**Transient Line Source Method**

The physical model behind this method is the infinite line source with constant power per unit length. The temperature profile at a distance at time is as follows

where

- is the power per unit length, in
- is the thermal conductivity of the sample, in
- is the exponential integral, a transcendent mathematical function
- is the radial distance to the line source
- is the thermal diffusivity, in
- is the amount of time that has passed since heating has started, in

When performing an experiment, one measures the temperature at a point at fixed distance, and follows that temperature in time. For large times, the exponential integral can be approximated by making use of the following relation

where

- is the Euler gamma constant

This leads to the following expression

Note that the first two terms in the brackets on the RHS are constants. Thus if the probe temperature is plotted versus the natural logarithm of time, the thermal conductivity can be determined from the slope given knowledge of Q. Typically this means ignoring the first 60 to 120 seconds of data and measuring for 600 to 1200 seconds.

Read more about this topic: Thermal Conductivity Measurement, Transient Methods

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