薄板在周期热流作用下的热响应(Ⅰ):温度响应

基于具有热流延迟相的双曲型热传导方程,研究了薄板在周期热流作用下的温度响应。首先采用分离变量法,求解了以热流矢量为基本未知量的热传导方程,得到了板内热流场分布,然后再利用能量守恒方程,获得了板内温度响应的解析表达式。通过计算,分析了板内温度响应随不同热流矢量延迟相以及边界热流频率的变化趋势,并与经典的Fourier热传导方程所得到的结果进行了比较。结果表明,在高频热流加热下,双曲型热传导模型所给出的温度响应与经典的Fourier热传导模型具有显著的差别。

THERMAL RESPONCES IN A THIN PLATE UNDER PERIODIC BOUNDARY HEAT FLUX (Ⅰ): TEMPERATURE FIELD

Based on hyperbolic heat conduction equation accounting for the phase lag between the heat flux and the temperature, the temperature responses of thin plate subjected to a periodic heat flux disturbance are investigated. Firstly, by using the method of separation of variables, the heat conduction equation is solved and the distribution of the heat flux is obtained. Then, an analytic solution of temperature field in the thin plate is found by using the energy conservation equation. The variation of the temperature response depending on the heat flux relaxation parameter and the frequency of heat flux at the boundary are examined quantitatively. A comparison of the present results with those obtained by using Fourier heat conduction equation is given. It shows that there exists a big difference between the temperature response obtained hyperbolic heat conduction model and that obtained by using classical Fourier model when the plate is excited by a heat flux with high frequency.