The present article is aimed at studying the effect of an induced magnetic field in an initially stressed homogeneous, isotropic, thermoelastic half-space. The corresponding mathematical modeling has been formulated in the context the memory-dependent heat transport equation in the context of three-phase lag model of generalized thermoelasticity involving two-temperature theory. The bounding plane of the medium is subjected to different types of prescribed temperature and variable mechanical loading. Employing the Laplace transform, the analytical results for the distributions of the thermophysical quantities have been derived and the corresponding vector-matrix differential equation is solved with the help of state space approach. The numerical inversion of the Laplace transform is carried out with the help of an efficient and pragmatic algorithm based on the Riemann-sum approximation technique. Numerical computations for a copper material is performed and have been demonstrated graphically. The result provides a motivation to investigate the problem and draw conducting remarks due to the influence of the magnetic field, memory effect and time-delay parameter also.

本文旨在研究感应磁场在初始应力均匀、各向同性、热弹性半空间中的影响。相应的数学模型已经在涉及两温度理论的广义热弹性的三相滞后模型的背景下，在与记忆相关的热传输方程的背景下制定。介质的边界平面受到不同类型的规定温度和可变机械载荷。利用拉普拉斯变换，推导出热物理量分布的解析结果，并借助状态空间方法求解了相应的向量矩阵微分方程。拉普拉斯变换的数值反演是在基于黎曼和近似技术的高效实用算法的帮助下进行的。对铜材料进行了数值计算，并以图形方式进行了演示。由于磁场、记忆效应和时延参数的影响，该结果提供了研究问题和发表指导意见的动力。