Convolved energy variational principle in heat diffusion

B.T. Darrall; G.F. Dargush

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Convolved energy variational principle in heat diffusion

机译：热扩散中的复杂能量变分原理

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摘要

One of the major, long-standing challenges in analytical mechanics involves the inability to address systems with dissipation in a rigorous manner. In this paper, we overcome that difficulty by formulating a novel temperature-based stationary variational principle for transient heat diffusion based upon a temporal convolution operator and fractional derivatives. The associated Euler-Lagrange equations provide the governing heat equation, along with the initial conditions on temperature and specified heat flux boundary conditions. A further integration-by-parts then leads to a formulation that is somewhat less symmetric but can be written without introducing fractional calculus. Finally, the resulting principle is used to solve two basic one-dimensional problems, as an illustration of a Ritz-type approach.

机译：分析力学中的主要长期挑战之一涉及以严格的方式消散的系统无法解决。在本文中，我们通过基于时间卷积算子和分数衍生物制定用于瞬态热扩散的新型温度的静止变分原理来克服该难度。相关的Euler-Lagrange方程提供控制热方程，以及温度和特定热通量边界条件的初始条件。然后，逐个部分地导致配方略微对称，但可以在不引入分数微积分的情况下写入。最后，由此产生的原理用于解决两个基本的一维问题，作为ritz型方法的图示。

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来源
《International Journal of Heat and Mass Transfer》 |2021年第8期|121315.1-121315.8|共8页
作者
B.T. Darrall; G.F. Dargush;
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作者单位

Department of Mechanical & Aerospace Engineering University at Buffalo The State University of New York Buffalo NY 14260;

Department of Mechanical & Aerospace Engineering University at Buffalo The State University of New York Buffalo NY 14260;

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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 diffusion; Variational methods; Hamilton's principle; Euler-Lagrange equations; Fractional calculus; Convolved energy;

机译：热扩散;变分方法;汉密尔顿的原则;euler-lagrange方程;分数微积分;卷绕能量;

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Convolved energy variational principle in heat diffusion

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