A novel electron-phonon coupling thermoelasticity with Burgers electronic heat transfer

• Published in: Applied mathematics and mechanics Vol. 44; no. 11; pp. 1927 - 1940
• Main Authors: Wu, Hua, Li, Xinyi, Yu, Yajun, Deng, Zichen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023; Springer Nature B.V; School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi'an 710072,China; MIIT Key Laboratory of Dynamics and Control of Complex Systems,Northwestern Polytechnical University,Xi'an 710072,China%School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi'an 710072,China; MIIT Key Laboratory of Dynamics and Control of Complex Systems,Northwestern Polytechnical University,Xi'an 710072,China; State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi'an Jiaotong University,Xi'an 710049,China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Conduction heating; Conduction model; Conductive heat transfer; Coupling; Electron phonon interactions; Electrons; Exact solutions; Extreme environments; Fluid- and Aerodynamics; Heat flux; Heat transfer; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Phonons; Thermal shock; Thermoelasticity; Transient response; Wave fronts; Burgers heat transfer; 74F05; electron-phonon coupling; O343.6; two-step generalized thermoelasticity
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-023-3053-5

The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals. The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments, such as micro-scale and ultrafast processes. In this work, the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the second-order heat flux rate for electrons. Then, a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer. Then, the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step (BTS) model. The thermoelastic analytical solutions are systematically derived in the Laplace domain, and the numerical Laplace inversion method is adopted to obtain the transient responses. The new model is compared with the parabolic two-step (PTS) model and the hyperbolic two-step (HTS) model. The results show that in ultrafast heating, the BTS model has the same wave front jump as the HTS model. The present model has the faster wave speed, and predicts the bigger disturbed regions than the HTS model. More deeply, all two-step models also have the faster wave speeds than one-step models. This work may benefit the theoretical modeling of ultrafast heating of metals.