### What is the transient hot wire method?

The transient hot wire (THW) method is the original version of the transient line source method, and offers advantages over its probe-based counterpart. The transient hot wire method uses the same principles as other transient methods to measure thermal conductivity; namely a current carrying wire, and a changing resistance due to a rise in temperature. The specific heat capacity and thermal diffusivity can also be measured with this instrument, although at a lower accuracy than thermal conductivity. The transient hot wire method is best used for isotropic and anisotropic pastes and fluids with thermal conductivities between 0.05 and 5 W/mK, and from sub-zero temperatures to approximately 1500 °C.

### Measurements with the transient hot wire

Similar to the transient line source, certain aspects of the theoretical calculations must be approximated when the transient hot wire is applied to real-world applications. For example, wires and cylinders that are theoretically infinitely long must be quantified so that heat flow does not extend past the edges of the samples. Also, convective heat transfer must be minimized in real world applications, which is accomplished by taking measurements over short time intervals. This coincides nicely with the short measurement times that are required to contain heat within the boundaries of the sample.

### Mathematical considerations of the transient hot wire method

The mathematics behind the transient hot wire and line source methods are much simpler than those used for the transient plane source technique. 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 $$t$$ is 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 $$K$$, given

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

Corrections can be made to this equation by accounting for the diameter of the wire. More often than not, transient hot wire devices contain a wheatstone bridge to improve the accuracy of resistance measurements.  A Wheatstone bridge is used to improve accuracy and precision during measurements by calculating the voltage drop from a change in resistance, due to a change in temperature. Platinum is often chosen as the heating wire material, because the wire used to carry current is a supposed perfect conductor.

Compared to the transient line source method, the transient hot wire method produces more accurate and reproducible results, and can also be used to measure diffusivity. Due to the exposed wire, great care must be taken when handling this instrument, and measurements should not be conducted on solid or high viscosity materials.

The transient hot wire provides accurate thermal conductivity measurements, in the order of 5% or better. When proper corrections are applied to the thermal diffusivity measurements, they will be accurate within 10%. These corrections stem from deviations between real-world experiments and theoretical scenarios.

### Internationally recognized standards

The transient hot wire method follows the ASTM Standard D7896, which is the standard test method for measuring thermal conductivity, thermal diffusivity, and the specific heat capacity of engine coolants and various other fluids.