特殊坐标系中特殊非牛顿流边界层方程的相似解

给出了在一个特殊坐标系中三阶流体的二维定常运动方程组．该坐标系中由无粘流体的势流确定，即以环绕任意物体的非粘性流动的流线为Ф-坐标，速度势线为ψ-坐标，构成正交曲线坐标系．结果表明，边界层方程与浸没在流体中的物体的形状无关．第一次近似假定第二梯度项与粘性项和第三梯度项相比，可以忽略不计．第二梯度项的存在，将防碍第三梯度流相似解的比例变换的导出．利用李群方法计算了边界层方程的无穷小生成元．将边界层方程组变换为常微分方程组．利用Runge-Kutta法结合打靶技术求解了该非线性微分方程组的数值解．

Similarity Solutions of Boundary Layer Eqnations for a Special Non-Newtonian Fluid in a Special Coordinate System

Two dimensional equations of steade motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid.For the inviscid flow around an arbitrary object,the streamlines are the phi_ coordinates and velocity potential lines are psi_coordinates which form an orthogonal curvilinear set of coordinates.The outcome,boundary layer equations,is then shown to be independent of the body shape immersed into the flow.As a first approximation,assumption that second grade terms are negligible compared to viscous and third grade terms.Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid.By using Lie group methods,infinitesimal generators of boundary layer equations are calculated.The equations are transformed into an ordinary differential system.Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge_Kutta algorithm and shooting technique.