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Nonlinear heat wave propagation in a rigid thermal conductor
Acta Mechanica ( IF 2.7 ) Pub Date : 2020-02-08 , DOI: 10.1007/s00707-020-02628-4
W. Mahmoud , G. M. Moatimid , A. F. Ghaleb , M. S. Abou-Dina

We present new nonlinear, one-dimensional equations of extended thermodynamics for temperature and heat flux that describe damped heat wave propagation and predict dependence of the second sound velocity on temperature and heat flux in a rigid thermal conductor. The aim of the present work is to investigate the implications of the considered nonlinearities on the process of heat propagation, especially that such nonlinear effects cannot be disregarded for nanosystems and in small-sized heat conductors, when temperature or heat flux variations are not always proportional to gradients. The characteristics of the nonlinear system of equations are investigated, and a formula for the breaking distance is obtained. For illustration, these equations are solved in the linear approximation by separation of variables, then in the nonlinear case by the homotopy perturbation method in the half-space, and numerically in a bounded interval under concrete initial and boundary conditions. The solutions are discussed in detail and presented graphically. They illustrate the effect of the different material parameters on the propagation of thermal waves and may be used to evaluate some material parameters. The proposed equations provide a closer insight into the thermal interactions in rigid thermal conductors.

中文翻译:

刚性热导体中的非线性热波传播

我们提出了新的非线性、一维扩展热力学温度和热通量方程,这些方程描述了阻尼热波传播,并预测了刚性热导体中第二声速对温度和热通量的依赖性。本工作的目的是研究所考虑的非线性对热传播过程的影响,特别是当温度或热通量变化并不总是成比例时,纳米系统和小尺寸热导体不能忽视这种非线性效应。到梯度。研究了非线性方程组的特性,得到了断裂距离的计算公式。为了说明,这些方程通过变量分离以线性近似求解,然后在非线性情况下通过半空间中的同伦微扰方法,并在具体的初始和边界条件下在有界区间内进行数值计算。详细讨论了解决方案并以图形方式呈现。它们说明了不同材料参数对热波传播的影响,并可用于评估某些材料参数。提出的方程可以更深入地了解刚性热导体中的热相互作用。
更新日期:2020-02-08
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