Free convection effects on the flow past an infinite vertical oscillating plate

The motion of a semi-infinite incompressible viscous fluid, caused by the oscillation of a plane vertical plate, has been studied, taking into account the presence of free convection currents. Closed form solutions to the velocity, temperature and the penetration distance through which the leading edge effect propagates have been derived on neglecting the transient part. Velocity profiles are shown forGr>0 (Grashof number) (cooling of the plate by the free convection currents),Gr<0 (heating of the plate) on graph. Also the penetration distance has been shown on graphs for different values ofP, the Prandtl number. It has been observed that for t=3/2, greater cooling of the plate may cause the flow to become unstable. Also, the penetration distance is not found to be affected by the frequency of the oscillating vertical plate.