运动水平平板上混合对流的群论分析

Group Theory Analysis of Mixed Convection over a Horizontal Moving Plate

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72 和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。

In the present paper, the investigation to the mixed convective boundary-layer behavior over a horizontal plate is carried out. By applying transformation group theory, the analysis of the governing equations of continuity, momentum. energy and diffusion shows the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x4/(7-5n) and that the moving speed of the plate is proportional to x(3-n)/(7-5n), furthermore, a set of similarity equations is obtained. The similarity equations are solved numerically by a fourth-order Runge-Kutta scheme. The numerical result s obtained for velocity, temperature and concentration distributions for Pr＝0.72 and various values of the parameters Sc, K1, K2, and K3 reveal the influence of these parameters on the flow, and heat and mass transfer behavior.