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基于分形导数、分数阶导数的新型生物热传递方程

发表时间:2010-02-15  浏览量:2377  下载量:794
全部作者: 孙逸飞,陈文
作者单位: 河海大学工程力学系
摘 要: 基于热力学第一定律与经典Pennes生物热传递方程的基本理论,结合非傅里叶热传导的相关概念,首次提出了2种新的生物组织热传递方程:分形导数、分数阶导数生物热传递方程。选取皮肤组织的分数 阶热传递模型与经典Pennes等模型做了数值比较,结果显示:分数阶导数生物热传递模型是合理的,适当选取阶数α值,可以得到与其他模型极为相近的预测结果;分数阶模型的预测值小于经典Pennes 模型预测值,但α越接近2时,其预测结果越接近于经典Pennes模型;皮肤组织分数阶热传递方程的阶数α的大致取值范围在1.85~2.00之间。
关 键 词: 生物物理学;生物热传递;非傅里叶热传导;分形导数;分数阶导数
Title: A general bio-heat transfer model based on fractal and fractional derivative
Author: SUN Yifei, CHEN Wen
Organization: Department of Engineering Mechanics, Hohai University
Abstract: This paper makes the first attempt to develop differential equation models of bio-heat transfer by using fractal and space-fractional derivative. The new models are based on the first law of thermodynamics and basic theories of the traditional Pennes model. In order to verify the new models' validity, a fractional bio-heat transfer model of the skin tissues is presented. Numerical comparison with the corresponding Pennes and some other models shows that the fractional bio-heat transfer model and the corresponding models can behave similarly by proper choice of fractional derivative order. Results from the fractional model are smaller than those from the Pennes model. Moreover, when the fractional derivative order α approaches to 2, the fractional model and the Pennes model observe very similar. It is also worthy to point out that the fractional derivative order of the bio-heat transfer model of the skin tissues falls between 1.85 and 2.00.
Key words: biophysics; bio-heat transfer; non-Fourier heat conduction; fractal derivative; fractional derivative
发表期数: 2010年2月第3期
引用格式: 孙逸飞,陈文. 基于分形导数、分数阶导数的新型生物热传递方程[J]. 中国科技论文在线精品论文,2010,3(3):231-238.
 
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