Recent Progresses and Future Directions of Lagging Heat Models in Thermodynamics and Bioheat Transfer.

The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro/nanosystems and biological tissues. In other words, the results obtained from the classical equations deviates from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inappropriate for modelling heat transport in these cases. Consequently, the development of novel models to improve the results of the classical equation while being less computationally expensive and more simple to use is always a topic of interest. There are several techniques for modelling non-Fourier heat conduction. The Dual-phase-lag (DPL) model as an accurate modified constitutive equation replacing the Fourier law to simulate the heat transport in some special cases such as micro/nanoscales, ultra-fast laser-pulsed processes, living tissues, and carbon nanotube have been trendy. There has been a sharp increase in the amount of research on non-Fourier heat conduction in recent years. Several studies have been performed in the fields of thermoelasticity, thermodynamics, transistor modelling, and bioheat transport. In the present review, the most recent non-Fourier bioheat conduction works and the related thermodynamics background will be presented. The various mathematical tools, modelling different thermal therapies and relevant criticisms and disputes, will be discussed. Finally, the novel other possible studies will be suggested, and the roadmap to the future researches and challenges ahead will be drawn up.