FORMULA LISTS
Q̇cond = kA
ΔT
L
Q̇ conv = hA(T∞ − TS )
4
Q̇rad = εσA(Tsurr
− TS4 )
Q̇
q̇ =
A
Ts, sphere = T∞ +
ė gen
1 ∂ ∂T
1 ∂T
(r ) +
=
r ∂r ∂r
k
α ∂t
ė gen
1 ∂ 2 ∂T
1 ∂T
(r
)+
=
2
r ∂r
∂r
k
α ∂t
ė gen L
h
𝑇𝑐𝑒𝑛𝑡𝑒𝑟 = 𝑇0 = 𝑇𝑠 + ∆𝑇𝑚𝑎𝑥
ė gen r0
2h
∆𝑇𝑚𝑎𝑥, 𝑝𝑙𝑎𝑛𝑒 𝑤𝑎𝑙𝑙 =
Ts, plane wall = T∞ +
Ts, cylinder = T∞ +
∂2 T ė gen
1 ∂T
+
=
2
∂x
k
α ∂t
ė gen r0
3h
𝑒̇𝑔𝑒𝑛 𝐿2
2𝑘
𝑒̇𝑔𝑒𝑛 𝑟02
∆𝑇𝑚𝑎𝑥, 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =
4𝑘
𝑒̇𝑔𝑒𝑛 𝑟02
∆𝑇𝑚𝑎𝑥, 𝑠𝑝ℎ𝑒𝑟𝑒 =
6𝑘
R wall =
Q̇ =
T∞1 − T∞2
R total
R cyl =
ln(r2 ⁄r1 )
2πLk
R sph =
r2 − r1
4πr1 r2 k
∆T = Q̇R
rcr,cylinder =
rcr,sphere =
k ins
h
2k ins
h
L
kA
R conv =
R rad =
1
hA
1
hrad A
2
)(Ts + Tsurr )
hrad = εσ(Ts2 + Tsurr
Bi =
hLc
< 0.1
k
𝐿𝑐 =
𝑉
𝐴𝑠
𝑇(𝑡) − 𝑇∞
= 𝑒 −𝑏𝑡
𝑇𝑖 − 𝑇∞
𝑏=
ℎ𝐴𝑠
ℎ
=
𝜌𝑐𝑝 𝑉
𝜌𝑐𝑝 𝐿𝑐
𝜏 =
𝛼𝑡
𝑟𝑜 2
𝑄𝑚𝑎𝑥 = 𝑚𝑐𝑝 (𝑇∞ − 𝑇𝑖 )
∑ Q̇ + ė Velement = 0
All sides
Tm−1 − 2Tm + Tm+1 ė m
+
=0
(∆x)2
k
Tleft + Ttop + Tright + Tbottom − 4Tnode +
CD =
FD
1
2
2 ρV A
𝑅𝑒 =
𝑇𝑓 =
𝑉𝐷
𝜈
𝑇𝑠 + 𝑇∞
2
𝑁𝑢 =
ℎ𝐿
𝑘
ė node ∆x∆y
=0
k
251
CHAPTER 4
TABLE 4–2
TABLE 4–3
Coefficients used in the one-term approximate solution of transient onedimensional heat conduction in plane walls, cylinders, and spheres (Bi 5 hL/k
for a plane wall of thickness 2L, and Bi 5 hro /k for a cylinder or sphere of
radius ro )
The zeroth- and first-order Bessel
functions of the first kind
Bi
0.01
0.02
0.04
0.06
0.08
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
20.0
30.0
40.0
50.0
100.0
`
Plane Wall
A1
l1
0.0998
0.1410
0.1987
0.2425
0.2791
0.3111
0.4328
0.5218
0.5932
0.6533
0.7051
0.7506
0.7910
0.8274
0.8603
1.0769
1.1925
1.2646
1.3138
1.3496
1.3766
1.3978
1.4149
1.4289
1.4961
1.5202
1.5325
1.5400
1.5552
1.5708
1.0017
1.0033
1.0066
1.0098
1.0130
1.0161
1.0311
1.0450
1.0580
1.0701
1.0814
1.0918
1.1016
1.1107
1.1191
1.1785
1.2102
1.2287
1.2403
1.2479
1.2532
1.2570
1.2598
1.2620
1.2699
1.2717
1.2723
1.2727
1.2731
1.2732
Cylinder
Sphere
l1
A1
l1
A1
0.1412
0.1995
0.2814
0.3438
0.3960
0.4417
0.6170
0.7465
0.8516
0.9408
1.0184
1.0873
1.1490
1.2048
1.2558
1.5995
1.7887
1.9081
1.9898
2.0490
2.0937
2.1286
2.1566
2.1795
2.2880
2.3261
2.3455
2.3572
2.3809
2.4048
1.0025
1.0050
1.0099
1.0148
1.0197
1.0246
1.0483
