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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等热学新概念的合理性。
Based on the theory of thermo-matter and analogy to classical mechanics, the Hamiltonian principle followed by the thermal-mass motion and the corresponding Lagrange equation are given. Due to the consideration of the thermal-kinetic energy, the Hamilton principle of thermal mass motion is expected to be applied to the discussion of non-Fourier effect. The thermal kinetic energy is returned to Fourier thermal.The Lagrange equation is used to approximate the one-dimensional transient thermal conduction problem with the internal heat source.The calculated results are in good agreement with the analytical solutions.From the analytical mechanics point of view, the heat transfer theory and the thermal and mechanical The paper points out that some existing problems in the existing literature when using analytical mechanics to discuss the problem of thermal conductivity provide a new idea for the approximate solution of the thermal conductivity problem and also shows that the thermal and thermal energy The rationality of new concepts such as heat.