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Analytical and numerical analysis of time fractional dual-phase-lag heat conduction during short-pulse laser heating

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Abstract

In this study, we analytically and numerically investigate the non-Fourier heat conduction behavior within a finite medium based on the time fractional dual-phase-lag model. Firstly, the time fractional dual-phase-lag model and the corresponding fractional heat conduction equation for short-pulse laser heating is built. Laplace and Fourier cosine transforms are performed to derive the semi-analytical expression of temperature distribution in the Laplace domain. Then, by the L1 approximation for the Caputo derivative, the finite difference algorithm is developed for the short-pulse laser heating problem. The solvability, stability, and convergence of this algorithm are also examined. Meanwhile, the efficiency and accuracy of this method have been verified by using three numerical examples. Finally, based on numerical analysis, we study the non-Fourier heat conduction behavior and discuss the effect of variability of parameters, such as fractional parameter and the ratio between the relaxation and retardation times, on the temperature distribution graphically. We believe that this analysis, besides benefiting the laser heating applications, will also provide a deep theoretical insight to interpret the anomalous heat transport process.

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Funding

This work was supported by the National Nature Science Foundation of China (Grant Nos. 11672163, 11771254), the Natural Science Foundation of Shandong Province (Grant No. ZR2015AM011), and the Fundamental Research Funds for the Central Universities (Grant No. 2019ZRJC002).

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  1. School of Mathematics and Statistics, Shandong University, Weihai, 264209, People’s Republic of China

    Xiaoping Wang, Huanying Xu & Haitao Qi

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  1. Xiaoping Wang
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  3. Haitao Qi
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Correspondence to Haitao Qi.

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Wang, X., Xu, H. & Qi, H. Analytical and numerical analysis of time fractional dual-phase-lag heat conduction during short-pulse laser heating. Numer Algor 85, 1385–1408 (2020). https://doi.org/10.1007/s11075-019-00869-6

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