Thermal diffusivity measurements in solids by photothermal infrared radiometry: Influence of convection–radiation heat losses

Abstract

This work demonstrates that in photothermal experiments performed in frequency domain the heat losses due to convection and radiation should be taken into account at low frequencies for poor heat conductors. From a model-solution of the heat diffusion equation a dimensionless frequency dependent parameter M = ZH, with sample's thermal impedance Z and H the convection-radiation heat transfer coefficient, turns out to adequately quantify the importance of the effect of those heat losses. A straightforward photothermal infrared radiometry setup was designed to demonstrate the above hypothesis. Disc shaped samples of different test materials were heated by square wave modulated illumination at one of their surfaces at different frequencies using an amplitude modulated laser beam, and the temperature at the rear surfaces was monitored as a function of time using an infrared sensor. The frequency dependence of peak-to-peak values of the temperature signals was found to be consistent with the amplitude spectrum obtained by Fourier transforming the data. The frequency dependence of the peak-to-peak amplitude was compared with a theoretical model with and without taking convection and radiation induced heat losses (CRHL) into consideration. It is found that for poor heat conductors at low modulation frequencies the conventional model without CRHL does not fit well the experimental data, while the extended model leads to good agreement, resulting in reliable values for the thermal diffusivity. For the investigated samples, the contribution to the signal of thermal wave reflection at the back side of the sample turn out to have a minor effect on the signal spectrum.