Free molecular flow of rarefied gas over an oscillating plate under a periodic external force

Abstract

The free molecular flow over an infinite oscillating plane wall under external periodic force is considered. The Boltzmann equation is solved by using moments method with two-stream distribution functions. The boundary condition is obtained by assuming that the reflection of the particles from the solid surface takes place with complete energy accommodation. An analytical form for the velocity (X) and shear stress (Y) at any point is obtained. The results show that the amplitude of both the velocity change (X1) and the shear stress change (Y1) due to the periodic external force at the boundary (y=0) is an increasing function of time (t).