Title: Lagging Heat Models in Thermodynamics and Bioheat Transfer: a Critical Review Show Chinese title

Title: 热力学和生物热传递中的滞后热模型：一项批判性综述

Abstract: The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro and nanosystems and biological tissues. In other words, the results obtained from the classical equations deviate from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inappropriate for modeling heat transport in these cases. There are several techniques for modeling non-Fourier heat conduction. In the present paper, we place our focus on the dual-phase-lag (DPL) approach. The DPL model, as a popular modification of Fourier's law, has already been utilized in numerous situations, such as simulating ultrafast laser heating and heat conduction in carbon nanotubes. There has been a sharp increase in research on non-Fourier heat conduction in recent years. Several studies have been performed in the fields of thermoelasticity, thermodynamics, transistor modeling, and bioheat transport. This review presents the most recent non-Fourier bioheat conduction works and the related thermodynamics background. The various mathematical tools, modeling different thermal therapies, and relevant criticisms and disputes are discussed. Finally, the novel and other possible studies are also presented to provide a better overview, and the roadmap to the future research and challenges ahead is drawn up. Show Chinese abstract

Abstract: 经典热传导模型，即傅里叶定律的准确性在处理微尺度和纳米系统以及生物组织时受到高度质疑。换句话说，从经典方程中得到的结果偏离了现有的实验数据。这意味着连续体热扩散方程在这些情况下不足以且不适用于建模热传导。有几种技术可用于建模非傅里叶热传导。在本文中，我们将重点放在双相滞后（DPL）方法上。作为傅里叶定律的一种流行修改，DPL模型已经被应用于许多情况，例如模拟超快激光加热和碳纳米管中的热传导。近年来，对非傅里叶热传导的研究显著增加。已在热弹性、热力学、晶体管建模和生物热传导等领域进行了多项研究。本综述介绍了最新的非傅里叶生物热传导工作及相关热力学背景。讨论了各种数学工具，用于模拟不同的热疗方法，以及相关的批评和争议。最后，还介绍了新颖和其他可能的研究，以提供更好的概述，并制定了未来研究和面临挑战的路线图。