
0.0851
0.0757
0.0669
1.075 ⫻ 10⫺7
1.044 ⫻ 10⫺7
9.773 ⫻ 10⫺8
8.906 ⫻ 10⫺8
7.974 ⫻ 10⫺8
7.069 ⫻ 10⫺8
6.233 ⫻ 10⫺8
5.460 ⫻ 10⫺8
4.634 ⫻ 10⫺8
5.857 ⫻ 10⫺4
5.088 ⫻ 10⫺4
4.460 ⫻ 10⫺4
3.942 ⫻ 10⫺4
3.510 ⫻ 10⫺4
3.146 ⫻ 10⫺4
Isobutane (R600a)
9.305 ⫻ 10⫺4
5.624 ⫻ 10⫺4
3.769 ⫻ 10⫺4
2.688 ⫻ 10⫺4
1.993 ⫻ 10⫺4
1.510 ⫻ 10⫺4
1.155 ⫻ 10⫺4
8.785 ⫻ 10⫺5
6.483 ⫻ 10⫺5
Glycerin
0
5
10
15
20
25
30
35
40
1276
1273
1270
1267
1264
1261
1258
1255
1252
2262
2288
2320
2354
2386
2416
2447
2478
2513
0.2820
0.2835
0.2846
0.2856
0.2860
0.2860
0.2860
0.2860
0.2863
9.773 ⫻ 10
9.732 ⫻ 10⫺8
9.662 ⫻ 10⫺8
9.576 ⫻ 10⫺8
9.484 ⫻ 10⫺8
9.388 ⫻ 10⫺8
9.291 ⫻ 10⫺8
9.195 ⫻ 10⫺8
9.101 ⫻ 10⫺8
0
20
40
60
80
100
120
140
150
899.0
888.1
876.0
863.9
852.0
840.0
828.9
816.8
810.3
1797
1881
1964
2048
2132
2220
2308
2395
2441
0.1469
0.1450
0.1444
0.1404
0.1380
0.1367
0.1347
0.1330
0.1327
9.097 ⫻ 10⫺8
8.680 ⫻ 10⫺8
8.391 ⫻ 10⫺8
7.934 ⫻ 10⫺8
7.599 ⫻ 10⫺8
7.330 ⫻ 10⫺8
7.042 ⫻ 10⫺8
6.798 ⫻ 10⫺8
6.708 ⫻ 10⫺8
⫺8
10.49
6.730
4.241
2.496
1.519
0.9934
0.6582
0.4347
0.3073
Engine Oil (unused)
3.814
0.8374
0.2177
0.07399
0.03232
0.01718
0.01029
0.006558
0.005344
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
0.00070
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Originally based on various sources.
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cen98128_App-A_p865-892.qxd
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Page 884
884
APPENDIX 1
TABLE A–15
Properties of air at 1 atm pressure
Temp.
T, ⬚C
Density
r, kg/m3
Specific
Heat
cp, J/kg·K
Thermal
Conductivity
k, W/m·K
Thermal
Diffusivity
a, m2/s
Dynamic
Viscosity
m, kg/m·s
Kinematic
Viscosity
n, m2/s
Prandtl
Number
Pr
⫺150
⫺100
⫺50
⫺40
⫺30
⫺20
⫺10
0
5
10
15
20
25
30
35
40
45
50
60
70
80
90
100
120
140
160
180
200
250
300
350
400
450
500
600
700
800
900
1000
1500
2000
2.866
2.038
1.582
1.514
1.451
1.394
1.341
1.292
1.269
1.246
1.225
1.204
1.184
1.164
1.145
1.127
1.109
1.092
1.059
1.028
0.9994
0.9718
0.9458
0.8977
0.8542
0.8148
0.7788
0.7459
0.6746
0.6158
0.5664
0.5243
0.4880
0.4565
0.4042
0.3627
0.3289
0.3008
0.2772
0.1990
0.1553
983
966
999
1002
1004
1005
1006
1006
1006
1006
1007
1007
1007
1007
1007
1007
1007
1007
1007
1007
1008
1008
1009
1011
1013
1016
1019
1023
1033
1044
1056
1069
1081
1093
1115
1135
1153
1169
1184
1234
1264
0.01171
0.01582
0.01979
0.02057
0.02134
0.02211
0.02288
0.02364
0.02401
0.02439
0.02476
0.02514
0.02551
0.02588
0.02625
0.02662
0.02699
0.02735
0.02808
0.02881
0.02953
0.03024
0.03095
0.03235
0.03374
0.03511
0.03646
0.03779
0.04104
0.04418
0.04721
0.05015
0.05298
0.05572
