Photothermal Response for the Thermoelastic Bending Effect Considering Dissipating Effects by Means of Fractional Dual-Phase-Lag Theory

Abstract

We analyze an extension of the dual-phase lag model of thermal diffusion theory to accurately predict the contribution of thermoelastic bending (TE) to the Photoacoustic (PA) signal in a transmission configuration. To achieve this, we adopt the particular case of Jeffrey’s equation, an extension of the Generalized Cattaneo Equations (GCEs). Obtaining the temperature distribution by incorporating the effects of fractional differential operators enables us to determine the TE effects in solid samples accurately. This study contributes to understanding the mechanisms that contribute to the PA signal and highlights the importance of considering fractional differential operators in the analysis of thermoelastic bending. As a result, we can determine the PA signal’s TE component. Our findings demonstrate that the fractional differential operators lead to a wide range of behaviors, including dissipative effects related to anomalous diffusion.