超急速传热过程中热惯性效应的解析分析

Analysis on Thermal Inertia Effects in Rapid Transient Heat Conduction

考虑到作用时间极短、尺度微观的超常传热行为,基于热质概念,根据牛顿力学分析方法建立了温度突变加热条件下热质运动的波动方程。借助Laplace正、逆变换,推导了半无限大薄板外表面受热冲击作用下热惯性效应的解析表达式。通过改变特征参数得到不同温度场分布,给出了超急速传热过程中热波的传递规律,并与常用CV模型作对比,揭示了超急速传热过程中热惯性效应对传热行为的影响。结果表明:热量在传递过程中同时受到时间惯性和空间惯性的影响,使得较CV模型的波速、波前位置、阶跃值等都发生了改变,并且能够很好的解释稳态导热下出现的非傅里叶现象。

Based on the thermomass theory and Newtonian mechanics, we established the wave equation for the motion of thermomass under sudden temperature change, as well as the analytical expression for thermal inertia effects. By changing the parameters, we obtained the propagation regulation of the thermal wave and compared it with the CV model to reveal the influence of thermal inertia effects on the behavior of heat transfer. The results showed that the thermal transfer was influenced by time inertia and spatial inertia, which caused wave velocity, wave locations and phase step values different from the CV model. It can explain the non-Fourier phenomenon under steady heat conduction.