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首页> 外文期刊>International Journal of Heat and Mass Transfer >Nonlocal thermal diffusion in one-dimensional periodic lattice
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Nonlocal thermal diffusion in one-dimensional periodic lattice

机译：一维周期晶格中的非局部热扩散

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摘要

Heat conduction in micro-structured rods can be simulated with unidimensional periodic lattices. In this paper, scale effects in conduction problems, and more generally in diffusion problems, are studied from a one-dimensional thermal lattice. The thermal lattice is governed by a mixed differential-difference equation, accounting for some spatial microstructure. Exact solutions of the linear time-dependent spatial difference equation are derived for a thermal lattice under initial uniform temperature field with some temperature perturbations at the boundary. This discrete heat equation is approximated by a continuous nonlocal heat equation built by continualization of the thermal lattice equations. It is shown that such a nonlocal heat equation may be equivalently obtained from a nonlocal Fourier's law. Exact solutions of the thermal lattice problem (discrete heat equation) are compared with the ones of the local and nonlocal heat equation. An error analysis confirms the accurate calibration of the length scale of the nonlocal diffusion law with respect to the lattice spacing. The nonlocal heat equation may efficiently capture scale effect phenomena in periodic thermal lattices.
机译：微结构棒中的导热可以用单向周期性格子模拟。在本文中，从一维热晶格中研究了导通问题的规模效应，更普遍在扩散问题中。热晶格受混合差分方程来控制，占一些空间微观结构。线性时间依赖性空间差分方程的精确解是在初始均匀温度场下的热晶格导出，在边界处具有一些温度扰动。该离散的热方程通过通过持续的热晶格方程而构建的连续非函数热方程来近似。结果表明，可以从非本体傅立叶定律等同地获得这种非局部热量方程。将热晶格问题（离散热方程）的精确解决方案与局部和非本地热量方程进行比较。误差分析证实了非识别扩散法的长度校准相对于晶格间距。非局部热方程可以有效地捕获周期性热晶格中的比例效应现象。

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