Generalized Boltzmann transport theory for relaxational heat conduction

• Published in: International journal of heat and mass transfer 2021-07, Vol.173, p.121225, Article 121225
• Main Authors: Li, Shu-Nan, Cao, Bing-Yang
• Format: Article
• Language: English
• Subjects: Anomalies; Boltzmann transport equation; Boltzmann transport equation (BTE); Boltzmann transport theory; collision term; Conduction heating; Conductive heat transfer; Convolution; drift term; Fourier law; Heat flux; Macroscopic models; relaxational heat conduction; Transport equations; Transport theory
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2021.121225

•A unified Boltzmann transport theory is established for relaxational heat conduction.•The unified Boltzmann transport theory can cover wave-like heat conduction and the fractional Fourier law.•The uniqueness of the Boltzmann transport theory is discussed based on thermodynamics. Relaxational heat conduction lacks a modified transport theory at the mesoscopic level. We establish a modified Boltzmann transport theory with the generalized collision term, which can give rise to the convolution relationship between the heat flux and temperature gradient as well as fractional Fourier law. The macroscopic relaxational behaviors are thereafter connected to mesoscopic memory effects in the generalized collision term. The modified Boltzmann transport theory not only provides an underlying explanation for macroscopic relaxational heat conduction but also possesses engineering applications to situations far from equilibrium. The generalized collision term is not unique framework for relaxational heat conduction, and generalizing the drift term in the Boltzmann transport equation (BTE) can also cover macroscopic models. However, this framework will be paired with anomalies in energy continuity and entropy balance, and as a consequence, it is not suggested for relaxational heat conduction.