 |
2.3.7 Thermal conductivities
Definition and units
The thermal conductivity, λ, of a substance may
be defined as the quantity of heat transmitted, Q, due to unit
temperature gradient, in unit time under steady conditions in a direction
normal to a surface of unit area, when the heat transfer is dependent only on
the temperature gradient.
|
λ =
− Q |
|
∂T |
|
∂n |
In this section thermal conductivity
values are assembled for metallic, semi-conducting and insulating elements,
representative groups of alloys, refractories and miscellaneous constructional
and insulating materials, some liquids and some gases. The values are expressed
in the SI unit W m−1 K−1 throughout. Factors
for converting to other units are as follows:
1 W m−1 K−1
= 0.01 J cm cm−2
s−1 K−1
=
0.002 388 cal cm cm−2 s−1
K−1
=
0.859 8 kcal m m−2 h−1
K−1
=
0.001 926 Btu in ft−2 s−1
°F−1
=
6.933 Btu in ft−2 h−1
°F−1
=
0.577 8 Btu ft ft−2 h−1
°F−1
=
0.000 160 5 Btu ft ft−2s−1
°F−1
More extensive collections of thermal conductivity data
will be found in Touloukian et al. (1970a, b and c).
Thermal conductivities
of metallic elements
The thermal conductivity values in the
table below are for metallic elements in the purest polycrystalline condition
for which reliable measurements have been reported. Entries in italics relate
to the liquid phase.
The thermal conductivities of less pure samples of these elements will
be lower than the values given below. Thermal conductivity invariably decreases
with decreasing purity; such dependence being weak at ambient and higher
temperatures but very strong at cryogenic temperatures.
|
λ/(W
m−1 K−1) |
|
Metal |
Temperature/K |
|
173.2 |
273.2 |
373.2 |
573.2 |
973.2 |
|
|
|
|
|
|
|
|
Aluminium |
241 |
236 |
240 |
233 |
92 |
|
Antimony |
33 |
25.5 |
22 |
19 |
27 |
|
Beryllium |
367 |
218 |
168 |
129 |
93 |
|
Bismuth |
11 |
8.2 |
7.2 |
13 |
17 |
|
Cadmium |
100 |
97 |
95 |
89 |
45 |
|
Caesium |
37 |
36 |
20 |
20.6 |
17.7 |
|
Cerium |
8 |
11 |
13 |
16 |
— |
|
Chromium |
120 |
96.5 |
92 |
82 |
66 |
|
Cobalt |
130 |
105 |
89 |
69 |
53 |
|
Copper |
420 |
403 |
395 |
381 |
354 |
|
Dysprosium |
9 |
10.5 |
— |
— |
— |
|
Erbium |
14 |
15 |
— |
— |
— |
|
Gadolinium |
12 |
10 |
— |
— |
— |
|
Gallium† |
43 |
41 |
33 |
45 |
— |
|
Gold |
324 |
319 |
313 |
299 |
272 |
|
Hafnium |
25 |
23 |
22 |
21 |
21 |
|
Holmium |
14 |
16 |
17 |
— |
— |
|
Indium |
92 |
84 |
76 |
42 |
— |
|
Iridium |
156 |
147 |
145 |
139 |
— |
|
Iron |
99 |
83.5 |
72 |
56 |
34 |
|
Lanthanum |
12 |
13 |
14.5 |
— |
— |
|
Lead |
37 |
36 |
34 |
32 |
21 |
|
Lithium |
94 |
86 |
82 |
47 |
59 |
|
Lutetium |
18 |
17 |
— |
— |
— |
|
Magnesium |
160 |
157 |
154 |
150 |
— |
|
Manganese |
7 |
8 |
— |
— |
— |
|
Mercury |
29.5 |
7.8 |
9.4 |
11.7 |
— |
|
Molybdenum |
145 |
139 |
135 |
127 |
113 |
|
Nickel |
113 |
94 |
83 |
67 |
71 |
|
Niobium |
53 |
53 |
55 |
58 |
64 |
|
Osmium |
93 |
88 |
87 |
87 |
— |
|
Palladium |
72 |
72 |
73 |
79 |
93 |
|
Platinum |
73 |
72 |
72 |
73 |
78 |
|
Plutonium |
4 |
6 |
8 |
— |
— |
|
Potassium |
105 |
104 |
53 |
45 |
32 |
|
Praseodymium |
9.9 |
12 |
13.4 |
— |
— |
|
Rhenium |
52 |
49 |
47 |
44 |
45 |
|
Rhodium |
156 |
151 |
147 |
137 |
— |
|
Rubidium |
59 |
58 |
32 |
29 |
22 |
|
Ruthenium |
123 |
117 |
115 |
108 |
98 |
|
Samarium |
10 |
13 |
13 |
14 |
— |
|
Scandium |
15 |
16 |
— |
— |
— |
|
Silver |
432 |
428 |
422 |
407 |
377 |
|
Sodium |
141 |
142 |
88 |
78 |
60 |
|
Tantalum |
58 |
57 |
58 |
58.5 |
60 |
|
Technetium |
— |
51 |
50 |
50 |
— |
|
Terbium |
11 |
10.5 |
— |
— |
— |
|
Thallium |
51 |
47 |
44 |
— |
— |
|
Thorium |
55 |
54 |
54 |
56 |
58 |
|
Thulium |
16 |
17 |
— |
— |
— |
|
Tin |
76 |
68 |
63 |
32 |
40 |
|
Titanium |
26 |
22 |
21 |
19 |
21 |
|
Tungsten |
188 |
177 |
163 |
139 |
119 |
|
Uranium |
24 |
27 |
29 |
33 |
43 |
|
Vanadium |
32 |
31 |
31 |
33 |
38 |
|
Yttrium |
16.5 |
17 |
— |
— |
— |
|
Zinc |
117 |
117 |
112 |
104 |
66 |
|
Zirconium |
26 |
23 |
22 |
21 |
23 |
|
|
|
|
|
|
|
Thermal conductivities of single crystals of
some non-cubic metals at normal temperature
|
λ/(W m−1
K−1) |
|
Metal |
Thermal conductivity in direction of |
|
c-axis |
a-axis |
b-axis |
|
|
|
|
|
|
Bismuth |
5.4 |
9.3 |
|
|
Cadmium |
83.05 |
104 |
|
|
Dysprosium |
11.65 |
10.25 |
|
|
Erbium |
18.4 |
12.6 |
|
|
Gadolinium |
10.7 |
10.3 |
|
|
Gallium |
16.0 |
40.8 |
88.3 |
|
Holmium |
22.1 |
13.6 |
|
|
Lutetium |
23.3 |
13.8 |
|
|
Mercury (at 227.7 K) |
33.0 |
25.9 |
|
|
Terbium |
14.5 |
9.45 |
|
|
Thulium |
24.2 |
14.1 |
|
|
Tin |
51.8 |
74.0 |
|
|
|
|
|
|
Thermal conductivities of
alloys
At low temperatures the thermal conductivity of a given metal tends to
increase in proportion to the reciprocal of its residual resistivity
ρ0. Many metals, especially good electrical conductors,
have thermal conductivities that follow the simple relation
at very low temperatures and at
temperatures higher than their Debye temperature; L0 being
the Lorentz coefficient 2.45 × 10−8 W
s−1 K−2, σ the electrical
conductivity in S m−1 and T the absolute
temperature. This behaviour enables the thermal conductivities of metallic
samples to be estimated fairly reliably from simple electrical resistivity
measurements.