0.06093
0.06581
0.07037
0.07465
0.07868
0.09599
0.11113
4.158 ⫻ 10⫺6
8.036 ⫻ 10⫺6
1.252 ⫻ 10⫺5
1.356 ⫻ 10⫺5
1.465 ⫻ 10⫺5
1.578 ⫻ 10⫺5
1.696 ⫻ 10⫺5
1.818 ⫻ 10⫺5
1.880 ⫻ 10⫺5
1.944 ⫻ 10⫺5
2.009 ⫻ 10⫺5
2.074 ⫻ 10⫺5
2.141 ⫻ 10⫺5
2.208 ⫻ 10⫺5
2.277 ⫻ 10⫺5
2.346 ⫻ 10⫺5
2.416 ⫻ 10⫺5
2.487 ⫻ 10⫺5
2.632 ⫻ 10⫺5
2.780 ⫻ 10⫺5
2.931 ⫻ 10⫺5
3.086 ⫻ 10⫺5
3.243 ⫻ 10⫺5
3.565 ⫻ 10⫺5
3.898 ⫻ 10⫺5
4.241 ⫻ 10⫺5
4.593 ⫻ 10⫺5
4.954 ⫻ 10⫺5
5.890 ⫻ 10⫺5
6.871 ⫻ 10⫺5
7.892 ⫻ 10⫺5
8.951 ⫻ 10⫺5
1.004 ⫻ 10⫺4
1.117 ⫻ 10⫺4
1.352 ⫻ 10⫺4
1.598 ⫻ 10⫺4
1.855 ⫻ 10⫺4
2.122 ⫻ 10⫺4
2.398 ⫻ 10⫺4
3.908 ⫻ 10⫺4
5.664 ⫻ 10⫺4
8.636 ⫻ 10⫺6
1.189 ⫻ 10⫺5
1.474 ⫻ 10⫺5
1.527 ⫻ 10⫺5
1.579 ⫻ 10⫺5
1.630 ⫻ 10⫺5
1.680 ⫻ 10⫺5
1.729 ⫻ 10⫺5
1.754 ⫻ 10⫺5
1.778 ⫻ 10⫺5
1.802 ⫻ 10⫺5
1.825 ⫻ 10⫺5
1.849 ⫻ 10⫺5
1.872 ⫻ 10⫺5
1.895 ⫻ 10⫺5
1.918 ⫻ 10⫺5
1.941 ⫻ 10⫺5
1.963 ⫻ 10⫺5
2.008 ⫻ 10⫺5
2.052 ⫻ 10⫺5
2.096 ⫻ 10⫺5
2.139 ⫻ 10⫺5
2.181 ⫻ 10⫺5
2.264 ⫻ 10⫺5
2.345 ⫻ 10⫺5
2.420 ⫻ 10⫺5
2.504 ⫻ 10⫺5
2.577 ⫻ 10⫺5
2.760 ⫻ 10⫺5
2.934 ⫻ 10⫺5
3.101 ⫻ 10⫺5
3.261 ⫻ 10⫺5
3.415 ⫻ 10⫺5
3.563 ⫻ 10⫺5
3.846 ⫻ 10⫺5
4.111 ⫻ 10⫺5
4.362 ⫻ 10⫺5
4.600 ⫻ 10⫺5
4.826 ⫻ 10⫺5
5.817 ⫻ 10⫺5
6.630 ⫻ 10⫺5
3.013 ⫻ 10⫺6
5.837 ⫻ 10⫺6
9.319 ⫻ 10⫺6
1.008 ⫻ 10⫺5
1.087 ⫻ 10⫺5
1.169 ⫻ 10⫺5
1.252 ⫻ 10⫺5
1.338 ⫻ 10⫺5
1.382 ⫻ 10⫺5
1.426 ⫻ 10⫺5
1.470 ⫻ 10⫺5
1.516 ⫻ 10⫺5
1.562 ⫻ 10⫺5
1.608 ⫻ 10⫺5
1.655 ⫻ 10⫺5
1.702 ⫻ 10⫺5
1.750 ⫻ 10⫺5
1.798 ⫻ 10⫺5
1.896 ⫻ 10⫺5
1.995 ⫻ 10⫺5
2.097 ⫻ 10⫺5
2.201 ⫻ 10⫺5
2.306 ⫻ 10⫺5
2.522 ⫻ 10⫺5
2.745 ⫻ 10⫺5
2.975 ⫻ 10⫺5
3.212 ⫻ 10⫺5
3.455 ⫻ 10⫺5
4.091 ⫻ 10⫺5
4.765 ⫻ 10⫺5
5.475 ⫻ 10⫺5
6.219 ⫻ 10⫺5
6.997 ⫻ 10⫺5
7.806 ⫻ 10⫺5
9.515 ⫻ 10⫺5
1.133 ⫻ 10⫺4
1.326 ⫻ 10⫺4
1.529 ⫻ 10⫺4
1.741 ⫻ 10⫺4
2.922 ⫻ 10⫺4
4.270 ⫻ 10⫺4
0.7246
0.7263
0.7440
0.7436
0.7425
0.7408
0.7387
0.7362
0.7350
0.7336
0.7323
0.7309
0.7296
0.7282
0.7268
0.7255
0.7241
0.7228
0.7202
0.7177
0.7154
0.7132
0.7111
0.7073
0.7041
0.7014
0.6992
0.6974
0.6946
0.6935
0.6937
0.6948
0.6965
0.6986
0.7037
0.7092
0.7149
0.7206
0.7260
0.7478
0.7539
Note: For ideal gases, the properties cp, k, m, and Pr are independent of pressure. The properties r, n, and a at a pressure P (in atm) other than 1 atm are
determined by multiplying the values of r at the given temperature by P and by dividing n and a by P.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Keenan, Chao, Keyes, Gas Tables, Wiley, 1984;
and Thermophysical Properties of Matter. Vol. 3: Thermal Conductivity, Y. S. Touloukian, P. E. Liley, S. C. Saxena, Vol. 11: Viscosity, Y. S. Touloukian, S. C.
Saxena, and P. Hestermans, IFI/Plenun, NY, 1970, ISBN 0-306067020-8.
END OF PAPER
13