1.0712
1.0931
1.1143
1.1345
1.1539
1.1724
1.1902
1.2071
1.3384
1.4191
1.4698
1.5029
1.5253
1.5411
1.5526
1.5611
1.5677
1.5919
1.5973
1.5993
1.6002
1.6015
1.6021
0.1730
0.2445
0.3450
0.4217
0.4860
0.5423
0.7593
0.9208
1.0528
1.1656
1.2644
1.3525
1.4320
1.5044
1.5708
2.0288
2.2889
2.4556
2.5704
2.6537
2.7165
2.7654
2.8044
2.8363
2.9857
3.0372
3.0632
3.0788
3.1102
3.1416
1.0030
1.0060
1.0120
1.0179
1.0239
1.0298
1.0592
1.0880
1.1164
1.1441
1.1713
1.1978
1.2236
1.2488
1.2732
1.4793
1.6227
1.7202
1.7870
1.8338
1.8673
1.8920
1.9106
1.9249
1.9781
1.9898
1.9942
1.9962
1.9990
2.0000
temperature u0 drops by 20 percent at a specified time, so does the dimensionless temperature u0 anywhere else in the medium at the same time.
Once the Bi number is known, these relations can be used to determine the
temperature anywhere in the medium. The determination of the constants A1
and l1 usually requires interpolation. For those who prefer reading charts to
interpolating, these relations are plotted and the one-term approximation solutions are presented in graphical form, known as the transient temperature charts.
Note that the charts are sometimes difficult to read, and they are subject to
reading errors. Therefore, the relations above should be preferred to the charts.
The transient temperature charts in Figs. 4–17, 4–18, and 4–19 for a large
plane wall, long cylinder, and sphere were presented by M. P. Heisler in 1947
and are called Heisler charts. They were supplemented in 1961 with transient
h
J0(h)
J1(h)
0.0
0.1
0.2
0.3
0.4
1.0000
0.9975
0.9900
0.9776
0.9604
0.0000
0.0499
0.0995
0.1483
0.1960
0.5
0.6
0.7
0.8
0.9
0.9385
0.9120
0.8812
0.8463
0.8075
0.2423
0.2867
0.3290
0.3688
0.4059
1.0
1.1
1.2
1.3
1.4
0.7652
0.7196
0.6711
0.6201
0.5669
0.4400
0.4709
0.4983
0.5220
0.5419
1.5
1.6
1.7
1.8
1.9
0.5118
0.4554
0.3980
0.3400
0.2818
0.5579
0.5699
0.5778
0.5815
0.5812
2.0
2.1
2.2
2.3
2.4
0.2239
0.1666
0.1104
0.0555
0.0025
0.5767
0.5683
0.5560
0.5399
0.5202
2.6
2.8
3.0
3.2
20.0968
20.1850
20.2601
20.3202
0.4708
0.4097
0.3391
0.2613
252
TRANSIENT HEAT CONDUCTION
T0 – T`
Ti – T`
1.0
0.7
0.5
0.4
0.3
0.2
u0 =
k
hL = 1
Bi
1.0
0.7
0.
