This study examines how heat travels as thermoelastic waves in a uniform, isotropic, and infinitely large solid material due to a constant line heat source. We leverage the theory of thermoelasticity with two phase lags to account for the time difference between temperature changes and the material’s stress response. By employing a potential function approach alongside Laplace and Hankel transforms, we can convert the governing equations into more manageable domains. This enables us to derive mathematical formulas for temperature, displacement, and stress distributions within the solid. Through a complex inversion process of the Laplace transforms, we obtain analytical formulas for these field distributions. These formulas, however, are only valid for short time periods and are most applicable in the initial stages of wave propagation. We then use these analytical formulas to visualize how temperature, displacement, and stress are distributed, revealing the influence of the heat source and phase lag parameters on these fields. This approach provides valuable insights into the characteristics of wave propagation, the heat source’s impact, and the time-dependent nature of the thermoelastic response. Furthermore, to demonstrate the method’s versatility and ability to connect with established theories, we incorporate specific examples from other thermoelasticity theories. This broadens our understanding of thermoelastic behavior under various conditions.

这项研究研究了由于恒定的线热源，热量如何在均匀、各向同性和无限大的固体材料中以热弹性波的形式传播。我们利用具有两相滞后的热弹性理论来解释温度变化和材料应力响应之间的时间差。通过采用势函数方法以及拉普拉斯和汉克尔变换，我们可以将控制方程转换为更易于管理的域。这使我们能够推导出固体内温度、位移和应力分布的数学公式。通过拉普拉斯变换的复杂反演过程，我们获得了这些场分布的解析公式。然而，这些公式仅在短时间内有效，并且最适用于波传播的初始阶段。然后，我们使用这些解析公式来可视化温度、位移和应力的分布，揭示热源和相位滞后参数对这些场的影响。这种方法为波传播的特征、热源的影响以及热弹性响应的时间依赖性提供了有价值的见解。此外，为了证明该方法的多功能性以及与既定理论联系的能力，我们结合了其他热弹性理论的具体例子。这拓宽了我们对各种条件下热弹性行为的理解。