Year: 2023
Author: Cui-Cui Ji, Weizhong Dai, Ronald E. Mickens
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 391–406
Abstract
Phase-lagging equation (PLE) is an equation describing micro/nano scale heat conduction, where the lagging response must be included, particularly under low temperature or high heat-flux conditions. However, finding the analytical or numerical solutions of the PLE is tedious in general. This article aims at seeking a fractional-order heat equation that is a good alternative for the PLE. To this end, we consider the PLE with simple initial and boundary conditions and obtain a fractional-order heat equation and an associated numerical method for approximating the solution of the PLE. In order to better approximate the PLE, the Levenberg-Marquardt iterative method is employed to estimate the optimal parameters in the fractional-order heat equation. This fractional-order alternative is then tested and compared with the PLE. Results show that the fractional method is promising.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1016
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 391–406
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Phase-lagging equation fractional-order heat equation numerical scheme parameter estimation.
Author Details
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