As the thermal conductivities of alloys depend strongly on their
mechanical and thermal history (heat treatment) as well as on their chemical
composition, the values tabulated below should be regarded as typical for the
compositions listed. For many groups of alloys the thermal conductivity of a
particular sample, near room temperature and above, can be estimated within
about 6% from its more easily
measured electrical conductivity using the relation λ = LσT
+ C. The optimum values for L and C for different alloy types are as
follows:
|
Main constituent metal |
L/(10−8 W s −1
K−2) |
C/(W m −1
K−1) |
|
|
|
|
|
Aluminium . . . . . . . . . . . . . . . . . . . . . . . . |
2.22 |
10.5 |
|
Copper . . . . . . . . . . . . . . . . . . . . . . . . . |
2.39 |
7.5 |
|
Alpha-iron . . . . . . . . . . . . . . . . . . . . . . . |
2.43 |
9.2 |
|
Gamma-iron . . . . . . . . . . . . . . . . . . . . . . |
2.39 |
4.2 |
|
Magnesium . . . . . . . . . . . . . . . . . . . . . . |
2.21 |
9.6 |
|
Nickel . . . . . . . . . . . . . . . . . . . . . . . . . |
2.13 |
8.4 |
|
Nickel-chromium (nimonic type)
. . . . . . . . . . . . |
2.20 |
6.0 |
|
Titanium . . . . . . . . . . . . . . . . . . . . . . . . |
2.30 |
2.9 |
|
Zirconium . . . . . . . . . . . . . . . . . . . . . . . |
2.50 |
2.2 |
|
|
|
|
Thermal conductivities of alloys at ambient and
elevated temperatures
| |
| Alloy |
|
| Composition / weight percent |
|
λ /
(W m−1 K−1) at Temperature /
K |
|
Al |
C |
Cr |
Cu |
Fe |
Mg |
Mn |
Ni |
Si |
W |
Zn |
Other |
273 |
373 |
573 |
773 |
973 |
1273 |
Aluminium alloys
Aluminium |
100 |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
236 |
240 |
233 |
— |
— |
— |
| Alpax gamma |
87 |
— |
— |
— |
0.3 |
0.3 |
0.3 |
— |
12 |
— |
— |
— |
188 |
188 |
184 |
— |
— |
— |
| Lo-Ex |
85 |
— |
— |
1 |
0.5 |
0.9 |
— |
1 |
11.8 |
— |
— |
— |
172 |
175 |
173 |
— |
— |
— |
| Y-alloy |
92 |
— |
— |
3.8 |
0.4 |
1.3 |
— |
1.8 |
0.4 |
— |
— |
— |
180 |
188 |
194 |
— |
— |
— |
| RR 59 |
93 |
— |
— |
2.3 |
1.2 |
1.5 |
— |
1.2 |
0.9 |
— |
— |
— |
168 |
176 |
186 |
— |
— |
— |
| RR 57 |
89 |
— |
— |
2.2 |
0.3 |
2.5 |
0.5 |
— |
0.3 |
— |
5 |
— |
161 |
171 |
178 |
— |
— |
— |
Copper alloys Copper |
— |
— |
— |
100 |
— |
— |
— |
— |
— |
— |
— |
— |
403 |
395 |
381 |
— |
354 |
— |
| Brass |
— |
— |
— |
70 |
— |
— |
— |
— |
— |
— |
30 |
— |
106 |
128 |
146 |
— |
— |
— |
| Bronze |
— |
— |
— |
90 |
— |
— |
— |
— |
— |
— |
— |
10 Sn |
53 |
60 |
80 |
— |
— |
— |
| German
Silver |
— |
— |
— |
62 |
— |
— |
— |
15 |
— |
— |
22 |
— |
23 |
29 |
45 |
— |
— |
— |
| Constantan |
— |
— |
— |
60 |
— |
— |
— |
40 |
— |
— |
— |
— |
22 |
24 |
27 |
— |
— |
— |
| Manganin |
— |
— |
— |
84 |
— |
— |
12 |
4 |
— |
— |
— |
— |
21 |
26 |
— |
— |
— |
— |
|
Nickel alloys Nickel |
— |
— |
— |
— |
— |
— |
— |
100 |
— |
— |
— |
— |
94 |
83 |
67 |
— |
71 |
— |
|
Alumel |
2 |
— |
— |
— |
— |
— |
2 |
95 |
1 |
— |
— |
— |
30 |
32 |
35 |
— |
— |
— |
|
Monel |
— |
0.2 |
— |
29.2 |
1.7 |
0.1 |
1.0 |
67.1 |
— |
— |
— |
— |
21 |
24 |
30 |
— |
43 |
— |
|
Chromel P |
— |
— |
10 |
— |
— |
— |
— |
90 |
— |
— |
— |
— |
— |
19 |
23 |
— |
— |
— |
|
Nichrome |
— |
0.1 |
21 |
— |
0.6 |
— |
0.65 |
77.3 |
0.4 |
— |
