Thermoelastic Component of Photoacoustic Response Calculated by the Fractional Dual-Phase-lag Heat Conduction Theory

This paper analyzes the influence of the anomalous diffusive effects caused by micro-scale heterogeneity and kinetic and inertial thermal relaxations on the optically induced thermoelastic bending component of the photoacoustic response. We calculated the temperature distribution for a one-dimensional heat transfer problem with planar and periodic excitation, neglecting the influence of thermoelastic strains on the temperature profile. Thermoelastic bending was evaluated using a theoretical approximation of a thin plate, while pressure fluctuations in the photoacoustic cell were obtained by assuming adiabatic changes in the closed air. The model analysis shows that the relaxation processes could significantly affect the mechanical piston component of the photoacoustic response at frequencies higher than the minima of the inverse of two thermal relaxation times, while the influence of micro-scale heterogeneity is observable in the whole frequency range.