以磁纳米粒子为热源的分数阶双相滞后热传输
Fractional Order Dual-Phase-Lag Heat Transfer with Magnetic Nanoparticles as Heat Source
DOI: 10.12677/AAM.2020.912270, PDF,   
作者: 赵娟霞, 菅永军*:内蒙古大学数学科学学院,内蒙古 呼和浩特
关键词: 双相滞后模型分数阶导数弛豫时间磁纳米粒子DPL Fractional Derivative Relaxation Time Magnetic Nanoparticles
摘要: 本文通过引入弛豫时间和分数阶导数对Pennes方程进行修正,得到了关于温度分布的双相滞后模型。并以此为基础求解了以磁纳米粒子为热源的传热问题,使用Laplace变化得到温度分布的数值解。本文以图像的方式分析了分数阶导数参数、弛豫时间和外加磁场性质对温度分布的影响。
Abstract: In this paper, the Pennes equation is modified by introducing relaxation time and fractional derivative, and a dual-phase-lag model of temperature distribution is obtained. On this basis, the heat transfer problem with magnetic nanoparticles as the heat source is solved, and the numerical solution of temperature distribution is obtained by using Laplace change. This paper analyzes the effects of fractional derivative parameters, relaxation time and the properties of the external magnetic field on the temperature distribution by figures.
文章引用:赵娟霞, 菅永军. 以磁纳米粒子为热源的分数阶双相滞后热传输[J]. 应用数学进展, 2020, 9(12): 2308-2316. https://doi.org/10.12677/AAM.2020.912270

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