Various qualitative properties of the dual/three-phase-lag heat equations are discussed. A refined model of coupled thermoelasticity is formulated to consider three delay times: a phase-lag of heat flux, a phase-lag of temperature gradient, and a phase-lag of thermal displacement gradient. Three special cases are considered to deal with all the considered models in the literature. In the first case one can obtain the simple and Tzou's dual-phase-lag, Lord–Shulman and the classical models. The Green–Naghdi type II model of generalized thermoelasticity without energy dissipation is obtained in the second case. Case 3 is devoted to considering the Green–Naghdi type III model. As an application, a unified form to a multi-phase-lag model is presented to yield all the preceding models as well as the Green–Lindsay generalized thermoelasticity model. A validation example is provided to discuss the coupled solution for photothermal semiconducting isotropic beam. Some illustrative flowcharts and plots are added and concluding remarks are presented.

中文翻译：

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耦合热弹性的多相滞后模型


讨论了双相/三相滞后热方程的各种定性特性。耦合热弹性的精细模型被制定为考虑三个延迟时间：热通量的相位滞后、温度梯度的相位滞后和热位移梯度的相位滞后。考虑三种特殊情况来处理文献中所有考虑的模型。在第一种情况下，我们可以获得简单模型和Tzou双相滞后模型、Lord-Shulman模型和经典模型。在第二种情况下获得了无能量耗散的广义热弹性 Green-Naghdi II 型模型。案例 3 致力于考虑 Green–Naghdi III 型模型。作为一种应用，提出了多相滞后模型的统一形式，以产生所有前述模型以及 Green-Lindsay 广义热弹性模型。提供了一个验证示例来讨论光热半导体各向同性束的耦合解决方案。添加了一些说明性流程图和图表，并提出了结论性意见。