In this article, a thermomagnetic viscoelastic nonlocal model has been introduced that incorporating the nonlocal elasticity theory of Eringen and the Kelvin–Voigt type. In the heat conductivity equation, the dual-phase-lag thermoelastic model (DPL) has been used to account for microstructural effects caused by high-rate heat transfer processes. The proposed DPL thermoelastic model illustrates the effects of material deficiencies and the thermomechanical relationship due to the extremely rapid heating. Within the framework of the nonlocal DPL model, a one-dimensional magneto-thermoelastic problem of half-space whose surface is exposed to an instantaneous heat source and magnetic field has been studied. With the eigenvalue approach technique and Laplace transform method, analytical solutions for the studied physical fields are provided. The transformed expressions to the field quantities are reversed into the physical domain by applying Zakian's algorithm. The effects of the nonlocal parameter, the viscosity and the applied heat source have been shown graphically on the differences in the fields within the medium.

在本文中，引入了结合 Eringen 非局部弹性理论和 Kelvin-Voigt 型的热磁粘弹性非局部模型。在导热系数方程中，双相滞后热弹性模型 (DPL) 已被用于解释由高速传热过程引起的微观结构效应。提议的 DPL 热弹性模型说明了材料缺陷的影响和由于极快加热引起的热机械关系。在非局部 DPL 模型的框架内，研究了表面暴露于瞬时热源和磁场的半空间的一维磁热弹性问题。利用特征值逼近技术和拉普拉斯变换方法，为所研究的物理场提供了解析解。通过应用 Zakian 算法，场量的变换表达式被反转到物理域中。非局部参数、粘度和施加的热源的影响已以图形方式显示在介质内场的差异上。