In this work, a nonlocal dual-phase-lag (NL DPL) model is introduced to accommodate the effects of thermomass and size-dependent thermophysical properties at nanoscale heat transport. Heat transfer at nanoscale is essentially nonlocal and quite different from that at the micro- or macro scale. To illustrate the nonlocal effect, a bi-layered structure is considered during magnetic fluid hyperthermia (MFH) treatment which is used successfully in prostate, liver, and breast tumors and the effect of size-dependent characteristic lengths is discussed in tumor and normal region of tissue. The problem is solved by using the finite difference scheme in space coordinate and Legendre wavelet Galerkin approach in time coordinate with the Dirichlet, Neumann and Robin boundary conditions. The effect of boundary conditions, characteristic lengths, phase lag parameters and nanomaterial parameters is discussed in tumor and healthy tissue domain and the results are presented graphically. This study is expected to be helpful for modeling of bioheat transfer equation at nano-scale, and may be beneficial to design nano-sized and multi-layered devices for heat transfer.

中文翻译：

---

双相滞后模型在磁流体热疗期间双层组织中的非局部导热方法。

在这项工作中，引入了非局部双相滞后（NL DPL）模型，以适应纳米级传热过程中热质量和尺寸相关的热物理性质的影响。纳米级的传热基本上是非局部的，与微观或宏观的传热有很大不同。为了说明非局部效应，在磁流体热疗（MFH）治疗期间考虑了双层结构，该结构已成功用于前列腺癌，肝癌和乳腺肿瘤，并讨论了肿瘤大小和正常区域的大小依赖性特征长度的影响。组织。通过在空间坐标中使用有限差分方案和在Dirichlet，Neumann和Robin边界条件下的时间坐标中的Legendre小波Galerkin方法来解决该问题。边界条件，特征长度，在肿瘤和健康组织领域讨论了相滞后参数和纳米材料参数，并以图形方式显示了结果。预期该研究将有助于在纳米尺度上模拟生物传热方程，并且可能有益于设计用于传热的纳米级和多层装置。