关于热波理论的研究

RESEARCH ADVANCES IN THE STUDY OF HEAT WAVES

当热传导服从经典的Fourier定律时,温度场由抛物型方程所控制,热扰动以无限大速度传播。在通常情况下,热波的迅速衰减掩盖了这种佯谬。但对于热爆炸,热核聚变,快速化学反应,强激光与物质相互作用这样一些时间尺度极短(与从非平衡态达到局部平衡态的时间相比)的情形,需对Fourier定律进行修正。本文从Cattaneo方程及其唯象修正,Boltzmann演化方程,分子动力学数值模拟以及连续介质热力学理论四个方面对热波理论近20年的进展进行了评述,并对热波的实验验证及数值分析的某些重要结果进行了介绍,且提出了关于热波非弹性理论的新认识,讨论了可能的应用前景。

As is known, the heat transportation follows the classical Fourier's law, and the temperature distribution is governed by a parabollic equation. This fact leads to a paradox, the heat pulse propagates at an infinite speed. In the normal condition, this 'paradox' may be explained away by the rapid decay of heat waves. However, under certain conditions when the relevant time scale is extremely small such as in the cases of thermo-explosion, nuclear fusion, very fast chemical reaction and the interaction of high power laser with materials, some modifications should be made for the Fourier's law. This paper gives a comprehensive review on the research advances in the study of heat waves, made during the last two decades, with respect to the four different theoretical backgrounds, that is, Cattaneo's equation with modifications of various kinds, Boltzmann evolution equation, numerical simulation of molecular dynamics as well as thermodynamics of continuum mechanics. Meanwhile, some important experimental work used to verify the theory and the associated numerical analysis are also introduced. In addition, a constitutive model of heat wave coupled inelastic theory is proposed and some possible future applications concerning the theory of heat wave are discussed.