基于热质理论的Hamilton原理

基于热质理论,类比经典力学,给出了热质运动遵循的Hamilton原理以及相应的导热Lagrange方程.由于考虑了热质动能,热质运动的Hamilton原理有望应用于非Fourier效应的讨论,在忽略热质动能时,回归到Fourier热学.应用Lagrange方程对含内热源一维瞬态导热问题进行了近似求解,计算结果与解析解符合较好.从分析力学的角度对传热理论以及热学与力学的统一做了新的阐释,指出了现有文献中采用分析力学方法讨论导热问题时存在的某些不足,为导热问题的近似求解提供了新的思路,同时也说明了热质和热质能

Hamilton's principle based on thermomass theory

Based on thermomass theory, the Hamilton's principle as well as the Lagrangian equations governing the motion of thermomass were established by methods analogous to those of classical mechanics. With the kinetic energy of thermomass taken into consideration, the Hamiltons principle for thermomass is expected to be capable of dealing with non-Fourier phenomena. When the kinetic energy is small enough to be ignored, the principle gets back to Fourier transfer. The application of Lagrangian equations was illustrated by the approximate solution of a 1D transient heat conduction problem with heat source. The unification of thermal and mechanical theories was demonstrated from the perspective of analytical mechanics, the drawbacks of existing theory are discussed, a new way to the approximate solution of heat transfer problem was suggested, and in the meantime the concepts of thermomass and energy of thermomass were to some extent justified.