Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives

Sergio M. Pineda; Gerardo Diaz; Carlos F. M. Coimbra

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Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives

机译：使用参数分数阶导数逼近有限域中的瞬态一维电导

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A solution to the problem of transient one-dimensional heat conduction in a finite domain is developed through the use of parametric fractional derivatives. The heat diffusion equation is rewritten as anomalous diffusion, and both analytical and numerical solutions for the evolution of the dimensionless temperature profile are obtained. For large slab thicknesses, the results using fractional order derivatives match the semi-infinite domain solution for Fourier numbers, Foe.[0,l 116]. For thinner slabs, the fractional order solution matches the results obtained using the integral transform method and Green's function solution for finite domains. A correlation is obtained to display the variation of the fractional order p as a function of dimensionless time (Fo) and slab thickness (0 at the boundary £=0.

机译：通过使用参数分数导数，可以解决有限域中瞬态一维热传导问题。将热扩散方程式改写为反常扩散，并获得了无因次温度分布演化的解析解和数值解。对于大板坯厚度，使用分数阶导数的结果与傅里叶数Foe。[0,1 116]的半无限域解匹配。对于较薄的平板，分数阶解与使用积分变换法和有限域格林函数解所获得的结果相匹配。获得相关性以显示分数阶p的变化与无量纲时间（Fo）和板坯厚度（边界£= 0处的0）的关系。

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来源
《Journal of Heat Transfer》 |2011年第7期|p.9-14|共6页
作者
Sergio M. Pineda; Gerardo Diaz; Carlos F. M. Coimbra;
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作者单位

School of Engineering,University of California,5200 North Lake Rd.,Merced, CA 95343;

School of Engineering,University of California,5200 North Lake Rd.,Merced, CA 95343;

School of Engineering,University of California,5200 North Lake Rd.,Merced, CA 95343;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
heat conduction; finite domain; fractional derivatives; anomalous diffusion;

机译：导热有限域分数导数异常扩散;

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Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives

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