Wave concepts in the theory of heat
Wave concepts in the theory of heat
复制标题
热理论中的波概念
DOI：
10.1016/0017-9310(76)90110-1
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发表时间：
1976
影响因子：
5.2
通讯作者：
V. Bubnov
中科院分区：
文献类型：
--
作者：
V. Bubnov
已知的基本解的热传导方程的泊松积分的形式是通过总结特定的相似性的解决方案，得到的帮助下，一个相似组。由于这些相似解不满足初始值，因此得到了确定通解的任意常数的积分条件。然后证明了泊松积分形式的解近似满足间断阶跃函数逼近初始函数形式的初始条件。这是经典热传导方程基本解的缺点之一.本文讨论了无限“热传播速度”的悖论.通过对等温线行为的分析，利用绿色定理，导出了以等温线沿沿着的传播速度为实验参数的一般非线性波动方程.示出了该速度与热扩散率之间的关系。研究了该波动方程的不同特例。证明了某些波动方程解与非线性抛物方程解的对应关系，然后从分子动力学的角度推导了波动热传导方程。利用麦克斯韦方法，并考虑到原子或分子的热速度分量之间的相关性，推广了时间弛豫的概念。
The known fundamental solution of the heat-conduction equation in the form of Poisson's integral is obtained by summing-up particular similarity solutions derived with the help of a similarity group. As these similarity solutions do not satisfy the initial data, then the integral condition is obtained from which the arbitrary constant of a general solution is determined. Then the solution in the form of Poisson's integral is shown to satisfy approximately the initial condition in the form of the discontinuous step function approximating the initial function. This is one of the drawbacks of the fundamental solution of the classical heat-conduction equation.The paradox on an infinite “heat propagation velocity” is discussed.Analysing the isotherm behaviour and using Green's theorem, the general non-linear wave equation is derived here in which the speed of isotherm propagation along the normal is used as an experimental parameter. The relationship between this speed and thermal diffusivity is shown. The different particular cases of this wave equation are studied. Some wave equation solutions are shown to correspond to those of the non-linear parabolic equation.Then, the derivation is given of the wave heat conduction equation from the point of view of molecular kinetic considerations. The conception on time relaxation is generalized using the Maxwell method and taking into account the correlation between components of a heat velocity of atoms of molecules.