Lagging Heat Models in Thermodynamics and Bioheat Transfer: a Critical Review

TL;DR

This review critically examines non-Fourier heat conduction models, especially the dual-phase-lag approach, highlighting recent advances, applications in bioheat transfer, and future research challenges in micro, nanosystems, and biological tissues.

Contribution

It provides a comprehensive overview of the latest non-Fourier bioheat models, their mathematical tools, and discusses future research directions and unresolved issues.

Findings

DPL model effectively simulates ultrafast laser heating.

Non-Fourier models outperform classical Fourier's law in micro/nanosystems.

Future research should address current limitations and explore new applications.

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.