Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source

Abstract We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$ P 1 and $$P_3$$...

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Autores principales:	Dominik Reitzle, Simeon Geiger, André Liemert, Alwin Kienle
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/554cdde4eb1e44ecbf26be97842b2749
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spelling	oai:doaj.org-article:554cdde4eb1e44ecbf26be97842b27492021-12-02T16:45:11ZSemianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source10.1038/s41598-021-87030-32045-2322https://doaj.org/article/554cdde4eb1e44ecbf26be97842b27492021-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-87030-3https://doaj.org/toc/2045-2322Abstract We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$ P 1 and $$P_3$$ P 3 approximations to the radiative transfer equation with closed form expressions for eigenvalues and eigenvectors, yielding a quickly computable solution, while the heat conduction was modeled by the Fourier equation. The solution was compared to a numerical solution using a Monte Carlo simulation for the light propagation and an FEM method for the heat conduction. The results showed that using the $$P_3$$ P 3 solution for the light propagation offers a large advantage in accuracy with only a moderate increase in calculation time compared to the $$P_1$$ P 1 solution. Also, while the $$P_3$$ P 3 solution is not a very good approximation for the spatially resolved absorbance itself, its application as a source term for the heat conduction equation does yield a very good approximation for the time-dependent temperature.Dominik ReitzleSimeon GeigerAndré LiemertAlwin KienleNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Dominik Reitzle Simeon Geiger André Liemert Alwin Kienle Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
description	Abstract We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$ P 1 and $$P_3$$ P 3 approximations to the radiative transfer equation with closed form expressions for eigenvalues and eigenvectors, yielding a quickly computable solution, while the heat conduction was modeled by the Fourier equation. The solution was compared to a numerical solution using a Monte Carlo simulation for the light propagation and an FEM method for the heat conduction. The results showed that using the $$P_3$$ P 3 solution for the light propagation offers a large advantage in accuracy with only a moderate increase in calculation time compared to the $$P_1$$ P 1 solution. Also, while the $$P_3$$ P 3 solution is not a very good approximation for the spatially resolved absorbance itself, its application as a source term for the heat conduction equation does yield a very good approximation for the time-dependent temperature.
format	article
author	Dominik Reitzle Simeon Geiger André Liemert Alwin Kienle
author_facet	Dominik Reitzle Simeon Geiger André Liemert Alwin Kienle
author_sort	Dominik Reitzle
title	Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
title_short	Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
title_full	Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
title_fullStr	Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
title_full_unstemmed	Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
title_sort	semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/554cdde4eb1e44ecbf26be97842b2749
work_keys_str_mv	AT dominikreitzle semianalyticalsolutionforthetransienttemperatureinascatteringandabsorbingslabconsistingofthreelayersheatedbyalightsource AT simeongeiger semianalyticalsolutionforthetransienttemperatureinascatteringandabsorbingslabconsistingofthreelayersheatedbyalightsource AT andreliemert semianalyticalsolutionforthetransienttemperatureinascatteringandabsorbingslabconsistingofthreelayersheatedbyalightsource AT alwinkienle semianalyticalsolutionforthetransienttemperatureinascatteringandabsorbingslabconsistingofthreelayersheatedbyalightsource
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Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source

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