Discontinuity waves in temperature and diffusion models

IF 1.9 4区 工程技术 Q3 MECHANICS
Michele Ciarletta , Brian Straughan , Vincenzo Tibullo
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引用次数: 0

Abstract

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate.

温度和扩散模型中的不连续波
我们分析了双曲扩散系统中的冲击波行为,该系统具有一般的强迫项,在性质上与逻辑增长项并无不同。振幅行为非常有趣,并严重依赖于强迫项中的一个参数。我们还对与温度演变耦合的双曲扩散理论进行了全非线性加速波分析。我们考虑了一个刚体,并证明了三维波存在快波和慢波。对于一维(平面)波,振幅方程是精确推导出来的,而对于进入恒定温度和溶质浓度区域的波,振幅是可以求出的。对这一分析进行了归纳,以考虑塞尔科夫-施纳肯伯格或阿尔古鲁-欧立方反应类型的强迫项。我们简要考虑了存在两种溶质的热传导理论中的非线性加速波,结果是一个包含温度方程和两种溶质浓度方程的模型。在这里,我们可以看到三种波的传播。
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来源期刊
CiteScore
4.10
自引率
4.20%
发文量
114
审稿时长
9 months
期刊介绍: Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.
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