ABSTRACT

Due to the shortcomings of power law distributions in the heat transfer laws of fractional calculus, some other forms of derivatives with few other kernel functions have been proposed. This literature survey focuses on the mathematical model of thermo-viscoelasticity which investigates the transient phenomena in a three-dimensional thermoelastic medium in the context of two-temperature Kelvin–Voigt three-phase-lag model of generalized thermoelasticity, defined in integral form on a slipping interval incorporating the memory-dependent heat transport law. The bounding plane is subjected to a time-dependent thermal loading and is free of tractions. Incorporating normal mode as a tool, the problem has been solved analytically in terms of normal modes and the physical fields have been depicted graphically for a copper-like material. 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, effect of delay time and viscosity also.

摘要

由于分数阶微积分传热定律中幂律分布的缺点，已经提出了一些其他形式的导数，而其他的核函数很少。本文献综述侧重于热粘弹性的数学模型，该模型在广义热弹性的两温度 Kelvin-Voigt 三相滞后模型的背景下研究三维热弹性介质中的瞬态现象，该模型以积分形式定义在滑动区间结合了记忆相关的热传输定律。边界平面受到与时间相关的热载荷并且没有牵引力。结合正常模式作为一种工具，该问题已在正常模式方面通过分析解决，并且已以图形方式描绘了类铜材料的物理场。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、延迟时间和粘度的影响，因此证明了出色的预测能力。