第二梯度流体的蠕变流和热传导相似解

Similarity Solutions for Creeping Flow and Heat Transfer in Second Grade Fluid

给出了在笛卡儿坐标系中,忽略惯性的缓慢流动的二维运动方程和二阶梯度流体的传热方程· 当Re 1时,若从运动方程中简单地省略惯性项,则结果方程的解仍然近似有效· 事实上,从无量纲的动量和能量方程也可导出这一结论· 利用李群分析,知道求得的方程是对称的· 李代数包括4个有限参数和一个无限参数组成的李群变换,其中一个是比例对称变换,另一个是平移变换· 利用对称性求得两种不同形式的解· 利用x和y坐标的平移,给出了指数形式的精确解· 对于比例对称变换,更多地涉及到常微分方程,只能给出级数形式的近似解。

The two dimensional equations of motions for the slowly flowing and heat transfer in second grade fluid are written in Cartesian coordinates neglecting the inertial terms.When the inertia terms are simply omitted from the equations of motions the resulting solutions are valid approximately for Re1.This fact can also be deduced from the dimensionless form of the momentum and energy equations.By employing Lie group analysis,the symmetries of the equations are calculated.The Lie algebra consists of four finite parameter and one infinite parameter Lie group transformations,one being the scaling symmetry and the others being translations.Two different types of solutions are found using the symmetries.Using translations in x and y coordinates,an exponential type of exact solution is presented.For the scaling symmetry,the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented.Finally,some boundary value problems are discussed.