Transient line source method Heating curve of a line source TK04 uses the widely-used transient line source method. A long and thin heating source is brought in contact with the sample and is heated with constant power, while simultaneously the temperature of the source is registered. The slower the source temperature rises, the higher is the thermal conductivity of the sample material.

Half-space and full-space method Full-space and half-space probe There are two different implementations of the measuring principle: the full-space and the half-space method. A full-space source is inserted into the sample and hence is completely surrounded by the sample material while a half-space source is positioned on the sample surface in one-sided contact with the material. Few instruments on the market, among them TK04, are able to use both methods. We offer interchangeable probes of both types for our instrument.

Basic principle of analytical evaluation TK04 uses an analytical method for evaluating the data. Analytical methods for determining thermal conductivity are based on the theoretical solution of the heat equation for a constantly heated line source surrounded by sample material on all sides. The heat equation is a differential equation describing the spatiotemporal variation of temperature in the probe and the sample.

The solution of the heat equation yields a formula for the temperature rise inside the heating source which contains (among others) the thermal conductivity of the sample as parameter. The theoretical curve is fitted to the measured temperature curve and the thermal conductivity value is calculated from the fit coefficients. In contrast to empirical methods, analytical methods yield absolute values and hence do not require reference standards or calibration tests.

Practical application For practical applications approximate solutions are used whose accuracy depends (among other factors) on how far the analytical solution is simplified. The common approximation method simply considers the temperature rise as linear if plotted against a logarithmic time scale. Evaluation is very easy and accuracy is often sufficient for non-scientific purposes.

Newly developed high precision method TK04 instead uses a newly developed higher order approximation method taking into account the characteristic nonlinear curve form of real temperature curves. Evaluation with the new method is more complex, but achieves excellent accuracy (± 2%). Additionally, a comparison of the curve forms of the theoretical and the measured temperature rise permits detection of typical disturbing effects (like bad contact between probe and sample) based on the measuring data.

Improvements in evaluating half-space tests Usually, half-space tests are evaluated using the same method as for full-space tests. For a half-space test, the calculated thermal conductivity value is multiplied by 2, because the generated heat amount only spreads in a half space to one side of the heating source, while the other half space is replaced by a probe body made of heat insulating material. It is assumed that the heating power is absorbed completely by the sample half space.

Heat distribution in probe and sample in half-space tests In practice, the probe material is no ideal thermal insulator, hence part of the generated heat will enter into the probe body. The resulting error increases the smaller the difference in thermal conductivity between sample body and probe material. For this reason, transient half-space tests show systematically elevated values compared to steady state tests. If the thermal conductivity of the probe body is 0.18 W/mK, samples around 1 W/mK already show an additional systematic error of approx. +10%. Existing attempts to subsequently correct this effect have been unsatisfying, because the correction not only depends on the thermal conductivity of the sample, but on the properties of the particular probe as well. From the thermal parameters of the probe body and the sample material, TK04 determines the heat loss into the probe half space and corrects the heating power to the amount effectively entering into the sample, guaranteeing identical results from half-space and full-space tests within the measuring accuracy.

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