Abouelregal Ahmed E, Ahmed Ibrahim-Elkhalil, Nasr Mohamed E, Khalil Khalil M, Zakria Adam, Mohammed Fawzy A
Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77423, Saudi Arabia.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Materials (Basel). 2020 Oct 8;13(19):4463. doi: 10.3390/ma13194463.
Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore-Gibson-Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space-time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously.
人们已经进行了许多尝试来研究傅里叶的经典热传递，并实施了一些改进。在这项工作中，我们考虑一种基于摩尔 - 吉布森 - 汤普森方程的新型热弹性模型，在某些这些模型无法为正的情况下。这个热机械模型是结合位移场变化的双曲型偏微分方程和温度增量的抛物型微分方程构建的。所提出的模型用于研究在连续热线源作用下各向同性无限体中的波传播。为了解决这个问题，结合拉普拉斯和汉克尔变换方法，使用了势函数方法。通过拉普拉斯和汉克尔逆变换来找到时空域中不同物理场的解。通过计算给定材料物理场的数值计算来验证该问题。已将其他热弹性模型的数值和理论结果与先前描述的结果进行了比较。
