具有延伸表面的驻点流动和传热问题的级数解

Analytic Solution of Stagnation-Point Flow and Heat Transfer Over a Stretching Sheet by Means of Homotopy Analysis Method

研究了在延伸表面上不可压缩二维驻点流动的动量和热量传输问题.通过一系列相似变换把轴对称和平面二维驻点流的控制方程组转化为常微分方程组,利用同伦分析方法求得了速度分布和温度分布的级数解.结果表明,当主流流速大于平面延伸的速度时,就形成了一个边界层,而当主流流速小于平面延伸的速度时,却形成一个反边界层.通过图形和表分析各个物性参数对速度边界层和温度边界层的影响.

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit is concerned. The governing system of partial differential equations was first transformed into a system of dimensionless ordinary differential equations. The analytical solutions for the velocity distribution and dimensionless temperature profiles were obtained for the various values of the ratio of flee stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in the series forms with the help of homotopy analysis method（HAM）. It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are plotted to discuss the effects of different parameters.