Improvement of the mathematical modeling of flash measurements
Jürgen Blumm, Johannes Opfermann
The laser flash technique allows measurement of the thermal diffusivity of solids and liquids up to very high temperatures. Various mathematical models have been developed over the past few decades to analyse the experimental data and to remove the influence of the pulse length of the laser and heat loss effects. The most sophisticated model was established by Cape and Lehman (1963 J. Appl. Phys. 34 1909 – 1913) which considers finite pulse effects as well as facial and radial heat losses. For simplification, various assumptions were made in this work to achieve an analytical solution. Improvements of the assumptions were made by other authors such as Jossell et al (1995 J. Appl. Phys. 78 6867 – 6868). Further improvements are proposed here. For accurate pulse-length correction, the original laser pulse is monitored by the hardware and used in the analysis. Furthermore, some improved approximations were integrated into the model. Finally, higher-order solutions of the mathematical description are considered in the analysis. The improved mathematical model is integrated in the nonlinear regression routine, allowing fitting of experimental data to yield thermal diffusivity values with high accuracy.