— |
— |
13 |
14 |
17 |
— |
21 |
— |
|
Inconel 600 |
— |
0.1 |
16 |
0.3 |
8 |
— |
0.5 |
74 |
0.4 |
— |
— |
— |
14.6 |
15.8 |
19.1 |
22.1 |
25.7 |
— |
|
Inconel X-750 |
0.8 |
0.04 |
15 |
0.05 |
6.8 |
— |
0.7 |
73 |
0.3 |
— |
— |
2.5Ti, 0.8 Nb |
11.3 |
13.0 |
16.5 |
20.1 |
23.6 |
27.9 |
|
Incoloy 800 |
0.4 |
0.05 |
21 |
0.5 |
— |
— |
1 |
33 |
0.7 |
— |
— |
0.4 Ti |
11.3 |
12.8 |
16.4 |
19.4 |
22.8 |
31 |
|
Incoloy 802 |
— |
0.3 |
21 |
0.5 |
— |
— |
1 |
33 |
0.4 |
— |
— |
— |
11.3 |
13.1 |
16.2 |
19.2 |
22.1 |
26 |
|
Hastelloy R-235 |
2 |
0.16 |
15.5 |
— |
10 |
— |
1 |
62 |
1 |
— |
— |
5.5 Mo, 2.5 Co |
— |
11.7 |
14.8 |
17.6 |
20 |
25.5 |
|
Nimonic 75 |
0.3 |
0.1 |
20 |
0.5 |
5 |
— |
1 |
bal |
1.0 |
— |
— |
2 Co, 0.3 Mo, 0.2 Ti |
13.9 |
17.5 |
21.0 |
24.3 |
— |
|
|
Nimonic 80 |
1.5 |
0.07 |
20 |
0.2 |
1 |
— |
1 |
bal |
1.0 |
— |
— |
2 Co, 0.3 Mo, 2 Ti |
— |
12.1 |
15.5 |
18.4 |
23.5 |
— |
|
Nimonic 90 |
1.5 |
0.07 |
20 |
0.2 |
1 |
— |
1 |
bal |
1.5 |
— |
— |
17 Co, 0.3 Mo, 2 Ti |
— |
13.0 |
16.5 |
20.0 |
23.7 |
— |
|
Nimonic 105 |
4.5 |
0.14 |
14.5 |
0.2 |
1 |
— |
1 |
bal |
1.0 |
— |
— |
20 Co, 5 Mo, 2 Ti |
— |
11.6 |
14.7 |
17.4 |
21.2 |
27.6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Carbon steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.08 C, 0.3 Mn |
— |
0.08 |
0.045 |
— |
bal |
— |
0.31 |
0.07 |
0.08 |
— |
— |
— |
59 |
58 |
49 |
40 |
32 |
28 |
|
0.23 C, 0.6 Mn |
— |
0.23 |
— |
0.13 |
,, |
— |
0.64 |
0.07 |
0.11 |
— |
— |
— |
52 |
51 |
46 |
39 |
32 |
27 |
|
0.42 C, 0.6 Mn |
— |
0.42 |
— |
0.12 |
,, |
— |
0.64 |
0.06 |
0.11 |
— |
— |
— |
52 |
51 |
46 |
38 |
30 |
27 |
|
0.8 C, 0.2 Mn |
— |
0.84 |
— |
0.02 |
,, |
— |
0.24 |
— |
0.13 |
— |
— |
— |
51 |
49 |
42 |
36 |
31 |
27 |
|
1.2 C, 0.35 Mn |
— |
1.22 |
0.11 |
0.08 |
,, |
— |
0.35 |
0.13 |
0.16 |
— |
— |
— |
45 |
45 |
40 |
35 |
28 |
26 |
|
0.2 C, 1.5 Mn |
— |
0.23 |
0.06 |
0.10 |
,, |
— |
1.51 |
0.04 |
0.12 |
— |
— |
— |
46 |
46 |
43 |
37 |
31 |
27 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Low alloy steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.3 C, 1 Cr |
— |
0.32 |
1.09 |
0.07 |
bal |
— |
0.7 |
0.07 |
0.20 |
— |
— |
— |
49 |
46 |
42 |
36 |
29 |
28 |
|
0.4 C, 1 Cr, 0.3 Ni |
— |
0.35 |
0.88 |
0.12 |
,, |
— |
0.6 |
0.26 |
0.21 |
— |
— |
— |
43 |
43 |
41 |
36 |
31 |
28 |
|
0.2 C, 0.6 Ni, 0.5 Mo |
— |
0.20 |
— |
— |
,, |
— |
1.35 |
0.6 |
0.25 |
— |
— |
0.5 Mo |
37 |
38 |
37 |
34 |
29 |
— |
|
0.3 C, 0.2 Cr, 3.5 Ni |
— |
0.33 |
0.17 |
0.08 |
,, |
— |
0.55 |
3.47 |
0.18 |
— |
— |
— |
36 |
38 |
38 |
34 |
28 |
28 |
|
0.3 C, 1 Cr, 3.4 Ni |
— |
0.33 |
0.80 |
0.05 |
,, |
— |
0.53 |
3.38 |
0.17 |
— |
— |
— |
34 |
36 |
37 |
35 |
29 |
28 |
|
0.4 C, 1 Cr, 3.6 Ni |
— |
0.4 |
0.8 |
— |
,, |
— |
0.66 |
3.6 |
0.2 |
— |
— |
— |
33 |
36 |
37.5 |
35 |
28 |
— |
|
0.3 C, ! Cr, 3.5 Ni |
— |
0.34 |
0.78 |
0.05 |
,, |
— |
0.55 |
3.53 |
0.27 |
— |
— |
— |
33 |
34 |
36 |
34 |
28 |
28 |
|
0.5 C, 1 Mn, 2 Si |
— |
0.49 |
0.04 |
0.09 |
,, |
— |
0.9 |
0.16 |
2.0 |
— |
— |
— |
25 |
28 |
31 |
31 |
28 |
26 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
High alloy steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1.2 C, 13 Mn |
— |
1.22 |
— |
0.03 |
