### What is the transient line source method?

The transient line source (TLS) method works on similar principles as the transient plane source technique, and identical principles as the transient hot wire method. The transient line source method is particularly useful because of its on-the-spot measurement capabilities, and its general ease of use. This technique is most often used to measure the thermal properties of powders and soils with thermal conductivities between 0.05 and 20 W/mK, and over a temperature range of -50 to 500 °C. Although the transient hot wire and transient line source operate under the same principles, the wire of the transient line source is surrounded by a protective casing, so it is more suitable for measuring high density materials.

### Measurements with the transient line source

The transient line source method is based on a transient system, created by a line source of theoretically infinite length, and an infinitesimal radius of heat, in the shape of a cylinder. However, in to real-world testing scenarios, the theoretical infinite lengths of the cylinder must be quantified by measuring the dimensions of the sample, and the theorized infinitesimal radius of heat is approximated by the thin heating wire. It is also necessary to assume that the measured material is isotropic. To satisfy this assumption and preserve local isotropy, measurements must be performed away from any deformities in the sample.

While the transient hot wire method exposes the wire directly to the material being measured, the transient line source method maintains the wire inside a protective steel sleeve. This sleeve shelters the wire from the environment, and allows it to be inserted into a sample without damaging the wire. Measurements can be conducted quickly over multiple locations within the sample because of the rugged needle.

### Mathematical considerations of the transient line source method

The mathematics behind the transient line source and transient hot wire methods are much simpler than those used for the transient plane source method. For an infinitely long and thin wire, the temperature difference due to a constant heat source at radial distance \(r\) from the wire will be,

\[ T = \frac{P}{4\pi K L} \int_{\frac{r^{2}}{4\kappa t}}^{\infty}\frac{e^{-u}du}{u} \]

Where \(\kappa\) is the diffusivity, \(K\) is the thermal conductivity, \(P/L\) is the power from the wire divided by its length, and \(t\) the time passed. For small values of \(r\), or large values of \(t\), this equation can be approximated by,

\[ T = \frac{P}{4 \pi K L}(ln\Big( \frac{4 \kappa t}{r^{2}} \Big)-\gamma) \]

Where \( \gamma \) is Euler’s constant, the limiting difference between the natural logarithm and the harmonic series. For a change in temperature from one time to another, the value will only depend on thermal conductivity. Once values of \(T\) are measured, the system can be solved for \( K \), giving

\[ K = \frac{P}{4 \pi L}\Big( \frac{1}{T_{2}-T_{1}} \Big)ln\frac{t_{2}}{t_{1}} \]

Corrections to this equation can be made by accounting for the diameter of the wire and the resistivity of the protective probe. The change in temperature of the sample is measured by calculating the voltage drop from a change in resistance as the wire emits heat. A resistance temperature detector (RTD) measures the voltage drop, which is then transferred into a resistance value. This value is then used to determine the change in temperature, which is finally used to calculate thermal conductivity.

### Instrument calibration

The transient line source requires multiple calibrations to offset the effects of contact resistance. Three reference materials with known thermal conductivities are used to calibrate the system; the results of these tests are then programmed into the instrument to make measurements user-friendly.

The transient line source method offers reduced accuracy when compared to the similar transient hot wire method, but is a much more versatile instrument. Measurements of thermal conductivity have an accuracy of 5%, which may vary slightly depending on certain parameters including the type of sample material.

### Internationally recognized standards

The transient line source follows the ASTM Standard D5334-14 and IEEE Standard 442-1981, the standard test method for finding the thermal conductivity of soils and soft rock. The transient line source also follows the ASTM Standard D5930, which is the standard test method for finding the thermal conductivity of plastics.

### Additional literature

The following article provides more information on the transient line source.

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