以磁纳米粒子为热源的双相滞后热传输
Dual-Phase-Lag Heat Transfer with Magnetic Nanoparticles as Heat Source
DOI: 10.12677/MOS.2020.93021, PDF,    科研立项经费支持
作者: 孙逸尧, 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；磁纳米粒子；分离变量法；滞后参数；Dual-Phase-Lag Heat Transfer Model； Magnetic Nanoparticles； Method of Separation of Variables； Lag Parameters
摘要: 磁感应热疗逐渐成为肿瘤治疗的热点领域。本文研究了以磁纳米粒子为热源的双相滞后传热模型。引入了描述温度和热流量的两个滞后参数τt和τq对Pennes热传导方程进行修正。利用分离变量法对修正的方程进行求解，得到温度的解析解，并分析了不同磁化率和磁场频率对温度分布的影响。结果表明，当磁化率或磁场频率增加，会使磁纳米粒子产生更多的热量，同时温度也会有所升高。此外，当无量纲时间为0.7左右时温度达到最大值。本研究对于磁流体热疗具有一定的理论指导作用。
Abstract: Magnetic induction hyperthermia has gradually become a hot field of tumor therapy. In this paper, a dual-phase-lag heat transfer model with magnetic nanoparticles as the heat source is studied. Two time-lag parameters τt and τq, describing temperature and heat flux lag times respectively, are introduced to modify Pennes heat conduction equation. The method of separation of variables is used to solve the modified equation. The analytical solution of temperature is obtained, and the influence of magnetic susceptibility and external magnetic field frequency on the temperature distribution is analyzed. The results show that as the magnetic susceptibility or the magnetic field frequency increases, the magnetic nanoparticles will generate more heat, and the temperature will also increase. Moreover, the temperature has a peak when dimensionless time is about 0.7. This study has some theoretical importance of magnetic induction hyperthermia.
文章引用：孙逸尧, 菅永军. 以磁纳米粒子为热源的双相滞后热传输[J]. 建模与仿真, 2020, 9(3): 195-205. https://doi.org/10.12677/MOS.2020.93021

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