bal |
— |
13.0 |
0.07 |
0.22 |
— |
— |
— |
13 |
15 |
18 |
21 |
23 |
26 |
|
0.3 C, 28 Ni |
— |
0.28 |
— |
0.03 |
,, |
— |
0.9 |
28.4 |
0.15 |
— |
— |
— |
13 |
15 |
18 |
21 |
23 |
28 |
|
4 Cr, 18 W, 1 V |
— |
0.72 |
4.26 |
0.06 |
,, |
— |
0.25 |
0.07 |
0.30 |
18.5 |
— |
1 V |
24 |
26 |
28 |
28 |
27 |
28 |
|
Kovar |
— |
0.02 |
— |
— |
54 |
— |
0.47 |
29 |
— |
— |
— |
17 Co |
14.1 |
14.7 |
15.6 |
17.5 |
19.3 |
— |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Stainless steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
304, 321, 347 |
— |
0.05 |
17.5 |
— |
bal |
— |
<2 |
9 |
<1 |
— |
— |
— |
14.5 |
16.5 |
20 |
22.5 |
25.5 |
29.5 |
|
316 |
— |
0.05 |
17 |
— |
,, |
— |
<2 |
12 |
<1 |
— |
— |
2.5 Mo |
13.5 |
15 |
18.5 |
21.5 |
24 |
28.5 |
|
310 |
— |
0.1 |
24 |
— |
,, |
— |
<2 |
20 |
<1 |
— |
— |
— |
12 |
13.5 |
17.5 |
20.5 |
23 |
— |
|
16 Cr, 20 Ni |
— |
0.01 |
16 |
— |
,, |
— |
1.2 |
20 |
0.3 |
— |
— |
— |
13.6 |
15.7 |
18.9 |
21.5 |
23.8 |
26.8 |
|
Era-ATV |
— |
0.5 |
15 |
— |
,, |
— |
1.2 |
27 |
1.3 |
2.8 |
— |
— |
11 |
12.5 |
15.5 |
— |
21.5 |
— |
|
403, 405, 409 |
— |
0.1 |
12 |
— |
,, |
— |
<2 |
— |
<1 |
— |
— |
— |
— |
25 |
26 |
27 |
— |
— |
|
430, 434 |
— |
0.05 |
17 |
— |
,, |
— |
<2 |
— |
<1 |
— |
— |
1 Mo |
— |
22.2 |
22.9 |
23.7 |
24.4 |
— |
|
410, 420 |
— |
0.3 |
13 |
0.1 |
,, |
— |
0.5 |
0.5 |
0.4 |
— |
— |
— |
— |
— |
23.6 |
24.6 |
26.3 |
28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Miscellaneous alloys |
|
|
|
|
|
|
|
Platinum 90%, iridium
10% . . . . . . . . . . . . . . . . . . . . |
31 |
— |
— |
— |
— |
— |
|
Platinum 90%, rhodium 10%
. . . . . . . . . . . . . . . . . . . . |
38 |
— |
— |
— |
— |
— |
|
Platinum 60%, rhodium 40%
. . . . . . . . . . . . . . . . . . . . |
46 |
51 |
58 |
69 |
— |
— |
|
Titanium 92.5%, aluminium 5%, tin 2.5%
. . . . . . . . . . . . . . . . |
7 |
8.3 |
10.5 |
— |
— |
— |
|
Titanium 96%, aluminium 2%, manganese 2%
. . . . . . . . . . . . . . . |
9.3 |
10.5 |
10.7 |
— |
— |
— |
|
Zirconium 93.1%, tin 6.7%, carbon 0.1%
. . . . . . . . . . . . . . . . |
— |
8.7 |
12 |
— |
— |
— |
|
Zirconium 97.5%, tin 2.3%, carbon 0.1%
. . . . . . . . . . . . . . . . |
— |
11.3 |
13 |
— |
— |
— |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Thermal conductivities of alloys used in low
temperature applications
|
Alloy |
λ/(W m−1 K−1) |
|
Composition/weight percent |
|
Temperature/K |
|
Al |
C |
Cr |
Cu |
Fe |
Mg |
Mn |
Ni |
Si |
Sn |
Zn |
Other |
273.2 |
173 |
100 |
50 |
20 |
4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Aluminium alloys† |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Aluminium |
99.99 |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
228 |
— |
295 |
870 |
4100 |
1075 |
|
(1 C) 1100-0 |
bal |
— |
— |
1 |
— |
0.05 |
0.05 |
— |
1.0 |
— |
0.05 |
— |
205 |
— |
228 |
315 |
225 |
45 |
|
(N3) 3003 F |
,, |
— |
— |
0.12 |
— |
— |
1.2 |
— |
— |
— |
— |
— |
170 |
158 |
143 |
117 |
58 |
11 |
|
2219 T81 |
,, |
— |
— |
6.3 |
— |
0.02 |
0.3 |
— |
0.20 |
— |
0.1 |
— |
118 |
— |
68 |
46 |
26 |
— |
|
(N8) 5083 0 |
,, |
— |
0.15 |
0.1 |
— |
4.5 |
0.7 |
— |
0.4 |
— |
0.25 |
— |
110 |
92 |
66 |
39 |
17 |
3.3 |
|
7039 T61 |
,, |
— |
0.2 |
0.1 |
