This article deals with thermal diffusion vibration analysis in an unbounded medium including a spherical cavity. Multi single/dual-phase-lag models based upon the Green–Naghdi theory are obtained to discuss the thermoelastic diffusion of the spherical cavity. The surface of the cavity is traction and chemical potential free, not isolated, and subjected to a flux varying harmonically with time. A comparison of results is made, and the validity of results is acceptable. Benchmark outcomes are tabulated to aid other researchers in their future investigations.

中文翻译：

---

通过改进的三相滞后Green–Naghdi模型，无边界固体与球形空腔的热扩散

本文讨论了在无边界介质（包括球腔）中的热扩散振动分析。获得了基于Green-Naghdi理论的多个单相/双相滞后模型，以讨论球形腔的热弹性扩散。腔体表面无牵引力和化学势，没有隔离，并且受到随时间谐波变化的磁通量的影响。比较结果，结果的有效性是可以接受的。将基准结果制成表格，以帮助其他研究人员将来的研究。