无限大平板非稳态导热过程的数字特征

对无限大平板非稳态导热过程的平均温度和耗散函数这2个数字特征进行了研究.得到了对流换热边界条件下无量纲平均过余温度的数学模型;分析了表面温度系数随特征值与毕渥数的变化规律;定义了相应的时间常数,它是衡量无量纲平均过余温度衰减速率快慢的指标;并对毕渥数取极限时无量纲平均过余温度的变化规律做了讨论.利用格林公式推导出了热势与耗散函数之间的关系,并与机械能耗散系统进行了相似性分析.得到了对流换热边界条件下耗散函数随时间的变化规律,并将其与平均过余温度的变化规律做了比较.

Research on Numerical Characteristics of Unsteady Heat Conduction of an Infinite Plate

In this paper, the two numerical characteristics of the average temperature and dissipation function of an infinite plate are studied. The mathematical model of the di- mensionless average excess temperature under convection heat transfer boundary condi- tions is obtained and the change law of surface temperature coefficient with eigenvalue and Biot number is analyzed. The time constant is defined and it reflects the decay rate of dimensionless average excess temperature. The change law of dimensionless average excess temperature are discussed in the cases of the Biot number tends to zero and infini- ty. The functional relationship between thermoelastic potential and dissipation function is derived by Green＇s formula and the similarity with dissipation system of mechanical energy is discussed. The variation of dissipation function under convection heat transfer boundary conditions is get and it is compared with that of average excess temperature.