Effect of fractional heat-transport operators on the photoacoustic response of aluminum

Abstract

This work investigates the influence of fractional heat-transport operators on the amplitude and phase delay of the photoacoustic signal measured in aluminum samples under transmission geometry using the rear photoacoustic signal technique at high modulation frequencies. Analytical calculations show that, for metals with extremely short thermal relaxation times, hyperbolic corrections are negligible within the explored frequency window, whereas fractional generalized Cattaneo equations produce a systematic reshaping of the PA response. The best overall agreement with the experimental data is obtained with subdiffusive fractional formulations, which exhibit similar trends and indicate a non-Fourier transport regime over the investigated band, with an effective fractional order below unity (0.7–0.9). These results show that the rear photoacoustic signal technique is sensitive to non-classical heat-transport signatures even in aluminum and that fractional transport models provide a more suitable phenomenological description of the measured response than the classical Fourier framework, particularly at high modulation frequencies.