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, Q ˙ ( W / m 2 ) {\displaystyle {\dot {Q}}(W/m^{2})} , to a sample with a surface area, A ( m 2 ) {\displaystyle A(m^{2})} , and thickness, x ( m ) {\displaystyle x(m)} ; once the sample's steady-state temperature is reached, the difference in temperature, Δ T {\displaystyle \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 {\displaystyle k} :
Q ˙ = − k Δ T x {\displaystyle {\dot {Q}}=-k{\frac {\Delta T}{x}}}
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. 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
… excerpt ends here. Continue reading the full article.
