• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>International Journal of Heat and Mass Transfer >Heat conduction in 1D harmonic crystal: Discrete and continuum approaches
【24h】

Heat conduction in 1D harmonic crystal: Discrete and continuum approaches

机译：1D谐波晶体中的热传导：离散和连续性方法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this work the energy transfer in a one-dimensional harmonic crystal is investigated. In particular, a comparison between the discrete approach presented by Klein, Prigogine, and Hemmer with the continuum approach presented by Krivtsov is made. In the pioneering work of Klein and Prigogine the transfer of thermal energy is considered. In particular, an expression is obtained, which allows to calculate the thermal energy of each particle as a function of time. Later, Hemmer derived and used similar expressions to solve several particular problems in context of heat conduction. In the work of Krivtsov-in contrast to the discrete approach-a partial differential continuum equation is derived from the lattice dynamics of a 1D harmonic crystal. This so-called ballistic heat equation describes the propagation of heat at a finite speed in a continuous one-dimensional medium. The current work compares analyses based on the discrete equation of Klein, Prigogine, and Hemmer with those from the continuum-PDE-based one by Krivtsov. There is an important difference between the approaches. The continuum approach is derived from the dynamics of the crystal lattice, in which only kinetic degrees of freedom were excited and then thermal equilibration occurred. In contrast to that we consider in the discrete approach explicitly given equal kinetic and potential initial energies. Several exactly solvable initial problems are studied by using both methods. The problem of point perturbation shows a discrepancy in the results obtained in the framework of the continuous and discrete approaches. It is caused by the fact that the smoothness conditions of the initial perturbation is violated for the continuum approach. For other problems it is shown that at large spatial scales, where the one-dimensional crystal can be considered as a continuous medium, the discrete and the continuum relations converge. The asymptotic behavior of the difference between two aforementioned approaches is analyzed.
机译：在这项工作中，研究了一维谐波晶体中的能量传递。特别是，由Krivtsov提出的克莱林，普罗宾和Hemmer呈递的离散方法之间的比较。在Klein和Prigogine的开创性工作中，考虑了热能的转移。特别地，获得表达，其允许作为时间的函数计算每个颗粒的热能。后来，升降机源性和使用类似的表达，以解决热传导背景下的几个特殊问题。在Krivtsov的工作与离散方法相反 - 局部差分连续式方程源自1D谐波晶体的晶格动力学。该所谓的弹道热方程描述了在连续一维介质中以有限速度的热量传播。目前的工作比较了基于KLEIN，PRIGOOM和HEMM的离散式与Krivtsov one的离散式的分析。这种方法之间存在重要差异。连续性方法来自晶格的动态，其中仅激发动力学自由度，然后发生热平衡。相反，我们考虑在离散的方法中明确给出相同的动力学和潜在的初始能量。通过使用两种方法研究了几个完全可溶性的初始问题。点扰动的问题显示了在连续和离散方法的框架中获得的结果中的差异。由初始扰动的平滑条件违反了连续性方法引起的。对于其他问题，表明，在大空间尺度上，其中一维晶体可以被认为是连续介质，离散和连续关系会聚。分析了两种前述方法之间的差异的渐近行为。

著录项

  • 来源
    《International Journal of Heat and Mass Transfer》 |2021年第9期|121442.1-121442.10|共10页
  • 作者

    Aleksei A. Sokolov; Wolfgang H. Mueller; Alexey V. Porubov; Serge N. Gavrilov;

  • 作者单位

    Technische Universitaet Berlin Einsteinufer 5 10587 Berlin Germany Peter the Great Saint Petersburg Polytechnic University (SPbPU) Politekhnicheskaja 29 195251 Saint Petersburg Russia;

    Technische Universitaet Berlin Einsteinufer 5 10587 Berlin Germany;

    Peter the Great Saint Petersburg Polytechnic University (SPbPU) Politekhnicheskaja 29 195251 Saint Petersburg Russia Institute for Problems in Mechanical Engineering Bolshoy 61 V.O. 199178 Saint-Petersburg Russia;

    Peter the Great Saint Petersburg Polytechnic University (SPbPU) Politekhnicheskaja 29 195251 Saint Petersburg Russia Institute for Problems in Mechanical Engineering Bolshoy 61 V.O. 199178 Saint-Petersburg Russia;

  • 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

    Low-dimensional materials; Discrete media; Thermal processes; Anomalous heat transfer; Harmonic crystal;

    机译：低维材料;离散媒体;热过程;异常的传热;谐波水晶;

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号