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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.13852 |
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| _version_ | 1866909247114051584 |
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| author | Escamilla-Herrera, L. F. Domínguez-Derramadero, J. M. Alba-Rosales, J. E. García-Rodríguez, F. J. Medina-Cázares, O. M. Gutiérrez-Juárez, G. |
| author_facet | Escamilla-Herrera, L. F. Domínguez-Derramadero, J. M. Alba-Rosales, J. E. García-Rodríguez, F. J. Medina-Cázares, O. M. Gutiérrez-Juárez, G. |
| contents | 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} $τ_p$. 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 $τ_{_T}$, 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 $τ_{_T}< τ_{p}$, the DPL temperature has a similar thermal profile of the Fourier heat equation, however, when $τ_{_T}\ge τ_{p}$ 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 $τ_{_T}$ 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 $τ_{_T}$; the transference function was also calculated, which allowed us to find the maximum response in frequency for the considered experimental setup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach Escamilla-Herrera, L. F. Domínguez-Derramadero, J. M. Alba-Rosales, J. E. García-Rodríguez, F. J. Medina-Cázares, O. M. Gutiérrez-Juárez, G. General Physics Optics 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} $τ_p$. 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 $τ_{_T}$, 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 $τ_{_T}< τ_{p}$, the DPL temperature has a similar thermal profile of the Fourier heat equation, however, when $τ_{_T}\ge τ_{p}$ 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 $τ_{_T}$ 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 $τ_{_T}$; the transference function was also calculated, which allowed us to find the maximum response in frequency for the considered experimental setup. |
| title | On the Dual-Phase-Lag thermal response in the Pulsed Photoacoustic effect: 1D approach |
| topic | General Physics Optics |
| url | https://arxiv.org/abs/2406.13852 |