8
45
9
8
35
7
6
25
0.6
0.5
40
30
16
3
2 1.8
1.6 1.4
1.2
0.05
2.5
0
2
50
20
18
5
4
0.2
0.1
1
12
10
0.4
0.3
0.01
0.007
0.005
0.004
0.003
0.002
0
100
80 90
60 70
14
0.1
0.07
0.05
0.04
0.03
0.02
0.001
Plate
3
4 6 8 10
14
18
22
26
30
50
70
100
120
150
300
400
500
600 700
t = at/L2
T`
h
(a) Midplane temperature.
From M. P. Heisler, “Temperature Charts for Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted by permission of ASME International.
u
T – T`
=
u0 T0 – T`
x/L = 0.2
1.0
0.9
0.4
Bi = hL/k
0.4
0.8
50
20
10
5
2
1
0.5
0.05
0.1
0.2
0.3
0.9
0.1
1.0
0
0.01
0.1
0.00
5
0.01
0.02
0.5
0.2
x
2L
0.00
1
0.00
2
0.6
0.5
0.3
L
0.7
0.6
0.6
0.4
0
0.8
0.8
0.7
T`
h
Bi =
0.9
Q
Qmax
1.0
Initially
T = Ti
0.2
Plate
1.0
10
100
0.1
0
10–5
Plate
10– 4
1
k
=
Bi
hL
(b) Temperature distribution.
(c) Heat transfer.
From M. P. Heisler, “Temperature Charts for
Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted
by permission of ASME International.
From H. Gröber et al.
10–3
10–2
10–1
1
Bi 2t = h2at/k 2
10
102
103
FIGURE 4–17
Transient temperature and heat transfer charts for a plane wall of thickness 2L initially at a uniform temperature Ti
subjected to convection from both sides to an environment at temperature T` with a convection coefficient of h.
104
253
CHAPTER 4
u0 =
T0 – T`
Ti – T`
1.0
0.7
Cylinder
0.5
0.4
0.3
5
0.2
3.5
8
1.
16
= 1
Bi
25
20
12
1.6
90
18
70
14
10
0
80
60
9
1.2
50
10
7
0.8
0.6
8
45
35
30
0.3
0.1
0
0.5
6
40
0.4
0.2
0.01
0.007
0.005
0.004
0.003
3
2
1.4
1.0
0.02
k
o
4
2.
5
0.1
0.07
0.05
0.04
0.03
hr
0.002
0
1
2
3
4 6 8 10
14
18
22
26
t = at/ro2
30
50
70
100
120
(a) Centerline temperature.
Q
Qmax
1.0
r/ro = 0.2
0.9
0.4
0.4
0.8
50
10
5
2
1
0.5
0.5
0.05
0.1
0.2
0.6
0.4
0.2
Bi = hro /k
0.7
0.6
0.5
0.3
ro r
0.8
0.7
0.6
0
0.00
1
0.00
2
0.00
5
0.01
0.02
0.8
0.9
350
Bi =
1.0
250
T` Initially T`
h
T = Ti h
From M. P. Heisler, “Temperature Charts for Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted by permission of ASME International.
u
T – T`
=
u 0 T0 – T`
140 150
20
0.001
0.3
0.2
0.9
0.1
1.0
0
0.1
0.01
1.0
1
k
=
Bi
hro
(b) Temperature distribution.
Cylinder
10
From M. P. Heisler, “Temperature Charts for
Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted
by permission of ASME International.
100
0.1
0
10–5
Cylinder
10– 4
10–3
10–2
10–1
1
Bi 2t = h2at/k 2
10
102
103
104
(c) Heat transfer.
From H. Gröber et al.
FIGURE 4–18
Transient temperature and heat transfer charts for a long cylinder of radius ro initially at a uniform temperature Ti
subjected to convection from all sides to an environment at temperature T` with a convection coefficient of h.