— |
2.8 |
0.25 |
— |
0.2 |
— |
4 |
— |
150 |
— |
96 |
64 |
30 |
14.7 |
| |
|
Copper alloys |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Copper |
— |
— |
— |
99.96 |
— |
— |
— |
— |
— |
— |
— |
— |
400 |
— |
480 |
1230 |
3700 |
1450 |
|
ETP Cu |
— |
— |
— |
99.95 |
— |
— |
— |
— |
— |
— |
— |
— |
395 |
— |
445 |
880 |
1320 |
325 |
|
OFHC Cu |
— |
— |
— |
99.95 |
— |
— |
— |
— |
— |
— |
— |
— |
400 |
— |
460 |
750 |
900 |
200 |
|
Brass |
— |
— |
— |
70 |
— |
— |
— |
— |
— |
— |
30 |
— |
106 |
92 |
70 |
45 |
21 |
4 |
|
Brass |
— |
— |
— |
65 |
— |
— |
— |
— |
— |
— |
35 |
— |
113 |
— |
59 |
— |
— |
— |
|
Cupro-nickel |
— |
— |
— |
90 |
— |
— |
— |
10 |
— |
— |
— |
— |
— |
— |
— |
31 |
14 |
1 |
|
German Silver |
— |
— |
— |
62 |
— |
— |
— |
15 |
— |
— |
22 |
— |
23 |
20 |
— |
— |
— |
— |
|
Copper Beryllium |
— |
— |
— |
98 |
— |
— |
— |
— |
— |
— |
— |
2 Be |
— |
— |
— |
24 |
10 |
2 |
|
|
|
Nickel alloys |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Nickel |
— |
— |
— |
— |
— |
— |
— |
99.99 |
— |
— |
— |
— |
94 |
115 |
154 |
320 |
865 |
138 |
|
Inconel X |
0.9 |
0.04 |
15 |
— |
7 |
— |
0.7 |
73 |
0.3 |
— |
— |
2.5 Ti |
11.4 |
10 |
8.7 |
— |
— |
— |
|
K. Monel |
3 |
0.15 |
— |
30 |
1 |
— |
0.6 |
65 |
0.15 |
— |
— |
— |
17 |
14 |
12 |
— |
— |
— |
|
Hastelloy X |
— |
0.15 |
22 |
— |
24 |
— |
— |
45 |
— |
— |
— |
9 Mo |
9.9 |
8 |
6.5 |
5 |
3 |
0.5 |
|
Inconel 718 |
0.4 |
0.04 |
18.6 |
— |
18.5 |
— |
— |
— |
— |
— |
— |
1 Ti, 5 Nb, 3 Mo |
10 |
8.7 |
7 |
4.8 |
2.6 |
0.4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Armco iron |
— |
0.02 |
— |
— |
99.8 |
— |
0.03 |
— |
— |
— |
— |
— |
76 |
83.6 |
95 |
109 |
65 |
13 |
|
2.5% Ni |
— |
0.1 |
— |
— |
bal |
— |
0.8 |
2.5 |
0.2 |
— |
— |
— |
38 |
33 |
— |
— |
— |
— |
|
3.5% Ni |
— |
0.1 |
— |
— |
,, |
— |
0.8 |
3.5 |
0.2 |
— |
— |
— |
34 |
29 |
21 |
— |
— |
— |
|
5% Ni |
— |
0.1 |
— |
— |
,, |
— |
0.8 |
5 |
0.2 |
— |
— |
— |
31 |
26 |
19 |
10.5 |
— |
— |
|
9% Ni |
— |
0.1 |
— |
— |
,, |
— |
0.8 |
9 |
0.2 |
— |
— |
— |
28 |
23 |
16 |
8.5 |
3.5 |
1 |
|
Invar 36% Ni |
— |
0.07 |
— |
— |
,, |
— |
0.4 |
36 |
0.2 |
— |
— |
— |
13.5 |
11 |
7.7 |
4.3 |
1.6 |
— |
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Stainless steels |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
304/306/321/347 |
— |
0.05 |
18 |
— |
bal |
— |
2 |
8–12 |
1 |
— |
— |
— |
14.5 |
11.5 |
9 |
5.5 |
2 |
0.3 |
|
310 |
— |
0.2 |
25 |
— |
,, |
— |
2 |
20 |
1.5 |
— |
— |
— |
11 |
8.3 |
6.9 |
4.3 |
1.7 |
— |
|
16 Cr, 20 Ni |
— |
0.01 |
16.2 |
— |
,, |
— |
1.2 |
20.2 |
0.28 |
— |
— |
— |
13.6 |
11.5 |
9.3 |
6.0 |
2.4 |
0.4 |
|
15 Cr, 26 Ni |
— |
0.05 |
15 |
— |
,, |
— |
1.4 |
26 |
0.4 |
— |
— |
1.3 Mo, 0.3 V |
11.2 |
— |
7.6 |
5.0 |
2.2 |
1.0 |
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Titanium alloys |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Titanium |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
— |
99.9 Ti |
22 |
26 |
31 |
40 |
28 |
14 |
|
Ti 5 Al 2.5 Sn |
5 |
0.1 |
— |
— |
0.4 |
— |
0.2 |
— |
— |
2.5 |
— |
— |
7.8 |
6.1 |
4.8 |
3.6 |
2.0 |
— |
|
Ti 6 Al4 V |
6 |
0.05 |
— |
— |
— |
— |
— |
— |
— |
— |
— |
4 V |
7.0 |
5.4 |
4.0 |
2.5 |
1.3 |
— |
|
