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On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach
- Publication Year :
- 2024
-
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.<br />Comment: 32 pages, 11 figures
- Subjects :
- Physics - General Physics
Physics - Optics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.13852
- Document Type :
- Working Paper