Blasius问题中剪应力函数的分析估计

Analytic Estimates on the Shear Stress Involved in the Blasius Problem

Blasius问题用来描述稳定不可压缩流体流过平板的情况,常出现在流体力学边界层理论中.主要对Blasius问题中的剪应力进行分析估计.从与Blasius问题等价的积分方程入手,对积分方程的解z(t)进行分析估计,得出z(t)的性质.从而获得Blasius问题中的剪应力的分析估计,其结果如下:(1)f″(0)≥36|β|-β,(2)

The Blasius problem is used to describe the case of stable incompressible fluids flowing through plate. It of- ten appears in the hydrodynamic boundary layer theory. In this paper, we focus on the analysis and estimation of shear stress in the Blasius problem. By studying the integral equation which is equivalent to the Blasius problem, we analyze and evaluate the solution of the integral equation, then obtain the properties of z （t）. Thus we get the fol- lowing results of the shear stress involved in the Blasius problem：∫^＂（0）≥3/√6/β/√-β,9/4√27≤∥∫^＂∥≤3√3√1-3β^2-2β^