Oscillating Flat-Plate Flow for Maxwellian Fluids

Oscillating Flat-Plate Flow for Maxwellian Fluids 

Stokes second problem deals with the behavior of a semi-infinite fluid if the wall bounding the fluid performs harmonic oscillations in its plane. This problem is stated as a problem without initial data [181,482] only the boundary condition 

The problem is reduced to solving a linear partial differential equation of hyperbolic type (the telegraph equation [482]) in the region t 0, 0 Y oo. Specifically, we have the equation 

Strictly speaking, to obtain a unique solution in an infinite region, condition (6.10.17) must be supplemented by the Sommerfeld radiation condition [234, 317], so as to eliminate waves coming from infinity. The solution of this problem has the form 

Obviously, the oscillation frequency is the same and is equal to ui at any point of the half-space, whereas the amplitude and the phase of the oscillations varies with the spatial coordinate Y. 

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