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 < | |