On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach

L. F. Escamilla-Herrera; J. M. Domínguez-Derramadero; J. E. Alba-Rosales; F. J. García-Rodríguez; O. M. Medina-Cázares; G. Gutiérrez-Juárez

arXiv · 2406.13852

On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach

L. F. Escamilla-Herrera·J. M. Domínguez-Derramadero·J. E. Alba-Rosales·F. J. García-Rodríguez·O. M. Medina-Cázares·G. Gutiérrez-Juárez

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Abstract

In a recent work, assuming a Beer-Lambert optical absorption and a Gaussian laser time profile, the exact solutions for a 1D-photoacoustic(PA)-boundary value problem predict a null pressure for optically strong absorbent materials. To overcome this, a heuristic correction was introduced by assuming that heat flux travels a characteristic length during the duration of the laser pulse\cite{Ruiz-Veloz2021} $\tau_p$. In this work, we obtained exact solutions in the frequency domain for a 1D-boundary-value-problem for the Dual-Phase-Lag (DPL) heat equation coupled with a 1D PA-boundary-value-problem via the wave-equation. Temperature and pressure solutions were studied by assuming that the sample and its surroundings have a similar characteristic thermal lag response time $\tau_{_T}$, which was assumed to be a free parameter that can be adjusted to reproduce experimental results. Solutions for temperature and pressure were obtained for a three-layer 1D system. It was found that for $\tau_{_T}< \tau_{p}$, the DPL temperature has a similar thermal profile of the Fourier heat equation, however, when $\tau_{_T}\ge \tau_{p}$ this profile is very different from the Fourier case. Additionally, via a numerical Fourier transform the wave-like behavior of DPL temperature is explored, and it was found that as $\tau_{_T}$ increases, thermal wave amplitude is increasingly attenuated. Exact solutions for pressure were compared with experimental signals, showing a close resemblance between both data sets, particularly in the time domain, for an appropriated value of $\tau_{_T}$; the transference function was also calculated, which allowed us to find the maximum response in frequency for the considered experimental setup.

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L. F. Escamilla-Herrera, J. M. Domínguez-Derramadero, J. E. Alba-Rosales, F. J. García-Rodríguez, O. M. Medina-Cázares, G. Gutiérrez-Juárez. 2024-06-19. On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach. https://arxiv.org/abs/2406.13852

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