Transient or Oscillatory Motion of an Infinite Flat Plate

Transient or Oscillatory Motion of an Infinite Flat Plate 

Let us consider a semi-infinite fluid bounded by a by a rigid plane -oo X oo, Y 0. Two exact solutions are known for the transient flow near a plate [427], These solutions correspond to rather simple flows governed by linear equations of motion. However, in these cases the Navier-Stokes equations are linearized because the nonlinear convective terms are identically zero (Vx dVx /dX = 0) rather than because we neglect these terms. The equation of motion has the form 

Transient motion of a flat plate. One of these problems (known as Stokes first problem) describes the flow near an infinite flat plate instantaneously set in motion at a velocity Uq in the plate plane. In this case, the initial and boundary conditions for Eq. (1.9.1) are written as follows  

The problem admits a generalization to the case in which the plate velocity is a given function of time. Then instead of (1.9.2) the following conditions are used  

Oscillatory motion of aflat plate. Another nonstationary problem that admits an exact solution [427] (known as Stokes second problem) describes the flow near an infinite plate oscillating in its plane. This is a problem without initial data. In this case the boundary conditions are posed as follows  

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