Thermal Conductivity Science
This chapter contains an
overview of "the art of thermal conductivity measurement", focusing on soils
and granular materials. Any suggestions for changes and additions are most welcome.
Thermal conductivity is a
property of materials that expresses the heat flux f (W/m2) that will flow through the material if a certain temperature gradient
DT (K/m) exists over the material.
The thermal conductivity
is usually expressed in W/m.K. and called l. The usual formula is:
f = l * DT
It should be noted that
thermal conductivity is a property that is describes the semi static situation; the
temperature gradient is assumed to be constant. As soon as the temperature starts
changing, other parameters enter the equation.
This immediately explains
why it is so very difficult to measure thermal conductivity. Ideally this would require a
steady state situation. This is far form easy because it usually requires a carefully
planned laboratory experiment and a lot of time to get to an equilibrium.
Orders of magnitude of
the thermal conductivity:
|
|
Thermal
conductivity @20° C
W/mK
|
Density
@20° C
Kg/m3
|
Volumetric heat
capacity @20° C
106
J/m3K
|
Thermal
diffusivity
@20° C
10-8
m2/s
|
|
|
|
|
|
|
Air |
0.025 |
1.29 |
0.001 |
1938 |
|
|
|
|
|
|
Glycerol |
0.29 |
1260 |
3.073 |
9 |
|
Water |
0.6 |
1000 |
4.180 |
14 |
|
Ice |
2.1 |
917 |
2.017 |
104 |
|
Olive oil |
0.17 |
920 |
1.650 |
10 |
|
Gasoline |
0.15 |
720 |
2.100 |
7 |
|
Methanol |
0.21 |
790 |
2.500 |
8 |
|
Silicone oil |
0.1 |
760 |
1.370 |
7 |
|
Alcohol |
0.17 |
800 |
2.430 |
7 |
|
|
|
|
|
|
Aluminium |
237 |
2700 |
2.376 |
9975 |
|
Copper |
390 |
8960 |
3.494 |
11161 |
|
Stainless Steel |
16 |
7900 |
3.950 |
405 |
|
|
|
|
|
|
Aluminium Oxide |
30 |
3900 |
3.413 |
879 |
|
Quartz |
3 |
2600 |
2.130 |
141 |
|
Concrete |
1.28 |
2200 |
1.940 |
66 |
|
Marble |
3 |
2700 |
2.376 |
126 |
|
|
|
|
|
|
Glass |
0.93 |
2600 |
2.184 |
43 |
|
Pyrex 7740 |
1.005 |
2230 |
1.681 |
60 |
|
|
|
|
|
|
PVC |
0.16 |
1300 |
1.950 |
8 |
|
PTFE |
0.25 |
2200 |
2.200 |
11 |
|
Nylon 6 |
0.25 |
1140 |
1.938 |
13 |
|
Corian (ceramic
filled) |
1.06 |
1800 |
2.307 |
46 |
|
|
|
|
|
|
Sand (dry) |
0.35 |
1600 |
1.270 |
28 |
|
Sand
(saturated) |
2.7 |
2100 |
2.640 |
102 |
|
Glass pearls
(dry) |
0.18 |
1800 |
1.140 |
16 |
|
Glass pearls
(saturated) |
0.76 |
2100 |
2.710 |
28 |
|
|
|
|
|
|
Wood |
0.4 |
780 |
0.187 |
214 |
|
Cotton |
0.03 |
-- |
0.001 |
-- |
|
Leather |
0.14 |
-- |
0.001 |
59 |
|
Cork |
0.07 |
200 |
0.047 |
150 |
|
|
|
|
|
|
Foam glass |
0.045 |
120 |
0.092 |
49 |
|
Mineral
insulation materials |
0.04 |
100 |
0.090 |
44 |
|
Plastic
insulation materials |
0.03 |
50 |
0.100 |
30 |
A list of typical
values of thermal properties of various materials.
This list is only indicative.
|
Range of all
reported values for soil |
0.15 to 4 |
|
Saturated soil |
0.6 to 4 |
|
|
|
Sand perfectly
dry |
0.15 to 0.25 |
|
Sand moist |
0.25 to 2 |
|
Sand saturated |
2 to 4 |
|
Clay dry to
moist |
0.15 to 1.8 |
|
Clay saturated |
0.6 to 2.5 |
|
Soil with
organic matter |
0.15 to 2 |
|
|
|
Solid Rocks |
2 to 7 |
|
Tuff (porous
volcanic rock) |
0.5 to2.5 |
|
|
Table 8.6.2 Reported
values, as known to the author, of thermal
conductivity in different soil types in W/mK.
In case of changing
thermal parameters, also the heat capacity C (J/K.m3) starts playing a role.
The heat capacity is again a material property. It expresses the fact that for changing
the temperature DT (K) of a certain
volume V (m3) of material energy E (J) must flow in or out.
The heat capacity is usually linked to the density r (kg/m3) f the material. The heat capacity is usually found in the
textbooks a specific heat capacity Cp (J/K.kg), which must be multiplied by the
density to get the full picture.
C = r * Cp
When dynamic processes
are involved, the change of temperature versus time, at known boundary conditions is
determined by both thermal conductivity and heat capacity.
a = l / r * Cp
The thermal diffusivity a
( m2/s) is always encountered in the equations multiplied by the time t (s).
To give an example: the
thermal diffusivity of building insulation material is of the same order of magnitude as
the thermal diffusivity of concrete, both about 4. 10-7 m2/s. The insulation of
concrete is much less, but it requires much more energy to heat the material itself, so
that the overall "response time" about the same for both materials.
Overview of currently used techniques
Generally speaking, there
are a number of possibilities to measure thermal conductivity, each of them suitable for a
limited range of materials, depending on the thermal properties and the medium
temperature. There can be made a distinction
between Steady-State and Non-Steady-State techniques.
In general the Steady-State techniques perform a
measurement when the material that is analyzed is in
complete equilibrium. This makes the process of signal
analysis very easy (steady state implies constant
signals). The disadvantage generally is that it takes
a long time to reach the required equilibrium.
The
Non-Steady-State techniques perform a measurement
during the process of heating up. The advantage is
that measurements can be made relatively quickly.
Hukseflux measures thermal properties with
the Non-Steady-State Probe technique
The
Hukseflux product range includes two sensors
specifically made for thermal conductivity
measurements. The primary focus of the TP02
design is for laboratory experiments measuring in
soils and foodstuff. The Primary focus of TP01
is in long term installation under the soil, as part
of a meteorological station.
The
TP02 is a needle shaped probe, suitable for repeated
insertion into the medium. It behaves like the needle
designs described in the literature. The TP01 is a
unique Hukseflux design, and in fact a variation on
the needle principle. More details about the measurement
principle can be found in non-steady state probe science
and in the product manuals.
TP01 now is also
available as a turn key system: TPSYS.
In the STP01 Soil Temperature Profile Sensor,
(although it is not specifically designed for high
accuracy measurements of thermal conductivity) there
is an additional possibility to crudely measure soil thermal conductivity at various
depths. This is in the experimental stage. The measurement utilizes the heat-pulse or
non-steady state probe technique.
The technique of
measurement of thermal conductivity using the non-steady state probe or heat pulse, is
special because it does not require a fully steady state. Generally speaking it utilizes
line source heater, and analyses the temperature rise of the heater relative to the
starting temperature, versus time.
Hukseflux measures thermal properties with
the Thin Heater Apparatus
For
the latest development at Hukseflux see THA-SYS.
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