Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of elasto-thermodiffusion to investigate the transient phenomena for an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, the effect of delay time and thermodiffusion also.

摘要

受 Caputo 分数导数的启发，本研究处理了一种新的弹性热扩散数学模型，以研究各向同性三维热弹性介质在矩形热脉冲引起的渗透气体作用下的瞬态现象，其中热传导方程为通过结合与记忆相关的热传递，定义为滑移区间的公共导数的积分形式。还假设化学势在边界平面上是已知的。采用拉普拉斯变换和双傅里叶变换技术，该问题已在变换域中解析解决。拉普拉斯变换和双傅里叶变换的数值反演是使用傅里叶级数展开技术进行的。根据数值结果对应的图形表示，构建了新理论的结论。由于存在依赖于记忆的导数、延迟时间和热扩散的影响，因此证明了出色的预测能力。