This present work is devoted to investigate the transient phenomena for a novel mathematical model of elasto-thermodiffusion in 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 involving a nonsingular kernel interval by incorporating the Caputo-Fabrizio (CF) heat transfer law. The time-dependent 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 the CF parameter and thermodiffusion also.

本工作致力于研究一种新的弹性热扩散数学模型在受矩形热脉冲引起的渗透气体影响的各向同性三维热弹性介质中的瞬态现象，其中热传导方程定义为积分形式通过结合 Caputo-Fabrizio (CF) 传热定律，涉及非奇异核区间的常见导数。还假设在边界平面上已知时间相关的化学势。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 CF 参数和热扩散，因此证明了出色的预测能力。