Thermal Conductivity Measurement
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:
flux = thermal conductivity* temperature difference
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 |
| 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 |
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 T (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 = density * 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.
thermal diffusuivity = thermal conductivity/ density * Cp
The thermal diffusivity ( 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
The Hukseflux product range includes several measurement systems.
One category are needle probes. The primary focus of the TP02 design is for laboratory experiments measuring in soils and foodstuff.
More details about the measurement principle can be found in non-steady state probe science and in the product manuals.
The THASYS and THISYS systems are steady-state systems, specially designed for measurements of plastics, composites, thin films.
Non-Steady-State Probe Science
Hukseflux is specialised in design and manufacture of non-steady-state (hot wire, needle) probes for thermal conductivity measurement. Main applications are in soil thermal resistivbity measurments, analysis of foodstuff, powders, slurries etc.
All non-steady-state probes are based on the same phenomenon: that one can determine the thermal conductivity of a medium from the temperature response to heating. After an initial transition period, the temperature rise close to the heater depends only on the thermal conductivity of the surrounding medium, and no longer on heat capacity. Generally, this method avoids the necessity of reaching a real thermal equilibrium with constant temperatures. Non-steady-state techniques are fast and also there is no need for careful sample preparation. Sensors based on this principle are therefore suitable for quick experiments and also for field use.
Some conventional sensor designs have a temperature measurement at a large distance from the heater (typically some centimeters away, sometimes using a physically separated heater and probe). Other designs measure the temperature rise of the heater itself.
The central equation governing these probes is determined by the temperature field around a heating wire that is switched on at t = 0 remaining constant from that moment on:
Below we treat the working principle of TP02 (also that of STP01) and of TP01.
TP01 and STP01 are generally used in long term monitoring as part of meteorological field observations.
TP02 is typically used as a sensor for analysis of soil samples and foodstuff in the laboratory. If necessary, TP02 can also be used in field experiments.