Ti 13 V 11 Cr 3 Al |
3 |
0.08 |
11 |
— |
0.3 |
— |
— |
— |
— |
— |
— |
13 V |
7.4 |
5.0 |
3.4 |
1.9 |
0.9 |
— |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Thermal conductivities of elements which are
semi-conductors or insulators
| |
λ/(W
m−1 K−1) |
|
Substance |
Temperature/K |
|
173.2 |
273.2 |
373.2 |
573.2 |
973.2 |
| |
|
|
|
|
|
|
Boron |
72 |
32 |
19 |
11 |
10 |
|
Carbon: |
|
|
|
|
|
|
amorphous |
1.1 |
1.5 |
1.8 |
2.2 |
2.5 |
|
diamond |
1700–4900 |
1000–2600 |
700–1700 |
— |
— |
|
graphite |
70–220 |
80–230 |
75–195 |
50–130 |
35–70 |
|
Pyrolytic graphite: |
|
|
|
|
|
|
parallel to planes |
3870 |
2130 |
1510 |
936 |
549 |
|
normal to planes |
10.8 |
6.4 |
4.4 |
2.8 |
1.6 |
|
Germanium |
113 |
67 |
46.5 |
29 |
17.5 |
|
Iodine |
— |
0.5 |
0.4 |
0.09 |
— |
|
Phosphorus: |
|
|
|
|
|
|
black |
20 |
13 |
— |
— |
— |
|
white (or yellow) |
— |
0.25 |
0.18 |
0.16 |
— |
|
Selenium: |
|
|
|
|
|
|
amorphous |
0.23 |
0.43 |
— |
— |
— |
|
crystalline: |
|
|
|
|
|
|
parallel to
c-axis |
6.8 |
4.8 |
4.8 |
— |
— |
|
normal to
c-axis |
2.0 |
1.4 |
1.4 |
— |
— |
|
Silicon |
330 |
168 |
108 |
65 |
32 |
|
Sulphur: |
|
|
|
|
|
|
amorphous |
0.18 |
0.20 |
— |
0.17 |
— |
|
polycrystalline |
0.39 |
0.29 |
0.15 |
0.17 |
— |
|
Tellurium: |
|
|
|
|
|
|
parallel to c-axis |
5.1 |
3.6 |
2.9 |
2.4 |
6.3 |
|
normal to c-axis |
2.9 |
2.1 |
1.7 |
1.5 |
6.3 |
|
|
|
|
|
|
|
Thermal conductivities of refractory materials:
Dense, polycrystalline, single-phase
compounds
| |
|
λ/(W m−1
K−1) |
|
Material |
Chem. formula |
Temperature/K |
|
298 |
373 |
773 |
1273 |
1773 |
|
|
|
|
|
|
|
|
|
Oxides: |
|
|
|
|
|
|
|
Alumina |
Al2O3† |
38 |
35 |
11 |
7 |
6 |
|
Aluminosilicate |
Al6Si2O13 |
— |
6 |
4.5 |
4 |
— |
|
Beryllia |
BeO |
300 |
220 |
70 |
18 |
14 |
|
Calcia |
CaO |
— |
15 |
8.7 |
7.8 |
— |
|
Magnesia |
MgO† |
40 |
35 |
16 |
7 |
6.5 |
|
Spinel |
MgAl2O4 |
16 |
15 |
9 |
6 |
— |
|
Silica |
SiO2
(vitreous)† |
1.6 |
1.7 |
2.1 |
5.0 |
— |
|
Thoria |
ThO2 |
14 |
12 |
6 |
2 |
2 |
|
Titania |
TiO2 |
— |
9.2 |
4.5 |
3.3 |
— |
|
Urania |
U2O |
12 |
8 |
4.5 |
3.2 |
— |
|
Zirconia |
ZrO2
(stabilised)† |
1.8 |
1.8 |
2.0 |
2.2 |
2.4 |
|
Zircon |
ZrSiO4 |
8 |
5.8 |
4.8 |
4.2 |
— |
|
Quartz |
SiO2 (single crystal) |
|
|
|
|
|
|
|
along
c-axis |
11 |
8.3 |
5 |
— |
— |
|
|
normal to
c-axis |
6.5 |
5 |
3.6 |
— |
— |
|
|
|
|
|
|
|
|
|
Carbides: |
|
|
|
|
|
|
|
Boran carbide |
B4C |
30 |
25 |
21 |
71 |
15 |
|
Silicon carbide |
SiC |
110 |
90 |
65 |
45 |
40 |
|
Titanium carbide |
TiC |
30 |
32 |
36 |
40 |
45 |
|
Tungsten carbide |
WC |
40 |
— |
— |
45 |
50 |
|
Zirconium carbide |
ZrC |
— |
— |
31 |
35 |
— |
|
|
|
|
|
|
|
|
|
Nitrides: |
|
|
|
|
|
|
|
Aluminium nitride |
AlN |
36 |
33 |
23 |
— |
— |
|
Silicon nitride |
Si3N4 (1% MgO) |
30 |
28 |
21 |
14.5 |
13 |
|
Titanium nitride |
TiN |
— |
25 |
27 |
— |
— |
|
|
|
|
|
|
|
|
|
Borides: |
|
|
|
|
|
|
|
Titanium diboride |
TiB2 |
— |
70 |
64 |
— |
— |
|
Zirconium diboride |
ZrB2 |
— |
73 |
67 |
— |
— |
|
Silicon (AXM–5Q) |
Si |
150 |
110 |
45 |
26 |
— |
|
Graphite (POCO) |
C (1.77 Mg m−3) |
108 |
107 |
76 |
— |
— |
|
|
|
|
|
|
|
|
Thermal conductivities of oxide and silicate
ceramics: Commercial products.
