A theoretical model for the photoacoustic signal with an analytical solution for the open photoacoustic cell technique is performed. The thermal diffusion (TD) and thermoelastic bending (TE) contributions from the sample and window of the open-cell are considered in the model. The analytical solution was submitted to simulations varying the thermal diffusivity, optical absorption coefficient, thickness and the amplitudes of the TD and TE contributions. The proposed theoretical model was applied to experimental data from different glasses, and quantitative analysis was achieved by calibrating the PA signal based on the TD and TE in an aluminum foil. The results demonstrate the reliability of the analytical solution for determining the thermal diffusivity of the samples.

We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption–desorption processes. We use the Green function approach to obtain solutions and evaluate the spreading of the system to show a rich class of behaviors. We also connect the results obtained with the anomalous diffusion processes.

In this work, we developed a theoretical model with anomalous thermal diffusion by considering the modified Generalized Cattaneo Equations (GCEs) of Compte and Metzler, GCEI and GCEII, merged in a single operator by a linear combination in function of the fractional derivative order. This operator was compared with the generalization of Youssef for GCEIII. The range of the superdiffusive and subdiffusive regions was determined through phase velocity. In conclusion, both operators present unexpected sub- and superdiffusive intervals. Moreover, the temperature variation due to the heating by a pulsed light beam was determined. At the end, the photoacoustic signal for opaque samples was simulated varying the relaxation time and the fractional-order derivative.