Investigation of thermal diffusivity measurement technique based on photoacoustic signal response under the influence of three-dimesional heat transfer

•A photoacoustic method for measuring thermal diffusivity of thick sample is proposed.•A simulation model to replicate a PA effect on 3-D heat diffusion is developed.•The effect of lateral heat diffusion on the phase lag of the PA signal is examined.•A correlation between PA signal phase lag and sample thermal diffusivity is found.•The effect of heat diffusion of air can be eliminated by using reference sample. In this study, we investigated the feasibility of measuring the thermal diffusivity of thermally thick solid material using the photoacoustic (PA) signal response in a three-dimensional heat diffusion state. For this purpose, we developed a heat conduction simulation model based on cylindrical coordinates to replicate the PA effect on three-dimensional heat diffusion. By numerical analysis, it was found that the phase of PA signal deviates from one-dimensional theory prediction when the lateral heat diffusion of the solid sample reaches the chamber wall of PA cell. Specifically, it was found that the phase lag inflects at the frequency where the sample’s thermal diffusion length μs is 0.91 mm at a chamber radius of 3 mm. By utilizing this correlation, the infection frequency can potentially provide the thermal diffusivity of the thermally thick sample. The experimental validation qualitatively confirmed that the phenomena observed in the numerical analysis occur in practice. However, quantitatively, the experimental results showed discrepancies from the numerical analysis, which is likely due to the influence of the radial distribution of laser intensity. Nonetheless, this issue can be resolved in practical applications through calibration using a reference sample. Numerical analysis suggested that for materials with thermal diffusivity lower than that of air, measuring thermal diffusivity could be seemingly impossible. However, the experimental results demonstrated that calibration with a reference sample having sufficiently lower thermal diffusivity than that of air effectively compensates for the influence of air’s thermal diffusion. The significant factor affecting the accuracy of thermal diffusivity determination with the proposed method is identifying the inflection frequency. It will be necessary to explore an appropriate method for determining the frequency by integrating multiple sources of information, such as simultaneously observing the amplitude of the PA signal.