Thermal Conductivity Measurement

There are a number of possible ways to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Three classes of methods exist to measure the thermal conductivity of a sample: steady-state, time-domain, and frequency-domain methods.

Steady-state methods

In general, steady-state techniques perform a measurement when the temperature of the material measured does not change with time. This makes the signal analysis straightforward (steady state implies constant signals). The disadvantage is that a well-engineered experimental setup is usually needed.

Steady-state methods, in general, work by applying a known heat flux, $\dot Q (W/m^2)$, to a sample with a surface area, $A(m^2)$, and thickness, $x (m)$; once the sample's steady-state temperature is reached, the difference in temperature, $\Delta T$, across the thickness of the sample is measured. After assuming one-dimensional heat flow and an isotropic medium, Fourier's Law is then used to calculate the measured thermal conductivity, $k$:

:$\dot Q=-k A \frac$

Major sources of error in steady-state measurements include radiative and convective heat losses in the setup, as well as errors in the thickness of the sample propagating to the thermal conductivity.

In geology and geophysics, the most common method for consolidated rock samples is the divided bar. There are various modifications to these devices depending on the temperatures and pressures needed as well as sample sizes. A sample of unknown conductivity is placed between two samples of known conductivity (usually brass plates). The setup is usually vertical with the hot brass plate at the top, the sample in between then the cold brass plate at the bottom. Heat is supplied at the top and made to move downwards to stop any convection within the sample. Measurements are taken after the sample has reached to the steady state (with zero heat gradient or constant heat over entire sample), this usually takes about 30 minutes and over.

Other steady-state methods

For good conductors of heat, Searle's bar method can be used. For poor conductors of heat, Lee's disc method can be used.

Time-domain methods

The transient techniques perform a measurement during the process of heating up. The advantage is that measurements can be made relatively quickly. Transient methods are usually carried out by needle probes.

Non-steady-state methods to measure the thermal conductivity do not require the signal to obtain a constant value. Instead, the signal is studied as a function of time. The advantage of these methods is that they can in general be performed more quickly, since there is no need to wait for a steady-state situation. The disadvantage is that the mathematical analysis of the data is generally more difficult.

Transient hot wire method

The transient hot wire method (THW) is a very popular, accurate and precise technique to measure the thermal conductivity of gases, liquids, solids, nanofluids and refrigerants in a wide temperature and pressure range. The technique is based on recording the transient temperature rise of a thin vertical metal wire with infinite length when a step voltage is applied to it. The wire is immersed in a fluid and can act both as an electrical heating element and a resistance thermometer. The transient hot wire method has advantage over the other thermal conductivity method since there is a fully developed theory and there is no calibration or single-point calibration. Furthermore because of the very small measuring time (1 s) there is no convection present in the measurements and only the thermal conductivity of the fluid is measured with very high accuracy.

The most of the THW sensors used in academia consist of two identical very thin wires with only difference in the length. Sensors using a single wire, are used both in academia and industry with the advantage over the two-wire sensors the ease of handling of the sensor and change of the wire.

An ASTM standard is published for the measurements of engine coolants using a single-transient hot wire method.

Transient plane source method

Transient Plane Source Method, utilizing a plane sensor and a special mathematical model describing the heat conductivity, combined with electronics, enables the method to be used to measure Thermal Transport Properties. It covers a thermal conductivity range of at least 0.01-500 W/m/K (in accordance with ISO 22007-2) and can be used for measuring various kinds of materials, such as solids, liquid, paste and thin films etc. In 2008 it was approved as an ISO-standard for measuring thermal transport properties of polymers (November 2008). This TPS standard also covers the use of this method to test both isotropic and anisotropic materials.

The Transient Plane Source technique typically employs two samples halves, in-between which the sensor is sandwiched. Normally the samples should be homogeneous, but extended use of transient plane source testing of heterogeneous material is possible, with proper selection of sensor size to maximize sample penetration. This method can also be used in a single-sided configuration, with the introduction of a known insulation material used as sensor support.

The flat sensor consists of a continuous double spiral of electrically conducting nickel (Ni) metal, etched out of a thin foil. The nickel spiral is situated between two layers of thin polyimide film Kapton. The thin Kapton films provides electrical insulation and mechanical stability to the sensor. The sensor is placed between two halves of the sample to be measured. During the measurement a constant electrical effect passes through the conducting spiral, increasing the sensor temperature. The heat generated dissipates into the sample on both sides of the sensor, at a rate depending on the thermal transport properties of the material. By recording temperature vs. time response in the sensor, the thermal conductivity, thermal diffusivity and specific heat capacity of the material can be calculated. For highly conducting materials, very large samples are needed (some litres of volume).

Modified transient plane source (MTPS) method

A variation of the above method is the Modified Transient Plane Source Method (MTPS) developed b
Dr. Nancy Mathis
The device uses a one-sided, interfacial, heat reflectance sensor that applies a momentary, constant heat source to the sample. The difference between this method and traditional transient plane source technique described above is that the heating element is supported on a backing, which provides mechanical support, electrical insulation and thermal insulation. This modification provides a one-sided interfacial measurement in offering maximum flexibility in testing liquids, powders, pastes and solids.

Transient line source method

The physical model behind this method is the infinite line source with constant power per unit length. The temperature profile $T(t,r)$ at a distance $r$ at time $t$ is as follows

:$T(t,r) = \frac \mathrm \left( \frac \right)$

where
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:_$k$_is_the_thermal_conductivity_

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