Composition and density may vary, values should be taken as typical of
type.
| |
|
λ/(W m−1
K−1) |
|
Material type |
IEC classification |
Temperature/K |
|
298 |
373 |
773 |
1273 |
1773 |
|
|
|
|
|
|
|
|
|
Porcelains and clay-based |
|
|
|
|
|
|
|
materials: |
|
|
|
|
|
|
|
Siliceous |
C-110, C-111 |
1.7–2.1 |
1.7–2.0 |
1.8–2.0 |
1.9–2.0 |
— |
|
Steatite (normal) |
C-220 |
5.5–6.0 |
— |
2.8–3.7 |
— |
— |
|
Cordierite (dense) |
C-410 |
1.5–2.5 |
1.5–2.5 |
— |
— |
— |
|
Zircon (dense) |
— |
7 |
6 |
4 |
3.5 |
— |
|
Clay-based refractories |
C-512 |
2–3 |
2–3 |
2–3 |
2–3 |
— |
|
Mullite |
C-610 |
2–6 |
2–6 |
— |
— |
— |
|
|
|
|
|
|
|
|
|
Oxides: |
|
|
|
|
|
|
|
Alumina (>99.5%)† |
C-799 |
33 |
29 |
12 |
9 |
7 |
|
Alumina 95%† |
C-795 |
23 |
13 |
9 |
6 |
5 |
|
Alumina 90%† |
C-786 |
17 |
12 |
7 |
5 |
4 |
|
Alumina 85% |
C-780 |
15 |
12 |
7 |
4 |
— |
|
Beryllia > 99.5% |
C-810 |
300 |
220 |
70 |
18 |
14 |
|
Magnesia (30%
porous)† |
C-820 |
10–14 |
5–8 |
— |
— |
— |
|
Thoria (sintered) |
— |
8–10 |
6–8 |
3–5 |
2–3 |
— |
|
Titania (sintered) |
C-310 |
2.5–4 |
— |
— |
— |
— |
|
Urania (sintered) |
— |
8–10 |
6.8 |
4–5 |
2–3 |
2 |
|
Zirconia (stabilised) |
C-830 |
1.7–2.0 |
1.7–2.0 |
1.7–2.0 |
1.7–2.2 |
1.8–3.3 |
|
|
|
|
|
|
|
|
† Values at high
temperatures are influenced by radiation transmission.
For further information on refractory materials consult
Morrell (1985). For further information on the thermal conductivities of
solid materials generally at high temperatures see, for example, Powell
(1954).
Thermal conductivities of miscellaneous
solids
The values below are for normal temperature, except
where stated (K) and should be regarded as average values for the type of
material specified. Values for the commoner polymers will be found in
section
3.11.1.
|
Substance |
λ/(W
m−1 K−1) |
|
|
|
|
Asbestos cloth |
0.125 |
|
,, insulating
board |
0.11 |
|
,, paper |
0.104 |
|
,, wool |
0.055 |
|
Beeswax |
0.25 |
|
Bitumen |
0.17 |
|
Brick (dry) |
0.8–1.2 |
|
Cardboard |
0.21 |
|
Charcoal |
0.2 |
|
Coal (1400) |
0.2 |
|
Concrete* |
|
|
cellular |
0.1–0.2 |
|
lightweight aggregate |
0.2–0.6 |
|
dense |
0.6–1.8 |
|
Cotton wool |
0.03 |
|
Cork, baked slab |
0.038–0.046 |
|
,, granular
|
0.04 |
|
Diatomaceous powder |
0.07 |
|
Ebonite, solid |
0.17 |
|
,, cellular |
0.03 |
|
Felt |
0.04 |
|
Fibreboard, insulating |
0.055 |
|
,, hardboard |
0.125 |
|
Glass, borosilicate crown |
1.1 |
|
,, double
extra dense flint |
0.55 |
|
Glass, light flint |
0.85 |
|
,,
Pyrex |
1.1 |
|
Glass, mineral, ceramic fibre:** |
|
|
wool blanket |
0.035–0.07 |
|
rigid board |
0.030–0.036 |
|
Ice (268) |
2.3 |
|
,, (173) |
3.9 |
|
Kapok |
~ 0.035 |
|
Mica |
0.6–0.7 |
|
Paper |
~ 0.06 |
|
Paraffin wax |
0.25 |
|
Plasterboard (gypsum) |
~ 0.16 |
|
Plasticine |
0.65–0.8 |
|
Plastics, solid (see sec 3.11.1) |
|
|
Plastics, cellular: (varies with |
|
|
density) |
0.031–0.037 |
|
phenolic foam board |
0.031–0.038 |
|
polystyrene, expanded board |
0.035–0.055 |
|
polystyrene, expanded beads |
|
|
polyurethane, gas-filled board |
0.017–0.020 |
|
(fresh) |
|
|
polyurethane, gas-filled |
0.027 |
|
board
(aged) |
|
|
polyvinyl chloride, rigid
foam |
|
|
board |
0.035–0.041 |
|
urea formaldehyde foam
|
0.030–0.032 |
|
Plywood |
0.125 |
|
Pyrophyllite, normal to |
|
|
plane |
~ 2.0 |
|
Rubber, cellular* |
~ 0.045 |
|
,, natural |
~ 0.15 |
|
,, silicone |
0.25–0.4 |
|
Sand, silver |
0.3–0.4 |
|
Silica aerogel powder* |
0.024 |
|
Soil, clay |
~ 1.1 |
|
Timber, ordinary |
0.14–0.17 |
|
,, balsa |
0.055 |
|
Vermiculite granules |
~ 0.065 |
|
Wool |
~ 0.05 |
|
|
|
|
|
|
| |
|
Thermal conductivites of liquids
Values below are for the thermodynamic
temperature (K) shown in brackets. Linear relationships mostly hold for range
covered. Liquid metal values are given in the table Thermal conductivities of metallic elements.
