Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

In this work, the relaxation parameter (<i>τ</i>) and fractionality order (<i>α</i>) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are c...

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Autores principales:	Piran Goudarzi, Awatef Abidi, Seyed Abdollah Mansouri Mehryan, Mohammad Ghalambaz, Mikhail A. Sheremet
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	inverse fractional non-Fourier fractional heat conduction parameter estimations tissues Chemical technology TP1-1185 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/b5cdad053e284eff883469717254445d
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spelling	oai:doaj.org-article:b5cdad053e284eff883469717254445d2021-11-25T18:50:00ZEstimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues10.3390/pr91118772227-9717https://doaj.org/article/b5cdad053e284eff883469717254445d2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-9717/9/11/1877https://doaj.org/toc/2227-9717In this work, the relaxation parameter (<i>τ</i>) and fractionality order (<i>α</i>) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are chosen as the studied cases; single and three-layer skin tissues. Single-layer skin is exposed to laser radiation having the constant heat flux of <i>Q<sub>in</sub></i>. However, a heat pulse with constant temperature is imposed on the three-layer skin. The required inputs for the inverse problem in the fractional diffusion equation are chosen from the outcomes of the dual phase lag (DPL) theory. The governing equations are solved numerically by utilizing implicit approaches. The results of this study showed the efficiency of the CGIM to estimate the unknown parameters in the FSPL model. In fact, obtained numerical results of the CGIM are in excellent compatibility with the FSPL model.Piran GoudarziAwatef AbidiSeyed Abdollah Mansouri MehryanMohammad GhalambazMikhail A. SheremetMDPI AGarticleinverse fractional non-Fourierfractional heat conductionparameter estimationstissuesChemical technologyTP1-1185ChemistryQD1-999ENProcesses, Vol 9, Iss 1877, p 1877 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	inverse fractional non-Fourier fractional heat conduction parameter estimations tissues Chemical technology TP1-1185 Chemistry QD1-999
spellingShingle	inverse fractional non-Fourier fractional heat conduction parameter estimations tissues Chemical technology TP1-1185 Chemistry QD1-999 Piran Goudarzi Awatef Abidi Seyed Abdollah Mansouri Mehryan Mohammad Ghalambaz Mikhail A. Sheremet Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
description	In this work, the relaxation parameter (<i>τ</i>) and fractionality order (<i>α</i>) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are chosen as the studied cases; single and three-layer skin tissues. Single-layer skin is exposed to laser radiation having the constant heat flux of <i>Q<sub>in</sub></i>. However, a heat pulse with constant temperature is imposed on the three-layer skin. The required inputs for the inverse problem in the fractional diffusion equation are chosen from the outcomes of the dual phase lag (DPL) theory. The governing equations are solved numerically by utilizing implicit approaches. The results of this study showed the efficiency of the CGIM to estimate the unknown parameters in the FSPL model. In fact, obtained numerical results of the CGIM are in excellent compatibility with the FSPL model.
format	article
author	Piran Goudarzi Awatef Abidi Seyed Abdollah Mansouri Mehryan Mohammad Ghalambaz Mikhail A. Sheremet
author_facet	Piran Goudarzi Awatef Abidi Seyed Abdollah Mansouri Mehryan Mohammad Ghalambaz Mikhail A. Sheremet
author_sort	Piran Goudarzi
title	Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
title_short	Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
title_full	Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
title_fullStr	Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
title_full_unstemmed	Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues
title_sort	estimating relaxation time and fractionality order parameters in fractional non-fourier heat conduction using conjugate gradient inverse approach in single and three-layer skin tissues
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b5cdad053e284eff883469717254445d
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Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

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