254
TRANSIENT HEAT CONDUCTION
T0 – T`
Ti – T`
1.0
0.7
0.5
0.4
0.3
hr
0.2
100
80 90
60 70
12 14
Sphere
= 1
Bi
25 20
18 16
6
50
40
45
0
35 3
10
8
9
7
5
3.5
4
1.2
5
0.7
0.5
0.01
0.007
0.005
0.004
0.003
1.6
1.4
1.0
0.02
3.0
2.6 2
.8
2.4
.0
2 2
2.
8
1.
0.1
0.07
0.05
0.04
0.03
0
0.35
0.2 0.1
0.05
0.002
0
0.5
1.0
1.5
2
2.5
3
4
5
6
7 8
9 10
t = at/ro2
20
30
40
T`
h
(a) Midpoint temperature.
From M. P. Heisler, “Temperature Charts for Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted by permission of ASME International.
u
T – T`
=
u0 T0 – T`
r/ro = 0.2
0.9
0.9
0.4
T`
h
0
ro
250
r
0.4
0.4
0.3
0.8
0.3
0.2
0.9
0.2
0.1
1.0
1.0
10
1 = k
Bi hro
(b) Temperature distribution.
From M. P. Heisler, “Temperature Charts for
Induction and Constant Temperature Heating,”
Trans. ASME 69, 1947, pp. 227–36. Reprinted
by permission of ASME International.
50
20
10
0.1
Sphere
0.1
0.5
1
0.5
0.05
0.1
0.2
0.6
0.6
0.00
5
0.01
0.02
0.7
0.5
0
0.01
Initially
T = Ti
200
0.8
0.7
0.6
150
Bi = hro /k
0.00
1
0.00
2
0.8
100
Bi =
1.0
Q
Qmax
1.0
50
5
0.001
k
o
2
u0 =
100
0
10–5
Sphere
10– 4
10–3
10–2
10–1
1
10
102
103
Bi 2t = h2a t/k 2
(c) Heat transfer.
From H. Gröber et al.
FIGURE 4–19
Transient temperature and heat transfer charts for a sphere of radius ro initially at a uniform temperature Ti subjected to
convection from all sides to an environment at temperature T` with a convection coefficient of h.
104
443
CHAPTER 7
The characteristic length D for use in the calculation of the Reynolds and the
Nusselt numbers for different geometries is as indicated on the figure. All
fluid properties are evaluated at the film temperature. Note that the values
presented in Table 7–1 for non-circular geometrics have been updated based
on the recommendations of Sparrow et al. (2004).
TABLE 7–1
Empirical correlations for the average Nusselt number for forced convection
over circular and noncircular cylinders in cross flow (from Zukauskas, 1972,
Jakob 1949, and Sparrow et al., 2004)
Cross-section
of the cylinder
Fluid
Range of Re
Nusselt number
Gas or
liquid
0.4–4
4–40
40–4000
4000–40,000
40,000–400,000
Nu 5 0.989Re0.330 Pr1/3
Nu 5 0.911Re0.385 Pr1/3
Nu 5 0.683Re0.466 Pr1/3
Nu 5 0.193Re0.618 Pr1/3
Nu 5 0.027Re0.805 Pr1/3
Gas
3900–79,000
Nu 5 0.094Re0.675 Pr1/3
Gas
5600–111,000
Nu 5 0.258Re0.588 Pr1/3
Gas
4500–90,700
Nu 5 0.148Re0.638 Pr1/3
Gas
5200–20,400
20,400–105,000
Nu 5 0.162Re0.638 Pr1/3
Nu 5 0.039Re0.782 Pr1/3
Gas
6300–23,600
Nu 5 0.257Re0.731 Pr1/3
Gas
1400–8200
Nu 5 0.197Re0.612 Pr1/3
Circle
D
Square
D
Square
(tilted
45°)
D
Hexagon
D
Hexagon
(tilted
45°)
Vertical
plate
D
D
Ellipse
D
cen98128_App-A_p865-892.qxd
1/8/10
3:29 PM
Page 878
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.
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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.