|
Liquid |
λ/(W
m−1 K−1) |
Liquid |
λ/(W
m−1 K−1) |
|
|
|
|
|
|
Acetone . . . . . |
0.198 (193), 0.146 (333) |
Glycerine . . . . . |
0.286 (273), 0.292 (333) |
|
Aniline
. . . . . |
0.172 (293) |
Medicinal paraffin |
0.127 (273), 0.125 (423) |
|
Argon . . . . . |
0.1260 (84.2), 0.1216 (87.3) |
Methane . . . . . |
0.2153 (93.2), 0.1964 (108.2) |
|
Benzene . . . . . |
0.147 (293), 0.137 (323) |
Methyl alcohol . . |
0.223 (233), 0.186 (333) |
|
n-Butyl alcohol |
0.167 (213), 0.106 (353) |
Nitrogen . . . . . |
0.1511 (69.1), 0.1480 (71.4) |
|
Carbon monoxide |
0.1589 (72.0), 0.1421 (80.8) |
Oil,
cylinder . . . . |
0.152 (293), 0.142 (473) |
|
Carbon tetrachloride |
0.115 (253), 0.102 (333) |
,, transformer . . |
0.136 (273), 0.127 (373) |
|
Dichlorodifluoro- |
|
n-Propyl alcohol |
0.168 (233), 0.148 (353) |
|
methane . . . . |
0.09 (253), 0.073 (293) |
Toluene . . . . . |
0.159 (193), 0.119 (353) |
|
Ethyl alcohol . . . |
0.189 (233), 0.150 (353) |
Water . . . . . . |
0.561 (273), 0.673 (353) |
|
Ethyl benzene . . |
0.152 (193), 0.117 (353) |
|
0.686 (378–433), 0.598 (542) |
|
Ethyl glycol . . . |
0.252 (273), 0.264 (373) |
Xenon . . . . . . |
0.07 (173), 0.05 (223) |
| |
|
|
|
Thermal conductivities of some liquids and their
vapours (λ/(W
m−1 K−1))
In the table below the thermal
conductivities of liquids at their equilibrium saturation pressure are compared
with the values for their dilute vapours at the same temperatures.
|
|
|
|
|
|
|
|
|
Temperature/K |
4 |
20 |
90 |
298 |
373 |
683 |
|
|
|
|
|
|
|
|
|
Vapour |
1.25 × 10−4 |
0.0145 |
0.0057 |
0.0070 |
0.0217 |
— |
|
Liquid |
0.0275 |
0.1178 |
0.1198 |
0.1463 |
0.6819 |
0.425 |
|
|
|
|
|
|
|
|
Thermal conductivities of gases
The thermal conductivity of a gas is
independent of pressure at normal pressures. It increases at high pressures and
decreases at low pressures, e.g. for air below about 1 mm Hg. Values are given
for a pressure of 1 atm.
|
λ/(10−2 W
m−1K−1) |
|
Gas |
Temperature/K |
Gas |
Temperature/K |
|
73.2 |
173.2 |
273.2 |
373.2 |
1273.2 |
173.2 |
273.2 |
373.2 |
1273.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Argon |
— |
1.09 |
1.63 |
2.12 |
5.0 |
Air |
1.58 |
2.41 |
3.17 |
7.6 |
|
Bromine |
— |
— |
0.4 |
0.6 |
— |
Ammonia |
— |
2.18 |
3.38 |
— |
|
Chlorine |
— |
— |
0.79 |
1.15 |
— |
Carbon dioxide |
— |
1.45 |
2.23 |
7.9 |
|
Fluorine |
— |
1.56 |
2.54 |
3.47 |
— |
Carbon monoxide |
1.51 |
2.32 |
3.04 |
— |
|
Helium |
5.95 |
10.45 |
14.22 |
17.77 |
41.9 |
Ethane |
— |
1.80 |
— |
— |
|
Hydrogen |
5.09 |
11.24 |
16.82 |
21.18 |
— |
Ethylene |
— |
1.64 |
— |
— |
|
Krypton |
— |
0.57 |
0.87 |
1.15 |
2.9 |
R12(CF2Cl2) |
— |
0.85 |
1.35 |
— |
|
Neon |
1.74 |
3.37 |
4.65 |
5.66 |
12.8 |
Hydrogen sulphide |
— |
1.2 |
— |
— |
|
Nitrogen |
— |
1.59 |
2.40 |
3.09 |
7.4 |
Methane |
1.88 |
3.02 |
— |
— |
|
Oxygen |
— |
1.59 |
2.45 |
3.23 |
8.6 |
Nitric oxide |
1.54 |
2.38 |
— |
— |
|
Radon |
— |
— |
0.33 |
0.45 |
— |
Nitrous oxide |
— |
1.51 |
— |
— |
|
Xenon |
— |
0.34 |
0.52 |
0.70 |
1.9 |
Sulphur dioxide |
— |
0.77 |
— |
— |
|
|
|
|
|
|
|
Water vapour |
— |
1.53 |
2.35 |
— |
|
|
|
|
|
|
|
|
|
|
|
|
References
J. G. Hust and A. F. Clark (1971) The Lorentz ratio as
a tool for predicting the thermal conductivity of metals and alloys, Mat.
Research and Standards, 11(8), 22–24. R. Morrell (1985)
Handbook of Properties of Technical and Engineering Ceramics, Part
1, HMSO, London. R. W. Powell (1954) Thermal conductivities of solid
materials at high temperatures, Research, 7, 492–501.
R. W. Powell (1965) Correlation of metallic thermal and electrical
conductivities for both solid and liquid phases, Int. J. Heat and Mass
Transfer, 8, 1033–1045. Y. S. Touloukian, R. W. Powell,
C. Y. Ho and P. G. Klemens (1970a) Thermophysical Properties of Matter
Volume 1: Thermal Conductivity: Metallic Elements and
Alloys, IFI/Plenum Data Corp., New York, Washington. Y. S. Touloukian,
R. W. Powell, C. Y. Ho and P. G. Klemens (1970b) Thermophysical Properties
of Matter Volume 2: Thermal Conductivity: Nonmetallic
Solids, IFI/Plenum Data Corp., New York, Washington. Y. S. Touloukian,
P. E. Liley and S. C. Saxena (1970c) Thermophysical Properties of Matter
Volume 3: Thermal Conductivity: Nonmetallic Liquids and
Gases, IFI/Plenum Data Corp., New York, Washington.
R.Morrell
|
 |